If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath. If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.If Stardust Run has a million fans, I am none of them. If Stardust Run has ten fans, I am none of them. If Stardust Run has no fans, that means I am happy. If the World is against Stardust Run, I am against Stardust Run, too. I hate Stardust Run till my last breath.

Like

1

Write Comment Comments

Report

Dich vu tu van marketing thuong hieu tron goi chuyen nghiep tuvanmarketingthuonghieu_stm SIÊU TỐC Marketing mang đến dịch vụ tư vấn xây dựng thương hiệu chuyên nghiệp, giúp doanh nghiệp định vị nổi bật và tăng cường hình ảnh qua các chiến lược truyền thông liên kết. Với mô hình “Ma Trận Bao Vây” độc quyền và hơn 15 năm kinh nghiệm từ chuyên gia Võ Tuấn Hải, dịch vụ tối ưu hóa quảng cáo trên Google Ads, SEO, TikTok, đồng thời xây dựng lòng trung thành khách hàng. Quy trình khoa học gồm phân tích doanh nghiệp, nghiên cứu thị trường, lập kế hoạch, triển khai và đo lường hiệu quả, đảm bảo tăng trưởng bền vững. http://ofbiz.116.s1.nabble.com/Tu-van-Marketing-thuong-hieu-td4890921.html

Like

1

Write Comment Comments

Report

⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢀⣀⠀⠀⠀⣀⡀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⣾⠟⠉⠉⢻⣧⠈⣿⣇⠀⢠⡿⠀⢸⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠸⣿⠀⠀⠀⢸⣿⠀⠘⣿⣀⣾⠇⠀⢸⡿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣤⣤⣤⠀⠻⣷⣤⣤⡾⠏⠀⠀⠹⣿⡟⠀⠀⢸⣷⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡇⠀⢸⣿⣿⠀⣠⡾⠿⠿⢷⣄⠀⣿⡿⠿⠿⣷⡄⠀⣿⠿⠿⢿⣦⠀⢸⣿⠀⣿⡇⠀⠀⣿⡇⠀⣶⠿⠿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⢸⡿⣿⡀⣾⢸⣿⢠⣿⡇⠀⠀⢘⣿⡄⣿⣧⣤⣤⡾⠃⠀⣿⣦⣤⣾⣟⠀⢸⣿⠀⣿⡇⠀⠀⣿⡇⠀⠻⣷⣦⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⢹⣷⡇⢸⣿⠀⢿⣇⣀⣀⣸⡿⠀⣿⡇⠈⠻⣷⡀⠀⣿⣀⣀⣀⣿⡇⢸⣿⠀⢿⣇⡀⣀⣿⠀⠰⣦⣀⢀⣹⡗⠀⠀⠀⠀⠀ ⠀⠀⠘⠃⠈⠛⠁⠘⠛⠀⠀⠙⠛⠛⠋⠀⠀⠙⠃⠀⠀⠙⠓⠀⠛⠛⠛⠛⠋⠀⠘⠛⠀⠈⠙⠛⠛⠋⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⡴⠾⠃⠘⠛⢀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⠿⣦⣄⡀⢀⣀⠉⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠁⠈⠻⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Like

1

Write Comment Comments

Report

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭

Like

2

Write Comment Comments

Report

I made an edit of Nico into Serena

Like

2

Write Comment Comments

Report

▬▬▬▬▬.◙.▬▬▬▬▬ ▂▄▄▓▄▄▂ ◢◤█▀▀████▄▄▄▄▄▄ ◢◤ █▄ █ █▄ ███▀▀▀▀▀▀▀ ╬ ◥ █████ ◤ ══╩══╩═ ╬═╬ ╬═╬ just dropped down to say ╬═╬ ╬═╬ THIS WEBSITE SUCKS ╬═╬ ?/ ╬═╬ /▌ ╬═╬ / \

Like

1

Write Comment Comments

Report

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡄⠈⠁⠀⢸⡇⠀⢿⡇⠀⣿⠀⠹⣿⣿⠁⠈⣿⡏⣹⣿⠟⣽⣿⢟⣿⣿⠟⢹⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣷⣠⡀⠀⣾⠃⠀⢸⣇⣀⣿⠀⠀⣸⡟⠀⠀⢹⣿⡿⠁⢨⣿⠃⠀⢿⣯⣀⣈⣿⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣿⣿⣿⣿⡷⣶⣿⠀⠀⠈⣿⠉⠹⣦⣴⣿⠁⠀⢀⣸⡿⠀⠀⢸⡿⣦⣤⣼⡿⣿⣿⣽⣿⢟ ⣶⣶⣾⣿⣿⣿⣦⣤⣤⣿⠿⠿⠷⠿⣿⣿⣿⣦⡉⠻⣿⠾⣯⣀⣀⣠⡿⠀⠀⠀⠘⣷⣦⣤⡾⠿⠧⣤⣤⣿⣄⣴⠟⠁⠀⣿⡿⠿⠛⢛ ⠀⠀⢹⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣾⣯⡤⠤⠮⠥⠤⠤⠤⠤⣶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢦⣼⣿⣇⠀⣰⣿ ⡆⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⣿ ⢹⣿⣁⣤⣤⠶⠶⢶⣿⣿⡟⠛⠻⣷⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣾⠟⠟⠋⣿⠟⠛⣶⠶⣤⣄⣀⣿⢀⣰⠾ ⠀⠉⠁⠀⠀⠀⠀⠀⢀⣽⠇⠀⢀⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡀⠀⠀⠈⠁⠀⠀⠀⣇⠀⠘⣿⡀⠀⠉⢉⣴⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⡶⠞⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠛⠻⢶⡄⠀⠀⠀⠀⠘⢧⠀⠈⠻⠶⠴⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⣤⣶⣿⡄⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣼⣿⠛⠿⢶⣦⡈⠁⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⠀⠀⣀⣿⠇⢀⣾⣯⡐⠺⣧⣈⣩⣥⣤⣀⠉⠛⠦⠀⠀⠀⠀⣿⣶⣷⠆⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⣿⠷⢷⣿⣿⠀⢸⣿⡿⠋⠀⣸⣉⣀⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠫⠉⠀⠀⠀⣀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⠒⠤⣴⡾⠛⠉⠉⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢸⣿⣤⠀⠀⠀⠀⠀⠀ ⣤⡿⣥⣀⣀⣀⣿⡆⠀⢠⣾⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠟⠛⠷⠀⠀⢸⡿⢿⣿⣤⣴⠄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⠃⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⣠⠴⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⣸⡇⠀⠈⣻⣿⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣹⣿⡿⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⡿⠛⠓⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⣿⣦⣶⣷⣿⠛⣶⣤⠤ ⠉⠉⠛⠿⠛⠿⣿⣭⣿⣿⣰⣿⣿⣦⡀⠀⠀⠀⠀⢀⣀⡤⠞⠃⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠛⠻⠿⠛⢿⣶ ⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⡏⠈⠛⠟⠛⠷⠶⢿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠈⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠟⠉⠉⠉⠉⠉⠀⠀⠻⣿⣿⢆⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢀⣼⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀

Like

1

Write Comment Comments

Report

hey gays it is i, hanarika, aka yours truly, niggole on SIT.

Like

1

Write Comment Comments

Report

??OMG ? you’re so FUNNY ? ? so quirky ?? ? so different ?absolute crackhead energy ?? comedic genius? ? I literally can’t ❌ breathe ? i’m crying dude ?? that was so hilarious ? u really got the whole squad laughing ?‍?‍?‍???‍?‍?‍???‍?‍?‍? high IQ comedy ?? how’d you come up with that ?? really original work ? never seen ? or heard ? anything like that before ? ? ? great ? job ?? keep up the funnies ??? i love you ? ? you’re my inspiration ??? if only i were as funny ? or smart ? or cool ? as you ? but its whatever I’ll continue to watch ??? your content ?? because it ❌NEVER EVER❌ fails to make me laugh ?? thank you ? for existing ? and doing what you do ❤️❤️

Like

2

Write Comment Comments

Report

⢿⣿⣿⣿⣭⠹⠛⠛⠛⢿⣿⣿⣿⣿⡿⣿⠷⠶⠿⢻⣿⣛⣦⣙⠻⣿ ⣿⣿⢿⣿⠏⠀⠀⡀⠀⠈⣿⢛⣽⣜⠯⣽⠀⠀⠀⠀⠙⢿⣷⣻⡀⢿ ⠐⠛⢿⣾⣖⣤⡀⠀⢀⡰⠿⢷⣶⣿⡇⠻⣖⣒⣒⣶⣿⣿⡟⢙⣶⣮ ⣤⠀⠀⠛⠻⠗⠿⠿⣯⡆⣿⣛⣿⡿⠿⠮⡶⠼⠟⠙⠊⠁⠀⠸⢣⣿ ⣿⣷⡀⠀⠀⠀⠀⠠⠭⣍⡉⢩⣥⡤⠥⣤⡶⣒⠀⠀⠀⠀⠀⢰⣿⣿ ⣿⣿⡽⡄⠀⠀⠀⢿⣿⣆⣿⣧⢡⣾⣿⡇⣾⣿⡇⠀⠀⠀⠀⣿⡇⠃ ⣿⣿⣷⣻⣆⢄⠀⠈⠉⠉⠛⠛⠘⠛⠛⠛⠙⠛⠁⠀⠀⠀⠀⣿⡇⢸ ⢞⣿⣿⣷⣝⣷⣝⠦⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠛⣿⠈ ⣦⡑⠛⣟⢿⡿⣿⣷⣝⢧⡀⠀⠀⣶⣸⡇⣿⢸⣧⠀⠀⠀⠀⢸⡿⡆ ⣿⣿⣷⣮⣭⣍⡛⠻⢿⣷⠿⣶⣶⣬⣬⣁⣉⣀⣀⣁⡤⢴⣺⣾⣽⡇

Like

1

Write Comment Comments

Report

⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⢿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠯⠜⠀⠁⠀⠀⠀⠀⡀⢀⠉⠙⠫⢄⣿⣿⣿⡏⠁⣸⣿⡿⠋⣀⣠⣤⣄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⢽⢿⣿⣿⣿ ⣿⣿⣿⠿⡻⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⠀⠺⢿⣼⡉⠁⠐⠰⣯⣴⡖⢋⡁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠇⡴⠁⠀⠀⠀⢀⣠⣤⣔⡥⠔⠒⠂⠠⠤⢄⡀⠀⢜⡃⠱⡄⠀⠀⠐⡿⠛⠙⠉⣉⣉⣉⡁⣀⠈⠉⣷⡀⡀⠀⢤⡀⠀⠀⠁⠙⣿ ⣿⣿⢎⠁⠀⠀⢠⣦⣵⣾⣿⣿⣿⣶⣾⣷⣶⣦⣄⣉⠒⡄⠀⠀⠀⠀⢠⣮⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀⠀⠀⠀⠀⢀⣿ ⡿⣍⣀⣀⣠⣶⣿⣿⣿⡿⠟⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡿⣿⣿⠟⠋⣹⡿⣿⣷⡄⠙⢿⣿⣿⣿⣦⣌⠒⣲⣤⡖⢾⣿ ⠀⢼⣿⢷⢭⣿⣿⣿⠋⠀⢸⣿⣭⣿⣵⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣷⣶⣷⣾⠀⠀⠹⣿⣿⣿⣿⣿⡷⢻⣟⣁⣀ ⡀⢠⣈⡻⣶⣿⣿⣏⠀⠀⠘⢿⣿⣿⠟⠀⠀⣨⣌⣹⣿⣿⣿⠀⠀⠀⠹⣿⣧⡀⠀⠀⠻⢿⣿⡿⠃⠀⠀⣰⣴⣼⣿⣿⡧⣶⣿⠿⣷⣶ ⠉⣠⣈⠙⠿⣿⣿⣿⣷⣤⣀⣀⣉⣁⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣿⣿⣿⣶⣤⣤⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠈ ⠀⣾⣿⣿⣶⣤⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠙⠋⠙⠻⢿⡿⠉⠀⡀⢀⠀⠀⠠⠀⠀⠀⣀⣀⠉⠹⣿⡿⠟⠉⠙⠛⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣗ ⠀⣸⣿⣿⣿⡏⠫⢻⡿⠿⣿⣧⣤⣀⠀⠀⠘⠻⡾⣾⣟⠿⣷⣤⡶⢆⣠⠼⠟⢻⣿⣠⡟⠁⣀⣤⣴⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠃ ⡄⠸⣿⣿⣿⣷⣀⠀⢗⠄⠈⢹⠛⠛⠿⣿⣶⣤⣤⣀⣀⡀⠀⠉⠁⣠⣹⣄⣄⣠⣤⣾⣿⣿⣿⡿⠟⠻⠋⠻⠀⠃⢀⣨⣿⣿⣿⣿⠃⠀ ⡇⠐⣿⣿⣿⣿⣿⡆⣸⣤⡀⠀⠀⠀⠀⠹⠟⠉⠟⠛⣿⠿⠋⠷⣿⣿⣿⠿⠿⢿⠟⠛⡏⢻⠇⠀⠀⠸⠀⢀⡀⠀⣀⣿⣿⣿⣿⡿⠂⣀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣡⣠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠘⣧⣤⣿⣿⣿⣿⣿⠇⠀⡏ ⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⡄⠀⣀⠀⡀⠀⣶⡆⠀⢀⠀⢸⡀⠀⠀⢀⣠⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⠁ ⣯⠈⢻⣿⣿⣿⡿⠟⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⣿⣿⣿⣿⣶⣷⣾ ⣿⣶⡞⠛⢿⣿⣿⡄⠀⢰⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠂⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣦⠀⠘⠿⣧⣀⡎⠀⠰⠾⠀⠀⠐⣻⠿⠻⡿⠿⣿⣿⣿⣿⣿⠟⠻⡿⠟⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⣄⠀⣼⣿⣿⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢀⠈⢻⣿⣿⣀⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠀⠀⠀⡏⠀⠀⠁⠐⠀⠀⠀⣄⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⣿⣄⠀⠀⢰⣤⠀⠀⠀⠐⣦⠀⠀⠀⡟⠀⠀⠃⢀⠀⠈⠀⢸⣧⣤⢃⣼⣷⣿⡿⠛⣻⣏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⣶⣿⣿⡀⠀⠀⢰⡇⠀⠀⠀⠊⠀⠀⠀⢘⣷⠒⢀⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠻⠿⣿⣿⣦⣴⣿⣿⣦⣀⣤⣾⣦⣴⣤⣿⣿⣿⣿⣿⣿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠉⠙⠉⠙⠿⠿⠛⠛⠻⠿⠛⠛⠛⠛⠛⠉⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

Like

1

Write Comment Comments

Report

Three 10km eggs in progress. I can't wait to see what's inside :3

Like

3

Write Comment Comments

Report