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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
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⢿⣿⣿⣿⣭⠹⠛⠛⠛⢿⣿⣿⣿⣿⡿⣿⠷⠶⠿⢻⣿⣛⣦⣙⠻⣿ ⣿⣿⢿⣿⠏⠀⠀⡀⠀⠈⣿⢛⣽⣜⠯⣽⠀⠀⠀⠀⠙⢿⣷⣻⡀⢿ ⠐⠛⢿⣾⣖⣤⡀⠀⢀⡰⠿⢷⣶⣿⡇⠻⣖⣒⣒⣶⣿⣿⡟⢙⣶⣮ ⣤⠀⠀⠛⠻⠗⠿⠿⣯⡆⣿⣛⣿⡿⠿⠮⡶⠼⠟⠙⠊⠁⠀⠸⢣⣿ ⣿⣷⡀⠀⠀⠀⠀⠠⠭⣍⡉⢩⣥⡤⠥⣤⡶⣒⠀⠀⠀⠀⠀⢰⣿⣿ ⣿⣿⡽⡄⠀⠀⠀⢿⣿⣆⣿⣧⢡⣾⣿⡇⣾⣿⡇⠀⠀⠀⠀⣿⡇⠃ ⣿⣿⣷⣻⣆⢄⠀⠈⠉⠉⠛⠛⠘⠛⠛⠛⠙⠛⠁⠀⠀⠀⠀⣿⡇⢸ ⢞⣿⣿⣷⣝⣷⣝⠦⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠛⣿⠈ ⣦⡑⠛⣟⢿⡿⣿⣷⣝⢧⡀⠀⠀⣶⣸⡇⣿⢸⣧⠀⠀⠀⠀⢸⡿⡆ ⣿⣿⣷⣮⣭⣍⡛⠻⢿⣷⠿⣶⣶⣬⣬⣁⣉⣀⣀⣁⡤⢴⣺⣾⣽⡇
AmberlynnWEED
So the other day, I was playing rainbow six siege, and I heard one of my teammates make a callout in the voice chat. It was a real life gamer girl. God, I kid you not, I just stopped playing and pulled my dick out. “fuck, Fuck!” I was yelling in voice chat. I just wanted to hear her voice again. “Please,” I moaned. But she left the lobby. I was crying and covered in my own cum, but I remembered that I could find recent teammates in the ubiplay friends tab. I frantically closed down siege and opened the tab, to find out she had TTV IN HER NAME!!! She was streaming, and only had 100 viewers!!! The competition was low, so I made the first move and donated my months rent to her. I was already about to pre. She read my donation in the chat. God this is the happiest I’ve been in a long time. I did a little research, and found out where she goes to school, but I am a little nervous to talk to her in person, and need support. Any advice before my Uber gets to her middle school?
ShowTheHentai
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
ShowTheHentai
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭
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