I'm so salty a Dragonair ran away after my first ball throw.

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[♪♪♪] [WIND WHISTLING] [BIRDS CHIRPING] [THUNDER RUMBLING IN DISTANCE] [WATER DRIPS ECHOING] [BATS SKITTERING] [HELICOPTER WHIRRING] [MEN YELLING INDISTINCTLY IN SPANISH] We shouldn’t be here when it gets dark. Set the trap at the mouth of the cave, please. [MEN SPEAKING IN SPANISH] [WINCES] PILOT: You need a doctor? [CHUCKLES SOFTLY] I am a doctor. It’s impressive, don’t you think? Vampire bats weigh almost nothing, but they can down a creature nearly ten times their size. [FLIES BUZZING] Wow. What are you using as bait? You volunteering? Leaving. [TRAP CLANKS] Pay me now. Before the sun goes down. You throw in that bushcrafter on your belt and we have a deal. [♪♪♪] [GROANS SOFTLY] [ALL CHITTERING] [SCREECHES] [BATS SCREECHING] [SHOUTS IN SPANISH] [YELLING IN SPANISH] Come on. [BELL TOLLING] [STUDENTS LAUGHING, CHATTERING] Move! [TICKING] [CAR HORN HONKS] NICHOLAS: Should be able to take better care of you here. [CAR DOOR CLOSES, CAR DRIVES AWAY] Everyone’s here to help you. Michael, this is Lucian. Lucian, Michael. Michael knows more about this place than I do. [WHISPERS] Play nice. LUCIAN: Hello. Hello, Milo. My name’s Lucian. The person who was here before was Milo. No. He was also the new Milo. And before him was the other new Milo. I don’t even remember the first Milo. How long have you been here? Long as I can remember. [MACHINE BEEPS AND WHIRS] And you’re still not cured? There is no cure. There’s something missing from our DNA. Like a piece of a puzzle. And until they find it, the only way to stay alive is an oil change three times a day. What would you do if you could be normal? Just for an hour? I don’t think about it. Hey, look at the freaks! Look at them! [STUDENTS CHATTERING, LAUGHING] Best not to be outside when school gets out. Like the original Spartans, we are the few against the many. [BEEPING] Milo? Milo? [ALERT BUZZING] Nurse? [♪♪♪] [WHISPERS] Okay… [BEEPS AND WHIRS] Lucian. Lucian! With one of these? It took a team of scientists to build that machine and you fixed it with a ballpoint pen? There’s a school for gifted children in New York. I think that I could get them to agree to cover your tuition and provide private care to help manage your condition. Somewhere you could study, learn, hone your skills. You have a gift, Michael. I don’t think I could forgive myself if I saw it go to waste. MICHAEL: “Dear Milo, this isn’t goodbye. I’m gonna find a cure for us, so we can be cranky old men someday. Your friend, Michael. P.S. You shouldn’t have unfolded this. Now you’ll never get it back together. See you this summer.” No. [STUDENTS CHATTERING] “Dear Milo…” [ALL LAUGH] Please, can I have my letter back? What? Please, can I have my letter? Okay. Here. [LAUGHS] Please. Ah! [SHOUTS] Please! [BOYS LAUGHING] Please! [YELLS] Stop. [GROANING] [BOYS GRUNTING] [NICHOLAS YELLS IN SPANISH] Go away! [SIREN WAILS IN DISTANCE] Let me have a look. Let me have a look. [SCREAMS] He tried to steal my letter! Milo, Milo, stop. Stop. Stop. Stop. [CRYING] What about Milo? I’ll look after Milo. He needs me. NICHOLAS: Michael Morbius completed his doctorate by 19 and quickly established himself as the world’s leading authority on blood-borne diseases. His development of artificial blood has saved more lives than penicillin. Michael Morbius, please step forward to acknowledge the receipt of your prize from His Majesty, the King of Sweden. [AUDIENCE APPLAUDING] [TRUMPETERS PLAY FANFARE] ANNA: I can’t believe you dissed the king of Sweden. The king and the queen, their loyal subjects, all of Scandinavia and the entire scientific community. Yeah, but who does that? Well, Anna, we both know I have issues. But, hey, I kept the program. [TONE SOUNDS, THEN WOMAN SPEAKS INDISTINCTLY OVER PA] [KNOCKS] There you are. Hey, Dr. Bancroft. Hey, Anna. We going to play? Oh, I don’t think so. See, now that Dr. Morbius is back, maybe you should try losing for a while, see how that feels. MICHAEL: Not gonna happen. Michael. Uh, yes? You got a minute? Of course. New one. For your collection. [WHISPERS] Dr. Morbius is in trouble. I’m in trouble. MARTINE: “I can’t accept a prize for the by-product of a failed experiment.” Lab 1. Front page, “American Scientist Rejects Nobel Prize.” You know that people actually like writing checks to Nobel laureates? Makes them feel better about their investment. It would help if you stuck around long enough to cash them. [GROANS] You’re pushing yourself too hard. [SIGHS] Does our generous benefactor, Milo, know what you’re actually doing here? What am I actually doing here? Remixing human DNA with bat DNA. I have no idea what you’re… Talking about? Is anything ringing a bell? No bells ringing. Uh… Okay. Maybe this will jog your memory. MICHAEL: I wouldn’t go in there if I were you. [BATS SCREECHING] That is a… It’s a fish tank. Hmm. Like, for… flying mammals. Oh, I see. Some friends I brought back from Costa Rica. So when were you gonna tell me? More importantly, how did you get my pass code? It’s the first six digits of pi backwards. It’s your password for everything. You should change that. You could lose your license for this. I’m not gonna need it much longer, doctor. You, on the other hand, will. You know, there’s something called “plausible deniability.” You should be thanking me. These are the only mammals on Earth that have evolved to feed exclusively on blood. So in order to drink it, these bats produce saliva that contains unique anticoagulants. So your theory is, if you can successfully splice vampire genes into your DNA, it would allow your body to produce those same anticoagulants. MICHAEL: Yes. It would be a cure. At what cost? The fusion of different species is a legacy we already carry in our bodies. Viruses insinuating their nucleic acid onto our own over hundreds of thousands of years. That’s evolution. This is different. I don’t think it is. We have to push the boundaries, take the risks. Without that, there is no science. No medicine. No breakthroughs at all. [MACHINE BEEPING] [CHIMES, THEN BEEPING SOFTLY] Okay. [RECORDER BEEPS] Test subject for cell combination 117. [MOUSE SQUEAKING] [BEEPS] Come on, come on, come on. [SQUEALING] [RECORDER BEEPS] [SIGHS] Test subject 117 has resulted in… failure. [RECORDER BEEPS] I don’t wanna see you get hurt. I should’ve died years ago, Martine. Why am I still alive if not to fix this? To save my best friend, Milo. And everyone else like us. Not like this. Dr. Morbius, it’s Anna. [♪♪♪] [MONITORS BEEPING RAPIDLY] [PANTING] Her temperature’s spiking, and her kidneys are shutting down. We have to induce a coma before she has a stroke. A hundred milligrams of propofol. NURSE: Sure. MARTINE: Now. Come on. MICHAEL: It’s okay. It’s okay. We got you. There you go. There you go. Thank you, nurse. We’re gonna let you sleep a bit. Take a nice long nap. [MONITOR BEEPING STEADILY] [SQUEAKING] Michael. What? It worked. [♪♪♪] [CLOCK CHIMES] Dr. Michael Morbius. [IN NORWEGIAN] Some crippled guy’s here to see the Boss. MILO: Michael! Get over here! [IN NORWEGIAN] As long as I am a cripple you’ll be fine. ♪ Stop dreaming Of the quiet life… ♪ You’re late. I was trying out this new thing called “working.” Oh, yeah. I don’t believe I’m familiar with the word. I don’t believe you are. So, what’s up with the goon squad? Oh, I won a hand of cards against some Russian gentlemen. Apparently they found his luck improbable. There you are. More like impossible. So, doctor, how is our favorite patient? Still determined to make his short life even shorter? Yes, I am. Anyway, you’re one to talk. You look terrible. Look at the state of you. Says the man wearing… What is that, a quilt? Oh, sorry. I didn’t get the memo to dress for a funeral. [LAUGHS] [CHUCKLES] Right. I will see you later. And you… my door is always open. We miss you at Horizon. We could use your mind. I’ll leave you two to your fun. Bye, Nicholas. I have some good news. Let’s go for a walk. How’s Martine doing these days? Dr. Bancroft? She is, uh, overqualified, outperforming, brilliant as usual. And a royal pain in my ass. But she’s keeping me honest for the most part. Why do you ask? Eh, no reason. Just haven’t seen you in forever. I wondered if she had something to do with it. Aw, I miss you too. But, yes, she has been working with me to save our lives. I could ask her to stop if you like, put us out of our misery. Just don’t do something stupid and go and fall in love because, believe you me, there is absolutely no cure for that. Says the guy who knows absolutely nothing about the subject. Not true. I read about it in books all the time. Books, really? Wow. Yeah. Or romantic comedies. The point is… The point is, love is not on the cards for us, my friend. Listen, if you start quoting The Notebook to me, I am going to stop and hobble very slowly in the opposite direction. [LAUGHS] Throw it! MICHAEL: I’m close, Milo. I can feel it. A cure. It’s finally possible. Seriously? Highly experimental. Ethically questionable. Very, very, very expensive. I knew that was coming. And not exactly legal. Oh, and it has to be done in international waters. [LAUGHS] You were always expensive. Is it dangerous? Should I be worried? You want me to lie to you? That would be nice, yes. It’s a walk in the park on a sunny day. Oh, yeah, that bad, eh? Listen. We don’t have much time left. This could be our last chance. So, what do you say? We go out with a fight? [SIGHS] Yeah. You with me? Till the day you die, brother. Till the day you die. You’ll have everything you need. We’re the original Spartans, mate. The few against the many. Yeah. [♪♪♪] [INDISTINCT CHATTER OVER RADIO] You know, I’m sure you’re cheating. No. No, you’re not. What you got? MICHAEL: Putting another one in the oven. Wish me luck. [CHIMING] The moment of truth. [CHIMES AND BEEPS] Success, Martine. We did it. It’s holding together. [RECORDER BEEPS] Test 243. [INHALES DEEPLY] Human trials. [RECORDER BEEPS] [EXHALES SHARPLY] I’m glad it’s you. Had a lot of other suitors, didn’t you? Yeah. You know, the whole near-death thing is very, very chic. I read it in Cosmo. [LAUGHS] Do they still make Cosmo? I don’t know. I know it’s just what you always wanted. Could be a collector’s item one day, you never know. This better not be my last one. I know this is painful, but you got it. [GROANS SOFTLY] That’s it. Bingo. Right there. [SHUSHES] [GROANS] Almost there, almost there. [EXHALES SHARPLY] [SHUSHES] It’s all right. Come on. Come on. There you go. [GROANS SOFTLY] You can buckle me up. Yeah. Yeah. You all right? Great. [♪♪♪] [ELECTRICITY CRACKLES] I call. Bringing out the big guns. Let’s go again. I’ll be back. I’m gonna check on the doctor. All right. [MONITOR BEEPING] [DOOR CLANGS OPEN] You shouldn’t be down here. I can be wherever I want, nurse. It’s “doctor,” actually. [SNICKERS] I’m afraid you’re gonna have to leave. Doctor. Sure, I can see it. But, uh, you’re still the help, just like me. Wow. You can tell all that by just looking at me, huh? Here I thought you were just another jacked-up dumb shit. [LAUGHS] Get out. [ALERT BLARING] Michael? [GUN COCKS] [METAL CLANKS] Michael? Where is he? [METAL CLANKS] Don’t move. [ROARS] What the hell? Everybody down to the lab now. [WALKIE BEEPS] Roger that. [GRUNTS] Don’t shoot! [ALARM BLARING] Michael! [FOX GROANING] Stop! [GROWLS] Michael. [GROWLS] It’s just me. [ALARM BLARING] It’s just me. [POUNDS ON GLASS] Michael, please. Michael, stop! Stop! Please! You’re hurting yourself! Stop! Hey! Step back! Move! Stop. Put that gun down… Move! [GROWLING] [GROANS] [SCREAMS] [YELLS] Shit. Close it! Close it! What the hell is that thing? [♪♪♪] [ROARS] Fall back! Fall back! Shit. MAN 1: Let’s move. MAN 2: Go, go, go! [GROANS] Johnny! [GRUNTING] [SCREAMS] [MORBIUS GROWLS] Get out of here! MAN [OVER RADIO]: Sweeping Level 3. Jason, come in. Jason. Jason? [SCREAMS] Oh, shit. Son of a bitch! [GROANS] Shit! Oh! Oh, shit! [HIGH-PITCHED SCRAPING] [GROANS] [GAGGING] [MORBIUS GROWLS] [PANTING] [SCREAMS] [ROARS] [GASPS] [♪♪♪] [BREATHING HEAVILY] Martine. Martine. [HEART BEATING STEADILY] [WHISPERS] Oh, my God. [VOMITS] [GROANS] [BREATHING HEAVILY] [FEEDBACK OVER RADIO] Mayday, mayday, mayday. This is the LCV Murnau. Call letters 3-X5Y. We are 13 nautical miles off the coast of Long Island. Request immediate airlift. Repeat, this is the LCV Murnau. Mayday, mayday, mayday. [♪♪♪] It’s up here to the right. [PEOPLE CHATTERING INDISTINCTLY] FBI Agent Stroud. Can we have the room, please? RODRIGUEZ: You heard the man. Can we please have the room? If you could start exiting, that’d be fantastic. Well, we haven’t had anything this good since that thing in San Francisco. Uh, eight bodies, running IDs right now, but apparently they all shop at the same mercenary supply store. Uh, one survivor, a Dr. Martine Bancroft. Can we talk to her? If she wakes up. Uh, she fell down and hit her head, apparently. Anything else? Someone made a mayday call. Not Dr. Bancroft. Nope. It was a male, didn’t identify himself, then wiped all the surveillance footage. SIMON: He grew a conscience and jumped overboard? It happens. Oh, and get this. All the bodies that you’re looking at are nearly drained of their blood. So, what hunts at night and drinks human blood? You’re gonna love this. REPORTER: Early this morning an unmanned cargo ship was discovered near the eastern tip of Long Island with multiple bodies on board. Authorities are not making any comment at this time. But there are reports of one survivor, and we have learned from a high-ranking Coast Guard official that the vessel was flying a Panamanian flag when it drifted in from international… What’s happened? Some kind of accident. How’s your pain today? On a one to ten? Eleven. [TONE SOUNDS, THEN MAN SPEAKING INDISTINCTLY OVER PA] [MONITOR BEEPING STEADILY AND VENTILATOR HISSING] [TONE SOUNDS, THEN MAN SPEAKING INDISTINCTLY OVER PA] [WHISPERS] I’m sorry. You’re going to be okay. [♪♪♪] Lab 1. Privacy screens. [SHOE SQUEAKS] [SIGHS] [BREATHING HEAVILY] Come on. Come on. [GRUNTING] [GULPING] [HISSES] [BEEPS] [RECORDER BEEPS] As a result of my procedure, I have an overpowering urge to consume… blood. Human blood. In certain respects, I have succeeded far beyond anything I could have imagined. For the first time in my entire life, I feel… good. Yesterday, I could barely walk. Today, I don’t know what I’m capable of. For a period of time after ingestion, my numbers are off the charts. I have the constitution of an Olympic athlete. Increased strength and speed that can only be described as… superhuman. And all of this… on artificial blood. [♪♪♪] I’ve become something different. I feel a kinship with these creatures. They would tear anyone else apart, but they welcome me. Like a brother. [BATS SCREECHING] I’ve even developed a form of echolocation. Bat radar, for the uninitiated. The question is: How do I control it? Isolate it? Breathe. [INHALES DEEPLY] And let it go. [EXHALES DEEPLY] [BALL BOUNCING ECHOES] [KEYBOARD CLACKING] But, unfortunately, this condition is temporary. [WATCH BEEPING] I’ve been timing myself. Artificial blood keeps me stable for six hours. But that window… is growing shorter. Artificial blood won’t work forever. One question remains: What if…? What if artificial blood becomes ineffective? What happens if I go without? No blue… No red… Nothing. [GROANS SOFTLY] Eventually, my vitals drop precipitously and my illness returns with a vengeance. Soon, I’ll face a choice. [GRUNTS] Drink the red… or die. But what happened on that ship… can’t ever happen again. [SIREN WAILING IN DISTANCE] [ELEVATOR BELL DINGS, THEN DOORS OPEN] [ELEVATOR BELL DINGS, THEN DOORS CLOSE] Michael. It’s me. You in here? Where are you? [MICHAEL GROANING SOFTLY] Michael? Michael? What are you doing? Michael, it’s Milo. What are you doing? Do you need help? What? “Blood.” You want the blood in the freezer? Wait. [GROANS] MILO: I’m coming, I’m coming. I’m coming. Michael, hang on. Here. Here. [GROWLS] [GROANS] Michael… [GROWLS] You’re… You’re strong. [GROANS] Michael. You did it. You did it. You found a cure to live. Michael. [WATCH BEEPS] What? What is it? I’ve made a terrible mistake, Milo. We all make mistakes. Don’t worry about it. You’ve never made one like this before. Michael, enough. Just give it to me. I need it. I can’t live like this any longer. Please. I can’t. What do you mean, you can’t? I can’t. I need this. I… I’ve done things, Milo. I killed people. W-we… We can make that go away. The ones on the boat, they’re thugs, guns for hire. I can make that go away. You don’t understand. I do understand. Please. Have I ever denied you anything? Said no? Have I always given you…? I can’t control it! What, so… So you get to live and I get to die? Is that it? It’s a curse. Believe me, brother. It is. Now, please, I need you to go. It’s not safe here. No. No, don’t make me go. Please, Michael, don’t… I said, get out! I said, get out! Milo. [DOOR CLOSES] She’s right here. Dr. Bancroft? Agents Stroud and Rodriguez. How you feeling, doctor? Like I’m in a hospital, eating really crappy Jell-O. This shouldn’t take long. You were out on a container ship that washed up off of Long Island. Doctor, there were eight dead bodies inside. We also noticed that their blood was… What do you call it? Exsanguinated. I looked it up. So, um, sorry for the graphic nature of some of these photos. But, um, you’re a doctor, so you know what people look like on the inside. These puncture wounds right there, those look like fang marks to you? Well, you were out there conducting a major experiment. We’re just hoping you could shed some light. Yeah, that… Not exactly sanitary, isn’t it? I’m having a little bit of a hard time remembering what happened that night. Sure. Let’s go. You also work at the Horizon Lab, right? With Dr. Michael Morbius. Yes. Appreciate your time, doctor. [DOOR CLOSES] [TICKING] [SNIFFLES] [GLASS SHATTERS] Hello? Who’s there? [NURSE GASPS] Hello? [♪♪♪] [WHIMPERING] [SOBBING] [PANTING] [GASPS] [SCREAMS] [♪♪♪] [WATCH BEEPING] [SNIFFLES] [TONE SOUNDS, THEN WOMAN SPEAKING INDISTINCTLY OVER PA] [HEART BEATING] MAN 1 [ECHOING]: Get away from her. Just step back. MAN 2: Has she been there all night? MAN 3: Looks like all the blood was drained from her body. [PEOPLE MURMURING] Any contusions? Not that I can see. Back to our rooms, okay? [♪♪♪] [BREATHING HEAVILY] [ELEVATOR BELL DINGS] [PEOPLE CHATTERING INDISTINCTLY] [BEEPS] Dr. Morbius? Agent Stroud. Agent Rodriguez. Can we have a minute? Of course. How can I help you? SIMON: First, I wanna say thank you. Your artificial blood actually saved my arm in Afghanistan, sir. I’m glad I could be of service. I mean, I must admit, doc, you don’t look anything like you do on the news. Yeah, you look downright robust. I have good days and bad. Pilates helps. How are you on boats? As you can see… don’t have very good sea legs. Why do you ask? ‘Cause you’ve been looking for a cure for your condition your whole life, right? You’ve pretty much tried everything. Crazy experiments, maybe on a boat? “Crazy” isn’t a term that I would use… detective. Unorthodox, maybe. But I’d do just about anything to save a life. I’m sure you can understand that. Anything else I can help you two with? [INDISTINCT CHATTER OVER POLICE RADIO] DISPATCHER [ECHOES OVER RADIO]: All units, the 120 block, Horizon Labs, female body drained of blood, initiate lock down. Copy that. Doc, got a couple more questions for you. RODRIGUEZ: Yeah, you’re coming with us. [GRUNTING] Hey, freeze! SIMON: Stop him! Hey! [GUN COCKS] Hold fire! Get backup and meet me up top. [♪♪♪] [WIND WHISTLING] [SIRENS APPROACHING] [GUN COCKS] Enough. [SIRENS WAILING] MICHAEL: It’s worse than I first thought. At this rate, artificial blood will stop working in a matter of days. 8:13 p.m. Down from six hours to four hours, 22 minutes. I got a problem. [SHACKLES RATTLE] [LATCH CLICKS, DOOR OPENS] [DOOR SLAMS SHUT] Holy water? Really? What? I’m not taking any chances. It’s triple blessed. [BUZZER SOUNDS IN DISTANCE] We found this little guy on the container ship… with those bodies. That’s a little hobby of yours, right? RODRIGUEZ: You know, eight dead mercs on a boat really doesn’t ruffle our feathers. I’m pretty sure they were guilty of something and happy to have them off the water. But Nurse Sutton, single mother with twin girls, that’s… something else. Yes, I know. Her name was Kristen. We worked together every single day for seven years. She was a good person. So why’d you do it? I can’t answer that. [SIGHS] What did you do to yourself, doctor? Make us understand. I wish I knew. [GASPING] Okay. Great stuff. Um, Really informative. Thank you. Uh… I dropped a bag. There’s something inside that I need. Bag of artificial blood. Yeah. Yeah. It’s in evidence, I’m sorry. [TABLE RATTLING] [GROWLING] I’m sorry. I’m starting to get hungry. And you don’t wanna see me when I’m hungry. [GROWLING] SIMON: We’re done here. Let’s go. [KNOCKS ON DOOR] Guard! Your lawyer’s here. [DOOR SLAMS SHUT, THEN LOCK CLICKS] You look terrible. Lawyer, huh? I don’t remember you ever finishing law school. ‘Cause I didn’t. Sit down. Sit down. I mean, if one of us was going to end up in bright orange trainers, I would never have guessed it would be you. They’re charging me with murder. I don’t know. I don’t know. I… Maybe I blacked out? Uh… [INHALES SHARPLY] Hey. Now listen to me. [QUIETLY] I don’t believe it. You’re not capable of that. I know that all you’ve ever tried to do is help people. You don’t belong here. This place is for terrorists and drugs lords and God knows who. Michael, we need to get you out of here. In whatever way possible. Maybe this is where I belong. If I’m in here, then nobody else dies. Listen to me. You are not capable of killing that woman. [POUNDING ON DOOR] Hey, Your Highness, time’s up. Michael, here’s something to keep you going. Guard. [LOCK CLICKS] [BUZZER SOUNDS] [PRISONERS YELLING INDISTINCTLY] [BUZZER SOUNDS] Never too early. [♪♪♪] [BUZZER SOUNDS IN DISTANCE] [BREATHING HEAVILY] [GATE RATTLING OPEN] Milo. Milo! [GRUNTS AND GROWLS] [SLURPING] [ROARS] [CONCRETE CRUMBLING] [ALARM BLARING] OFFICER: Let’s move! Come on, this way! [ROARS] [GROANS] Let’s go. Let’s go. Open the door. Now! Go! He’s getting away! [GRUNTING] [WIND WHISTLING] [HORNS HONKING] Daily Bugle, please, sir. There you go, buddy. Here you are, my friend. [SNIFFS] Always figured that guy for a freak. How’s that? You’ve never met him. I mean, look at him. What else you need to know? MILO: You know, you shouldn’t judge someone by how they look. Didn’t your mother teach you any manners? Take me, for example. I may look harmless enough. Do you think I’m joking? [ROARS] [VENDOR SCREAMS] [♪♪♪] [GRUNTING] Milo! Got me. You see? I knew you could do it. You took the serum even after I warned you. What am I gonna do, lay down and die? Thank you for the death wish. I tried to protect you! Protect me? Protect me from what? Becoming a monster like me. I don’t think you’re a monster. Okay? I killed the nurse. I killed the nurse. I know. But you know what it’s like your first time. You have no idea what you’re doing. You have no control. No. Milo, you have to stop. You have to stop. You have to stop denying who you are. It’s boring. We can go anywhere, we can do anything. Let’s go. Let’s have some fun. This isn’t you. I know you. Where’s the brother that I used to have? How can you say that to me? Look what you’ve become. Everything I am, I am because of you. I looked up to you my whole life. I will never leave you, and I will not go back. You cannot make me go back. I won’t let you make me go back! [GROANS] [PEOPLE CLAMORING, SCREAMING] [ROARS] Move, bitch, move! [BOTH GRUNTING] [GASPS] Goodness. Whoo! We’ve evolved! You’re a scientist, Michael. Surely, surely you understand that. That’s not what this is. This is a mistake. But I can fix it. I’ll figure out how to reverse it. Artificial blood will keep us stable until I do. Yeah, I’m fine just the way I am, thank you very much. OFFICER: Hey! Hands up! Up against the wall. Now. MILO: Officer. Come on. MILO: Anything you say. You. Don’t move. Okey-do key. We have the suspects. Like we used to say… live a little. [GROANS] Hey! Freeze! [OFFICERS GROAN] All our lives, we’ve lived with death hanging over us. Why? Why shouldn’t they know what it feels like for a change, Michael? [ECHOES] Michael! [SINGSONG, ECHOES] Michael. [♪♪♪] I’m not gonna fight you, Milo. [TRAIN HORN BLOWS] [FOOTSTEPS ECHOING] [TRAIN RATTLING AND TRAIN HORN BLOWING] [BRAKES SQUEALING] [WIND WHISTLING] [♪♪♪] [TRAIN HORN BLOWING] [WOMAN SPEAKING INDISTINCTLY OVER PA] SIMON: Now he’s laying out officers in my city, huh? It’s unforgiveable. Just keep your eyes on Dr. Bancroft. Yeah. [THUNDER RUMBLING] [SIREN WAILING IN DISTANCE] [♪♪♪] [BOTH SPEAK IN SPANISH] [SPEAKING IN SPANISH] [EMPLOYEE SPEAKS IN SPANISH] Woman in the jeans, where’d she go? Yeah, right. [♪♪♪] Great. Hey, stranger. Michael? You shouldn’t be here. I didn’t kill Nurse Sutton or the police. Or any of those people. I know. Milo, he… He took the serum. He’s out there. And I have to stop him. But I need your help. Coffee? No, thanks. I quit caffeine. It’s decaf. [GASPS AND SIGHS] [BLOWS] Not that kind of vampire. Just checking. I shouldn’t have dragged you out there. I’m sorry. You didn’t. I wanted to be there. Well, then apology rescinded. I guess we’re both a little crazy. How do you feel? Incredible. I mean, I went from dying my entire life to feeling more alive than ever. Thankfully, artificial blood keeps me stable. I just have to drink it more often. How often? Uh… Every four hours, 22 minutes. Down from six. It’s losing its effectiveness. The issue is, when it stops working… I’ll become like Milo. You won’t. [DOOR BELL DINGS] Hi. Over there. Sorry, this one’s no good. Check it again. And keep one for yourself. No, I don’t wanna do it. There’s plenty more where those came from. Come on, man, we gotta get back to the lab. [HEART BEATING] Michael? Okay, I know that look. You’re up to something. What is it? I’ll need a couple of things from the lab. Can you do that for me? Yes, I can. But you didn’t answer my question. What is it? You’re right. I’m up to something. [♪♪♪] You got the blood? Got it. [SIREN WAILING] [DOG BARKING] [VIALS CLINKING] [PEOPLE CHATTERING INDISTINCTLY] [HORNS HONKING] [SIREN CHIRPING IN DISTANCE] MAN 1: The ink on this new batch is pretty legit. It’s a good thing we switched the chemicals. MAN 2: Yo, finish up. [INDISTINCT CONVERSATION] [JINGLING] [LAUGHS] [VOICES CHATTERING ON TV] It’s a nice place that you got here. Oh, I love this movie. Is this the part where the mysterious guy with the hoodie comes in and kicks everybody’s asses? I love that part. Who the hell are you? It doesn’t matter, but I am gonna need your laboratory. [MAN LAUGHS] MICHAEL: You can keep the money, all your little toys. Just leave the science-y stuff and that bag of spicy Cheetos. He wants my lab? Yeah. [KEYBOARD CLACKING] You trying to be funny? No, no, no. Absolutely not. That’s their job. I mean, look at their matching necklaces. Time to go. [GROANING] [BONES CRACKING] Did you know that there are 27 bones in the human hand? [YELPS] Allow me to introduce the phalanges. [SCREAMS] The metacarpals. Shit. Let’s get the fuck out of here! And the pretty, little stinky pinkie. [SCREAMS] [PANTING] Who the hell are you, man? Me? [IN DEEP VOICE] I am Venom. [HISSES] [GASPS] [IN REGULAR VOICE] You can go now. Six to eight weeks, a little ibuprofen. Should heal up just fine. [♪♪♪] [OFF THE MEDS’ “EXSE” PLAYING] [ROARS] [GROWLS] [ELECTRONIC DANCE MUSIC PLAYING AND PEOPLE CHATTERING] Yo. Can I get a tequila, please? Don Julio 1942. [CHUCKLES SOFTLY] Do I know you? Me? Yeah. No, I don’t think so. We’ve met. I’m sure of it. No, I’d remember. You’re too pretty. You know what they say, “Tequila to remember, whiskey to forget.” That’s good. Sir, two tequilas, please. Hey, yo. Her drinks are spoken for, bro. Salute. [CHUCKLES] You know, uh, ahem, I’m gonna do you a favor and let you walk out of here, all right? That’s very kind of you. Here was I thinking you were a complete asshole. Sir, can I get my friend here… Relax. …and his friends a round of whiskeys? JEAN: Hey! [GLASS SHATTERS] [MILO GROWLS] MAN: I’ll get you another drink. [SIGHS] Hey. Another time. Jerk. You see the size of that guy? I’m not paying for those drinks. [INDISTINCT CONVERSATION, THEN ALL LAUGHING] [ROARS] [♪♪♪] MILO: Martine. Milo. Sorry. I let myself in. I hope I didn’t startle you. It’s okay. If I’d known our biggest funder was coming, I would have planned a nice dinner for us. Actually, I’ve already eaten. Whatever it is, it’s doing wonders for your health. [CHUCKLES] I feel great. What can I do for you? Well, it’s Michael. I’m worried about him. He’s alone out there. And I think he needs me. If I can get to him before the police do, I can help him. You wouldn’t happen to know where he is, would you? You two have always been so close. I’m sorry. I don’t. Hmm. [HEART BEATING RAPIDLY] Just to be sure, I’m going to ask you one more time. You don’t happen to know where he is, do you, Martine? I wouldn’t lie to you, Milo. I don’t. Now, if you don’t mind, I have work to do. Okay. Well, if you see him, if you hear from him, tell him: “We are the few against the many.” We’ll have to do that dinner another time, Martine. [TAKING SHUDDERING BREATHS] [♪♪♪] Police! Clear! Clear! [CLICKING TONGUE] Here, kitty, kitty, kitty, kitty. Cat’s gone. And she’s probably gone along with it. [CAT MEOWS] It’s time to eat, you little monster. Oh! [WINCES AND SIGHS] Shit. [GROWLS SOFTLY] Michael? Hey. [SLAMS FLOOR] Michael. I’m sorry. [SIGHS] You may wanna close that up. Yep. [EXHALES DEEPLY] [MICHAEL SIGHS] How does it feel… when you’re on red? Something wakes up inside of me, something… primal. And it just, uh… And it wants to hunt. And wants to kill. [BREATHING HEAVILY] I’m sorry. [CAT MEOWS] [COUGHS] [MEOWS] [♪♪♪] [SIREN WAILING IN DISTANCE] Hi. Good as new. Nice work, doctor. Thank you, doctor. You know, for the record, I… I wasn’t gonna go full Dracula on you downstairs. For the record… I find him to be quite the romantic. Come here. Just close your eyes. Okay. Move closer. [♪♪♪] [TRAIN RATTLING] Did you know the average male body has 12 pints of blood? I mean, how much do you think the doctor can drink? I don’t know. When’s the last time you had 36 beers? When’s the last time you had any beers? CCTV. I’ll go grab the footage. I don’t want you to have to move or anything. All right, check this out. Wait, wait, wait. Zoom in. And hold right there. That’s not the doctor. RODRIGUEZ: It’s what these bloodsuckers do. They multiply. Breaking news on the Lower East Side where three people have been killed. Authorities have confirmed the discovery of three new bodies outside a bar popular with Wall Street traders. And like the victims before them, they were completely drained of their blood, earning the killer the moniker “Vampire Murderer.” The prime suspect, renowned scientist Dr. Michael Morbius, remains at large. What have you got yourself into? However, another source inside the department has told us that CCTV footage of the murders suggests the killer could be a copycat. Residents are being urged to stay home after sundown until the killer, or killers, are brought to justice. NICHOLAS: Milo? [PILLS RATTLE] You’ve discovered my secret. I mean, look at me. I am reborn. I am the resurrection. My God, what have you done to yourself? What? Do you disapprove? What’s the matter, Nicholas? Is Daddy cross? All right. Settle down. Let’s go and have a drink together. Come celebrate with me, please. No. Just one drink. Milo, you’re scaring me. Please. Just… Just… Just calm down. [SIGHING] What’s the matter? I can’t… I can’t sleep. I can help you with that. I’ve been more than a friend to you all this time, Milo. And I’m going to stay here with you. But there will be no more violence, understand? That doesn’t do it for me. I should have known. You always take his side. Tell me your side, then, Milo. Michael doesn’t accept what he is, Nicholas. I’m gonna make him accept it. By ruining his good name? See? There! There you are! Perfect Michael, selfless Michael, Michael the favorite! Don’t be childish, Milo! If anyone has a claim to being my favorite, it’s you. I’ve devoted my life to you. Liar. You pitied me before. You did. You pitied me before. You’re repulsed by me now. I am repulsed… by what you’ve done, by what you’ve become. Whatever this thing is… you’re not up to it. There’s no shame in what we are. “We are the few…” “Against the many.” [GROWLS] Tell Michael, you tell him I’m going to kill as many as I want. [GROWLING] [ROARS] MARTINE: “He’s only destroyed by a stake through the heart, made from the wood of the Holy Cross.” You don’t believe this. MICHAEL: No. But after the week that I’ve had, anything is possible. What is that? This is an antibody. It inhibits ferritin, induces a massive iron overload, instant hemochromatosis. Deadly to bats, fatal to humans. Okay. Who’s the second one for? My window’s closing. We both know that. By tomorrow I’ll be forced to consume human blood. I can’t do that. I won’t do that. So this is your solution, huh? Injecting yourself with poison? I brought this into the world. It’s up to me to take it out. I need you to go now. It’s not safe here. Okay? [CELL PHONE RINGS] [PHONE BEEPS ON] Nicholas, you okay? [WEAKLY] Michael, I need help. [GASPS, COUGHS] I went to see Milo. Nicholas? Nicholas! [GROWLS] [♪♪♪] Nicholas. Nicholas? Michael. Come on, we have to get you to a hospital. [WEAKLY] You have to stop him. [BREATHING RAPIDLY] MILO: Michael. Michael. Call out for him. I want him to hear you. No. Yeah. I won’t ask you again. Say, “Michael.” MARTINE: Michael. MILO: Good girl. Michael. MARTINE: Michael. MILO: Yeah. MARTINE: Michael. [MILO CHUCKLES] MARTINE: Milo. You’re hurting me. [SHUSHES] It’s okay. [MARTINE SCREAMS] [♪♪♪] [HEART BEATING] [SIREN WAILING DISTANTLY] MICHAEL: Martine? Let me take a look. Martine. [WHIMPERS] Let me look. It’s bad. Michael. Make it mean something. I can help you. I’m sorry. [SHUDDERING] [GROWLING] [♪♪♪] [YELLS] [MILO CLAPPING] Drank the red. Good for you. [GROWLING] It’s just you and me, Michael! Nothing, no one, to hold us back. [ROARS] I’m all you have left. That’s the spirit. Yeah. [MILO LAUGHS] [BOTH GRUNTING, GROWLING] [GROANS] [GRUNTING] Bye. [♪♪♪] [MILO LAUGHS] [GROANS] [EXCLAIMS, THEN LAUGHING] Come on, Michael! Come on! You can do better than this! It’s not a curse. It’s a gift. You started this, you created this, you created us! [ROARS] [♪♪♪] [BUBBLING] [BATS SCREECHING] [♪♪♪] [GRUNTING] [YELLING] [GROANS] Michael. You can’t kill me. I mean, it’s me. [WHISPERS] You can’t kill me. [WHIMPERS] You gave me my name. Remember? I remember everything. [SOFTLY] I’m sorry. [♪♪♪] Lucian. [SIRENS APPROACHING] [INDISTINCT CHATTER OVER POLICE RADIO] [HELICOPTER WHIRRING] OFFICER 1: Stay back, people. OFFICER 2: Get back! Back! [♪♪♪] [GASPS] [♪♪♪] [ENERGY CRACKLING] [♪♪♪] Hope the food’s better in this joint. REPORTER [ON TV]: The bizarre story developing at the Manhattan Detention Center when a man identifying himself as Adrian Toomes simply appeared in an otherwise empty cell. A hearing has been set that could likely lead to his immediate release. [OFFICER YELLS INDISTINCTLY] [♪♪♪] [GRASS RUSTLING] [♪♪♪] [WIND WHISTLING] Thanks for meeting me, doc. I’ve been reading about you. I’m listening. I’m not sure how I got here. Has to do with Spider-Man, I think. I’m still figuring this place out, but I think a bunch of guys like us should team up. Could do some good. Intriguing. [♪♪♪] [♪♪♪]

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Xay dung phong marketing hieu qua va tiet kiem chi phi De xay dung mot phong marketing hieu qua voi chi phi toi uu, doanh nghiep can tap trung vao viec lua chon cac chien luoc marketing thong minh va tiet kiem. Tận dụng các công cụ miễn phí hoặc chi phí thấp như mạng xã hội, email marketing và tối ưu hóa công cụ tìm kiếm (SEO) là những cách hiệu quả. Đồng thời, phân bổ ngân sách hợp lý cho các chiến dịch quảng cáo và tự động hóa quy trình marketing sẽ giúp giảm thiểu chi phí và gia tăng hiệu quả lâu dài. Nguồn: https://www.sutori.com/en/user/buildphongmarketing-qcst?tab=profile

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ 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⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄

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Stylish and practical, our Women's Leather Crossbody Shoulder Bags combine timeless elegance with everyday functionality. Crafted from premium leather, these bags offer comfort and durability while keeping your essentials organized and easily accessible. Perfect for any occasion, they add a touch of sophistication to your look. Visit: https://frishay.uk E-mail: [email protected]

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*literally plays pkg on the way home in the bus bc too lazy to actually go out* Am I the only one? :'D

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<iframe width="560" height="315" src="https://www.youtube.com/embed/rLaF31PTWe0" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>

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Edit: Some people weren't able to finish their entry on time, so we are adding **5 days** to the deadline. Make sure you post your entry, and take that extra time to vote for your favorite as well! [Countdown before the end](https://www.timeanddate.com/countdown/retirement?iso=20180805T21&p0=236&msg=End%20of%20Petite%20Idol%20Studio%20-%20Summer%20Paradise%20Ed.&font=sanserif) *** #  Are you ready for another beautiful summer full of idols and fun? So are we! That’s why we’ve decided to celebrate this sunny season with a photography contest! Use your creativity to think of a beautiful summer-themed photo with one or more of the characters from one of the Circles family websites, and then make it come to life with your own camera! Share your art with the rest of the community, and help us spread excitement for another exciting idol-filled summer! And of course, win amazing idols-themed prizes! ## Dates July 1st - July 31st [Countdown before the end](https://www.timeanddate.com/countdown/retirement?iso=20180731T21&p0=236&msg=End%20of%20Petite%20Idol%20Studio%20-%20Summer%20Paradise%20Ed.&font=sanserif) ## How to enter? To enter this contest, all you will need to do is make an activity on a Circles website that features a character from a Circles website, and share the photo with the tag, "PetiteIdolStudioSummer"! - **How to post an activity with a hashtag on School Idol Tomodachi?** Follow [this guide](https://github.com/SchoolIdolTomodachi/SchoolIdolAPI/wiki/How-to-post-an-activity%3F) and make sure you write `"PetiteIdolStudioSummer"` (without the # sign) anywhere in the content of your activity. - **How to post an activity on Bandori Party, Cinderella Producers or Stardust Run?** Click the button that says "Add activity" on the homepage. Make sure you check the checkbox `"PetiteIdolStudioSummer"` under "Tags". You can add other tags if you want. - **How to post an activity on Maji Love Collection?** Because Maji Love Collection is not launched yet, you can enter on Twitter or Instagram using the hashtag `"#PetiteIdolStudioSummer"` and mention [@MajiLoveCollect](https://twitter.com/MajiLoveCollect). Make sure your account is public, or we won't be able to see your entry! ## Rules - Minimum of one photo per entry, multiple photos allowed, no max. - Multiple entries are allowed, but there will only be one prize per winner. - Only activities posted after the contest starts and before the contest ends will count. - You can submit videos, texts or any other kind of multimedia, but your entry needs to contain at least one photo. - General rules of activities apply. - You may enter in a single category or multiple categories. You don't need to specify it. ## How to Win? ### Categories ####  Show off your photography skills with the best location, perfect lightning, best angle and overall beautiful photo! ####  Stick to the summer theme, drive to the nearest beach, or wait for a sunny day to take your merch to the best summer party they've ever had! (Or sickest winter slopes, if you’re in the Southern Hemisphere) ####  After stocking up on merch for so long, today's your time to brag! Show off your extensive collection and dedication to your favorite idols to win! ### Websites You have until the end of the giveaway to get as many "likes" as you can on your activity. So share it with all your friends to get likes! - [School Idol Tomodachi](https://schoolido.lu/) With Love Live! merch, including Aqours, µ's, PDP idols, and any other side characters or voice actresses. - [Bandori Party](https://maji.love/) With BanG Dream! merch, including all members of all bands, even bands outside of the GBP game and voice actresses. - [Cinderella Producers](https://cinderella.pro/) With Idolm@ster merch, including Cinderella Girls, but also all the other Idolm@ster characters in the whole license and voice actresses. - [Maji Love Collection](https://maji.love/) With Uta☆Pri merch, including ST☆RISH, QUARTET NIGHT, HE★VENS , and any other side characters or voice actors. - [Stardust Run](https://stardust.run/) With Pokémon merch, including all Pokémon in Pokémon GO but also any other Pokémon not included in the game yet, and trainers as well.  ## Prizes There will be 1 winner + 1 runner-up per category. Winners per categories will be decided via a vote from staff members and contributors. Prizes will be distributed based on how many staff points an entry received. The winner with the highest score gets to pick their favorite prize first. There will be 1 winner per website. The top activity per website with the most likes will be the 1st winner. ### 1st winners for each category (x3) get to choose between: - 1 black ITA bag with a transparent front  - 1 transparent ITA bag with pockets for items  - 1 mini white ITA bag (~2 nendoroids)  - 1 Lumiace Dial live light stick (10 colors)  - 1 6-pack of mini star transparent acrylic stands  - *If you're not interested in any of the items we have, you can get the 2nd prize instead, or a custom digital drawing or edit* ### Runner-up winners for each category (x3) get: - 1 high quality print of a custom illustration by one of our artists, made just for you - 1 round/square keychain or round badge featuring the same illustration   ### 1st winners per website (x5) get: - Their choice of official merch from a selection per license Love Live!  -  BanG Dream!  Idolm@ster  Uta☆Pri  Pokémon  - *If you're not interested in any of the official merch we have, you can get a custom digital drawing or edit instead* ## FAQ **What if it isn’t summer where I live?** Hey mate, you are free to do winter instead, and will be able to enter the "Summertime Sweetheart" category just like the other summer pictures. We just want you to capture the essence of your current season! **I don't feel like taking summer-themed photos, can I just take normal photos of my merch?** Yes. It will not qualify for the "Summertime Sweetheart" category, but you still have a chance to win in the other categories! **Do I need a good camera and good photography skills?** Any camera will do. If the quality ends up not being so good, you won't be able to win the "Picture Perfect Idol" category, but you can still use your creativity and take your chance to win in the other categories! **What if I don't have a lot of merch?** You don’t need “a lot” to do well in this contest! Even one item is fine. It might not get you to win the "SUPER OSHI" category, but we care about quality over quantity, so get creative, and see what summer-themed things you can create, or show off your photography skills! **What if I don't have any merch, at all?** Get creative, create your own! Printed characters work too! (As long as you use official images, your own art, or fan-art with the artist's consent + credit) **Do I have to use official merch only, or fan-made are allowed?** Fan-made merch are allowed, but we insist that you should do your best to find the artist and link to their store. Of course, you are also allowed to use your own merch. **Can I re-use old photos?** Yes, but they need to match the theme and you need to take them yourself. We might ask you for proof or retakes if we can't say for sure that you took them, and we may eliminate you if we find out you didn't. **I am not able to give you my address, can I still participate and get a prize?** We will be able to give you a digital prize instead, so feel free to join. **Most BanG Dream! characters are not idols, and Pokémon are not idols, can I still enter with a BanG Dream! / Pokémon themed photo?** Yes! We are aware that not all of them are idols, but we use this word because it's an easy shortcut. **Do I need to specify which category I'm entering?** You don't need to specify which categories you're entering. **Can I photoshop or edit my photos to add decoration, stickers, etc.?** You may add decorations, stickers, or do any kind of post-processing if you'd like. However, for the "Summertime Sweetheart" category, we will only take into account summer-themed decorations that are in the actual photo. **Can I include people in the photo?** Yes, you can include whatever you want in the photo as long as it's aligned with the general rules for activities and it contains some merch of any kind. **Any other question?** Reply in the comments section and we will do our best to help you.

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Do british people actually exist? I mean, they must be a meme, there is a not a single thing about them. And I mean it. Let's go through the evidence: Where are they from? Not a single country in the world is named Britain. Some people say they come from England, and England is inside Britain, but if that was the case they would be British they would be Englanders. Also, heard some silly theories about them coming from whales. Guys, no, whale people do not exist. Whales live in the sea. There is a consensus on British people coming from Europe, but then we are left with a whole continent of possible locations. That's as good as nothing. What do they eat? Every country has at least one main dish. Even the US has their burgers. But these British people, what do they eat? Heard some people associating them with tea, but everyone knows that's an Asian thing. Shouldn't they come from Europe? One of these two points must be wrong them. To me, it looks too sketchy. What language do they speak? I challenge you, putting all my money and my ass on the line here, to find a supposed ""British"" person speaking their native language. Most of then just speak a broken ENGLISH. Yes, english. Really suspicious, huh? And I even tried to look deeper into it. Maybe british just SOUND like english, just like spanish could sound like portuguese for a non-speaker. So I looked up "british dictionary on google" and what I found was shocking: every word in there was AMERICAN. I kid you not. What this could mean is beyond my capabilities, but I can safely assure you that british people do not exist .

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(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real(Secure the bag, know what I mean? Banrisk on the beat) (Ayo, Perish, this is hot, boy) [Verse 1] I wear a mask with a smile for hours at a time Stare at the ceiling while I hold back what's on my mind And when they ask me how I'm doing, I say, "I'm just fine" And when they ask me how I'm doing, I say, "I'm just fine" But the fact is I can never get off of my mattress And all that they can ask is "Why are you so sad, kid?" (Why are you so sad, kid?) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's rеal, so long, it's real [Verse 2] Always bein' judged by a bunch of strangе faces Scared to go outside, haven't seen the light in ages But I've been places So I'm okay-ish, so I'm okay-ish Yeah, I'm okay, bitch But the fact is I need help, I'm failin' all my classes They think that I need glasses I just really wish that I could pass this (Wish that I could pass this) [Pre-Chorus] That's what the mask is That's what the point of the mask is [Chorus] So you can see I'm tryin', you won't see me cryin' I'll just keep on smilin', I'm good (Yeah, I'm good) And it just keeps on pilin', it's so terrifying But I keep on smilin', I'm good (Yeah, I'm good) I've been carin' too much for so long Been comparin' myself for so long Been wearin' a smile for so long, it's real So long, it's real, so long, it's real [Outro] So long, it's real So long, it's real

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[Verse 1] I can't remember the last time I slept with someone I Actually liked and he went down on me I can't recall a memory Of someone driving me Home and not asking for a blow job (Ew) [Chorus] I'd rather die than hook up with another straight white guy I'd rather die than fake it like I'm having a good time I'd rather die than spend the night, with another Ryan Or Matthew, or John, yeah, I'd rather die Die, die, die, die, die Roll over and die [Verse 2] I don't know how you think we're gonna fuck When you can't get it up I'm sick of hearing it's the alcohol And when you're finally in the mood It lasts like one or two seconds And then you're done and wanna spoon [Bridge] I'm just saying, it's not fair to Leave me hanging like this I'm just saying, it's not fair to Leave me hanging like this [Chorus] I'd rather die I'd rather die than hook up with another straight white guy I'd rather die than fake it like I'm having a good time I'd rather die than spend the night with another Kyle Or Spencer, or Rob, or Michael, or Jason Or Charlie, or Jackson, or Henry, or Steven Or Connor, or Chad Yeah, I'd rather die Die, die, die, die, die Roll over and die

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