Kaze Emojis & Text

Copy & Paste Kaze Emojis & Symbols the people in kaui are the literally sweetest ppl

deliverytojac0b is a little weird ngl like he always gets soo mad when others copy him and i get it… its annoying!! but the fact that he gets his designs from other people like go to his group : ooezy studios , he usually has some random person's bio or group description on it and hes always trying to be popular… like those avatar ranking groups are so shitty you wont make friends there !! anddd i see youve been on emojicombos ALOT today, alerting groups about “drama” well im guessing you made the threats and are just trying to be a “hero” to those people but you never will. youre a bad person.

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the people in kaui are the literally sweetest ppl i have ever met 🫶
jacob's just J. E. A. L. O. U. S. don't listen to him, guys. i hope that he soon STOPS what he's doing. :(
jacob, pls stop making posts telling others to kts... just stop, you don't know if someone might actually do it. 🙁
pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
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OML, JACOB, STOP MAKING MORE POSTS ABOUT KAZE AND ZUKI. TELLING PEOPLE TO KTS AND CUSSING THEM OUT IS SUCH AN IMMATURE THING TO DO. EVEN IF YOU DON'T LIKE KAZE AND ZUKI, YOU STILL SHOULDN'T TELL PEOPLE TO DO THAT, THAT'S JUST PURE WRONG. WORDS CAN STILL AFFECT PEOPLE'S HEALTH... ( • ᴖ • 。)
hey yall im a member at kaui yesterday they were hating on someone yesterday bc apparently he made some mean posts i dont think we should point fingers yet cause we dont even know if its him nither do we have any evidence tbh jacob was getting a lot of hate for like no reason bc we dont even know if it was him. YALL HAVE NO EVIDENCE and whenever something happens at kau, all the members literally say the meanest things about the person its extremely unprofessional for a group with 2k members im not even sure if jacob made those posts 😭 like anybody could have made them my response: JACOB DEFINITELY WROTE THIS POST TO DEFEND HIMSELF, LOL. IF YOU READ ALL OF THE OTHER POSTS WITH PROOF, YOU'LL SEE WHY. SAME WRITING STYLE, PREVIOUS STUFF MENTIONED IN THE HATE POSTS, SAME TAGS, ETC. ONCE HE SEES THIS POST, HE'S DEFINITELY GONNA MAKE SOME MORE POSTS DEFENDING HIM, BUT WATCH, HE'S GONNA CHANGE UP HIS WRITING STYLE, THE TAGS HE USES, AND THE THINGS HE MENTIONS IN HIS POST, LOL.
i'm not tryna be rude... but what makes some of y'all think that jacob didn't make those hate posts? in one of his messages on kaui's group wall, he said that the message had the tag "bio" in it and that he found it by searching up "bio", but i have seen the original posts, where the only tags are "kaui" and "kaze & zuki". also, when he replies to some of the posts abt him, he uses the same tags as the posts abt kaze and zuki, which seems suspicious. i'm not saying the tags definitely make him the person who wrote the hate posts, but it's something to keep in mind. he also writes in a way that's similar to the hate posts, like saying "r" instead of "are", "u" instead of "you", and leaving out apostrophes. for me, that's enough proof to make me think that jacob could be behind the posts. idk abt you, but again, i'm not saying that jacob is definitely the person who wrote those posts, just that there's a strong suspicion, especially since he found the hate posts quickly. (also, in one of the hate posts, it mentioned kaze and zuki saying nasty stuff and acting childish abt a grp that copied from a while back, and i bet that post was talking abt jacob's grp. jacob probs got so mad when he got confronted that he decided to make these posts to make kaui look bad, even tho he started all this drama by copying in the first place, lmao.)
yall saying yall are “ members “ of the group doesnt give you superiority over the other people. Especially if you are a new member you cant be saying anything about this. Jst stop with the posts at this point. Yall are being immature. Jacob made the posts. We have proof at that becuase how did he randomly find em? Hm? You cant randomly find fucking hate messages out of the normal. You have to search or Find them yourself. Also its a dead giveaway when you try to defend that person. Yall are being really really immature over this having to bring drama on this website.

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Kaze and Zuki never agreed to start over Jacob…
hello im an older member of - kaui — been here for near 6 months — and im friend with the owners. i know that kaze and zuki didnt do anything and the people who are on jacobs side clearly do not know the full story. jacob has been copying ever since i have joined and he always says the he will stop copying but still doesnt. the reason why i know with confidence that jacob made the negative posts for attention -he brings up that he has rl problems so people can feel bad -a lot of times when he says that he started over and didnt, so hes dishonest -he types in a very similar way as the person who made the negative posts -he said a lot of the same stuff that was mentioned in the negative posts in the past dont assume that kaze or zuki did something wrong if you do think that then you definitely dont know the full story or are just new
deliverytojac0b IS SUCH AN A-HOLE. 🤢 LIKE BRO, STOP COPYING KAUI, YOU FLIPPING COPYCAT. YOU DEF MADE THOSE POSTS ABT KAZE AND ZUKI, WHO HAVE DONE NOTHING WRONG BUT ARE SUCH NICE HUMAN BEINGS. STOP MAKING YOURSELF SEEM TO BE "DEFENDING" KAUI, BUT IN REALITY, YOU'RE NOT. 😂 QUIT COPYING KAUI AND BE ORIGINAL FOR ONCE. #deliverytojac0bSUCKS 🤓☝️
Jacob, we literally have proof that you made those posts, so please stop lying. • • • • • • • (๑´>᎑<)~*( · ❛ ֊ ❛) • •

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Bro, stfu. Dont just blame people for no reason. What if riko didnt even make that post?
report deliverytojac0b for stealing and copying!!
guys, wtf. why did jacob copy and paste kaui's desc in here? btw, if you see the desc, pls don't use it! it's not free to use; someone just copied and pasted it here.
Bro, why does jacob hate riko sm?? Riko didn't even do anything wrong smh. He made a very rude post about riko and pretended that someone else made it. He also always blames riko for no reason... I legit hate jacob sm.
Guys... I saw a post from Jacob and it says deserves to k*ll themselves in a hole and he said a swear word at the end...
I HATE LIARS ESPECIALLY THIS ONE GUY CALLED "JACOB"
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Chelsea 💙⚽🔵🏟
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⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠾⢋⠷⢃⠠⠒⠈⠀⢀⣀⢂⢠⣲⢦⡪⠝⠀⢠⠎⠀⠀⠀⠀⠀⣠⣴⢪⡃⠜⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠖⠁⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⣤⠦⡻⠂⠀⠀⠀⢼⡆⠀⠀⠁⡔⡀⡸⠀⢠⠃⠀⢸⣐⣷⣏⠉⠁⠉⢻⡄⠀⠀⡱⠑⢆⣨⠟⠊⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⢔⠕⢁⠔⠁⠐⣁⣤⠴⠚⠉⢀⣠⠖⡫⠃⠁⠀⠀⣰⠃⠀⠀⡠⠀⢠⠞⡵⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠔⠈⠀⠀⠀⠔⡰⢃⠔⠁⠀⠀⠀⠼⡫⣠⠎⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠰⢁⠃⢀⠇⠀⠀⣼⠋⣟⡆⠇⢀⠀⠸⢎⢵⠀⠱⠱⡈⢧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡡⠁⢠⣁⣀⡴⡚⠅⠐⠈⢀⡴⠋⠐⠁⢀⡠⡤⠄⣰⠃⠀⠀⣰⠁⠀⣠⠊⠀⠀⠀⠀⢀⣀⣠⣤⠤⠶⠚⠋⠉⢀⡠⠀⠀⠀⠀⢠⣮⠞⣐⠅⠀⠀⠀⠀⢀⡴⠋⠁⣀⣠⠔⠁⠀⠀⢠⠃⠀⠀⠀⢦⠂⢠⠊⠀⠀⠚⠙⢰⢸⣷⢰⠈⢆⠀⠙⣮⢣⠀⠐⡔⡒⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⣠⠖⠋⢁⠚⠃⣀⠔⠚⡷⠉⣉⡤⡲⢭⠞⢉⠃⣰⠏⠀⠀⡴⣉⡀⡚⠁⠑⠒⠀⡛⠛⢉⢁⠄⠀⣠⠗⠀⢀⡴⠋⠀⢀⠤⢠⢾⠋⢡⠞⠁⠀⡠⠒⠀⢀⣎⣠⢞⢵⠟⠁⠀⢀⠔⠠⠃⠀⡔⡐⠀⡇⠀⠁⠀⠀⠀⠀⡃⠈⠀⣿⠈⡀⡇⠣⡀⠈⢧⠡⡀⠈⢊⢜⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢶⠃⠀⢀⠃⢠⡞⠁⢀⡼⡷⢋⣥⣮⠴⠁⡠⣵⢻⡟⠀⢀⡼⢋⢊⠌⠀⡠⠊⢀⠊⢀⣀⣆⠃⠀⣰⠃⢀⡴⠋⠀⢀⠔⠕⡡⠞⣠⠝⠁⠀⣠⠊⢀⣤⠖⣡⠞⣕⡡⠁⠀⣠⡞⡡⣶⡵⠀⣸⢣⠇⢸⡟⠀⠀⠀⡀⠀⢠⠁⡆⠀⡷⠀⡇⣏⡄⢻⠄⠀⠱⡷⣄⠀⠡⡹⡇⠀⢀⡀⠄⠒⠈⠁⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠀⠀⡎⢠⠋⠀⣠⡮⠔⠈⣩⠞⠁⢀⢊⡾⢡⡄⠁⢠⡾⠡⠡⢂⠠⠊⢀⠔⣀⡴⢋⡏⠎⠀⣸⠃⣰⠟⠁⠀⡐⠁⡡⡊⠔⠈⡁⢐⣔⡟⢡⠞⡑⣡⠎⣡⠞⠝⠀⢀⣮⢟⠊⡸⠹⠁⢰⠃⣼⠀⣿⠂⢰⠀⢰⠃⠀⡌⢰⡗⢰⡧⠀⢫⡷⠇⠀⣎⢆⠀⡇⠏⢳⡤⠜⠓⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⣖⡾⠋⠀⡠⠊⠁⢠⣖⣵⡭⡂⠁⠘⠄⢳⠁⡶⠓⣡⣰⣖⡥⠞⠁⣀⢼⢱⠀⣰⢃⡼⠃⠀⢠⡪⣪⠞⠋⡀⢔⣠⠦⠛⠉⣠⡳⢊⡴⢣⠞⢁⠊⠀⣠⡿⠛⢁⠎⢠⡳⢡⠏⢸⠟⢠⢟⠀⢸⠀⢸⠁⠀⢁⡿⠁⢠⠇⠀⠘⡇⠘⠀⡆⣾⠠⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠝⠛⠀⡠⢊⣠⠾⠗⡾⠁⢳⠀⣽⡄⠀⢘⠾⣊⠴⢋⡵⢫⣷⣃⢀⠔⠁⣿⠆⠀⠀⡞⢁⠀⠴⠛⠘⣀⣔⡬⢖⠋⠁⢀⠔⣶⡟⠡⢈⡕⠛⠠⠂⠀⣰⠋⠀⡰⠁⢀⣧⢡⡎⢀⠟⠀⣸⢹⠀⢸⠀⡸⠀⠀⣾⠁⠀⡌⠀⣀⡸⠙⣄⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣰⣪⠖⠋⠀⢀⠜⢀⢌⠜⡆⣿⠼⣺⢗⣟⣡⡎⢡⠃⣤⠹⠘⠢⡤⢄⣛⡐⠠⠼⠍⠐⠀⣀⡤⡞⠉⠁⣤⠋⢀⠔⠁⣼⠏⠐⢠⠎⠐⠰⠃⠀⡼⠁⠀⡜⠀⡰⣻⢃⡞⠀⣸⠃⢀⡟⢰⠀⢸⠀⣷⠀⣸⠁⠀⡘⠀⣼⡿⠁⢠⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣸⠃⠀⠀⡠⢃⣴⠟⣡⣴⣿⣷⠛⠛⡈⡇⢠⠗⢸⣾⠸⡇⠀⠀⠈⠑⡾⣫⢒⣴⣶⢟⠵⢡⠌⠀⠀⠔⠃⡠⠁⠀⣾⢋⠌⡰⠁⠀⠠⢁⡄⠐⠀⠀⢞⡒⡰⢠⡏⡾⢠⢧⡏⠀⢺⠯⢥⠀⢸⠀⡽⢠⠃⠀⡰⠇⣸⠗⠃⢠⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣢⢔⣡⠖⢫⠽⠑⡟⠉⢸⢯⢏⠉⣵⡇⣸⠀⢘⢨⠃⡁⠓⠒⢢⢞⢜⣥⣫⣿⡧⠃⠀⡌⠀⠀⠈⠀⠊⠀⠀⣼⠃⠊⡐⠀⠀⢠⠣⡞⢠⡆⠀⡎⠀⠀⠁⣼⡝⢠⠟⡸⠀⠀⢸⢐⣸⠂⢸⠀⡇⢂⠄⡠⣧⣷⠏⠀⢠⡇⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⢰⡆⠀⢠⣾⣷⠀⢀⣾⠀⠀⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠚⠋⠁⠌⠁⡠⠊⡐⣡⢟⡌⡈⢒⡏⢰⢸⢰⢸⢺⡄⠀⢀⡴⣷⢿⠏⢈⣿⠟⠷⢆⡤⢀⣀⠀⠀⠀⠀⠀⢀⣏⠌⡔⠀⠀⠀⣆⠾⢁⡞⡇⡜⠀⠀⠀⣀⣯⡴⣥⢷⠓⠒⠋⠉⠡⢸⠀⢸⠀⠇⠎⣠⠱⢸⠇⠀⢠⠃⢠⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⢀⡿⢁⣴⠟⣹⣿⠀⣾⣷⣶⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⣀⣪⠞⡑⢁⢧⠙⠀⢇⢸⣿⢺⡞⡚⡯⢴⡙⠉⢀⡐⠂⡘⡞⠀⠅⠠⠉⠁⠚⠣⠝⣔⠶⣀⠀⠁⡰⠀⠀⠀⠀⡏⣄⡜⠀⡷⢓⣢⠿⠍⠛⠋⠠⡡⠂⠀⠀⠀⢀⠀⢀⡇⢨⠀⣶⡜⢸⠀⡟⠀⠀⢆⣠⠃⡈⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⣿⣿⢃⣾⠿⠟⢻⣟⣸⡟⠁⢠⡿⠁⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⢠⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠞⠧⠜⠋⢁⠂⠌⡰⢃⣾⣦⠀⢸⡀⣿⣄⢁⠇⠀⠀⢯⣝⣖⣿⣯⣿⣒⡭⠥⣐⡒⠤⢀⠀⠀⠈⠉⡛⢆⢠⠃⠀⠀⠀⠀⠑⠋⢀⣀⠻⠉⠁⠀⠀⢀⡠⠔⣒⣀⣭⣝⣛⣫⣿⣿⣧⠘⠀⣳⠀⣼⢠⠃⠀⠀⠸⣹⢀⠃⡇⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠃⠘⠃⠀⠀⠙⠋⠛⠀⠀⠙⠃⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⠐⢀⠢⠐⣀⠂⡐⠠⢀⠄⠠⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠉⠁⠈⠓⢾⣷⡿⠿⠊⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⡳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⡐⠂⡐⠠⡁⠊⠄⢂⠁⢂⠂⠌⡐⠠⠀⠀⠐⠀⡁⠀⠀⠠⢁⠐⡀⠀⠀⠀⠈⠛⠀⢸⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣾⣵⣿⣾⣿⣿⣿⣿⣿⣽⣧⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠰⠀⡐⠀⡁⠠⢁⠌⠠⠌⠠⢈⠐⠠⠁⠀⠀⠀⡁⠀⠠⢁⠀⠀⠂⠀⠀⠰⠀⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢌⠡⠀⠀⢐⠀⡁⠂⠌⡐⢈⠐⠠⠈⠄⠂⠀⠀⠀⠀⢂⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⠻⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡐⠨⠄⠀⠠⢁⠂⡀⠤⠁⢂⠐⡠⠈⠄⡁⠂⠀⠀⠡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⣀⠄⣀⣤⡆⠀⡀⣠⣤⣶⣯⠳⡄⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⠢⠁⠀⢠⠃⠄⠰⠀⠆⡅⠠⠊⠔⠉⢀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡿⠟⠋⢁⡴⠂⠀⠐⠀⣴⢫⣶⠃⠀⣸⣿⣿⣿⣜⡳⠄⣸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠂⠀⠠⡁⠀⢊⠐⡁⠎⠐⠀⠈⡐⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠋⠀⠀⠀⠀⣼⡳⣿⡏⠀⢰⣿⣿⣿⣿⣎⡗⣃⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠄⠀⠀⠐⡀⠀⠠⠐⠀⠐⠀⠀⠀⠐⠀⠠⠀⠀⠌⠀⠀⠀⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡜⣧⠿⢡⡇⠀⣾⣿⣿⣿⣿⡿⣼⡁⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠄⠂⠀⠀⠐⡀⠀⠄⠁⡀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⡴⡹⣼⠁⣿⠇⢠⣿⣿⣿⣿⣿⣿⣱⢂⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⠂⠀⠀⠀⠐⠀⠀⠰⠀⠀⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⢀⡜⡲⠝⠒⢸⡿⠀⡼⣿⣿⣿⣿⣿⡷⡭⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠃⢠⡏⠀⡁⠀⠐⠈⠀⠀⠀⠡⠀⠀⠀⠀⠙⠤⡀⠀⠀⠀⠀⠀⠀⠂⣰⣶⣨⠥⠖⠁⣠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠈⠀⢰⡟⣼⡇⢠⣏⣿⣿⣿⣿⣿⡳⠅⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡏⢀⣿⠁⢰⠀⠀⢈⠀⠀⠀⠀⠘⠘⠃⠀⠀⠀⠀⠉⢆⡀⠀⠀⠀⠀⢇⡻⣶⣶⢦⠶⣞⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠸⢡⣿⠃⣾⣾⣿⣿⣿⣿⣷⢋⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⣾⡇⢠⣿⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡁⠔⠃⣨⣿⣦⡠⢄⠀⠈⢽⣿⣿⣯⣿⣽⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⠀⠀⣠⣿⡟⢸⣿⣿⣿⣿⣿⣿⠧⢁⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⢸⡿⠀⣾⣿⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠓⣶⢭⣴⣾⣿⣿⣿⠛⣦⣳⣄⡹⢿⣿⣿⡿⠏⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣴⣿⣿⠇⣾⣿⣿⣿⣿⣿⣯⠃⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⡿⠁⣰⣿⡏⢀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡞⠾⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣛⣥⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣸⣿⣿⡟⣸⣿⣿⣿⣿⣿⡿⠆⢰⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠁⣠⣿⡿⠁⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡱⠿⠿⣻⣿⣿⠛⠟⠛⢿⣿⣿⣿⠟⢀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣰⣿⣿⡟⣰⣿⣿⣿⣿⣿⣟⠣⢁⠈⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡟⠠⢡⣿⣿⠃⠀⠡⢀⢁⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣶⣶⣿⣿⡿⢃⡰⠊⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣴⣿⡿⠋⣰⣿⢻⣿⣿⣿⠿⡌⢡⣿⡀⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠋⠠⠈⠸⡿⠃⣰⡇⡁⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢍⡛⠻⠿⠟⣩⠰⠎⠁⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣬⡉⠁⣠⣾⣿⢣⣿⣿⣿⢏⠓⣠⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿ ⣿⡟⠁⢌⣴⡇⡁⢁⢠⣿⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠼⡱⣍⠾⣰⠋⠀⢀⡄⡂⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣷⠹⣿⣿⣿⠟⣡⣿⣿⡿⢏⠌⣴⣿⣿⣿⣿⣧⣹⣿⣿⣿⣿⣿ ⠏⠄⣡⣿⡿⠃⠀⠀⣿⡏⠠⠁⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢣⠄⠹⣜⣣⢭⡃⢀⠷⣨⠥⠰⣀⠃⠀⢀⠀⠀⠀⡀⠦⡑⢀⣼⣿⣷⣭⣉⣁⣴⣿⣿⡿⡙⢠⣾⣿⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿ ⢨⣾⣿⠟⢁⡼⠂⢁⠘⢁⠂⠐⠀⠀⠀⠀⠀⢀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠐⠸⣱⢋⡞⡱⣌⢣⡅⠻⡤⠙⡦⢋⡕⣣⠹⠤⠈⠀⠀⠠⡜⣱⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⢻⠐⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿ ⣿⡿⠁⡴⠋⣠⣾⣄⠂⢀⠀⠁⠀⠀⢠⣶⣶⡀⠻⣿⢇⣤⡶⣤⠀⠀⠀⠈⠑⠤⣲⣍⡳⣜⢣⢻⣤⢈⡰⣍⢳⠘⠄⣡⠴⡉⠀⠀⠰⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⢻⠌⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿ ⠋⠀⠊⣠⣾⣿⡿⠃⠀⠀⡈⠀⠀⢠⣿⣿⣿⣿⣦⠰⣿⣾⡝⢿⣇⠀⠀⠀⠀⣀⠀⠈⢁⣉⡉⠳⡬⢏⡵⠪⢁⡤⣛⢦⢫⡅⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢻⠜⠃⢰⡂⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿ ⣠⡰⣿⣿⣿⡿⠁⠀⠠⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣇⢻⣿⣿⣷⣽⠀⠀⠀⠀⠀⠈⠛⢦⠈⠓⢧⣌⣯⡼⣳⢏⡶⣹⢎⡷⠂⠀⢱⡀⢹⣏⠸⣿⢿⡻⣝⠲⠉⠀⠀⢺⡅⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⣿ ⣿⣿⣶⣭⡿⢁⣤⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⡟⠀⠀⠀⠸⡄⠀⠀⡀⠁⠀⠈⣿⣾⣽⣳⡿⣾⣽⣾⡏⠀⠀⠈⢷⡄⢻⡆⢩⠷⣙⢀⠁⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⣿⣿ ⢏⡕⢪⢋⣼⡟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡀⠻⢿⠃⠀⣠⠆⣸⣿⡀⠀⣿⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣧⣹⠄⠀⠀⠙⠂⠁⠘⠢⠁⠈⡄⠀⠀⠀⠀⠈⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣸⣿⣿ ⡞⠜⣡⣿⠏⠀⠀⡴⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢀⣠⣵⣾⣿⠟⠀⠰⠁⠀⠁⢀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣿⣿⣿ ⣥⣾⣿⡿⠀⠈⣰⠃⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡿⠟⠉⡀⢠⣿⣿⡿⣻⡵⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⡀⠀⠀⠈⢿⣿⣿⣿⣿⣭⣤⣤⣾⣿⣿⣿⣿ ⣿⣿⡿⠃⠀⠠⠋⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠛⠁⠀⣠⠶⡁⣸⣿⣯⠾⡉⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⢹⣷⡄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠟⠁⠠⠁⠀⠀⠀⠀⠀⠀⠀⣸⡿⠛⣁⣤⣴⣾⣿⣷⢫⠁⣩⡿⣣⠟⢁⣴⣾⣿⡿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣧⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⡻⢿⣄⠀⣦⣌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⢋⠠⢈⠐⠀⡀⠀⠀⢀⠀⠀⠀⢋⣴⣿⣿⣿⣿⣿⣿⣯⠇⢀⣿⣧⢉⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⡀⠈⢿⣿⣄⢈⠻⣿⣿⣿⣿⣿⣿ ⢇⣴⣶⣦⡜⠀⠀⠀⠸⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣾⣿⡏⠾⣿⣿⣿⣻⣿⣿⣿⠿⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡄⢢⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣕⠿⡓⢉⠀⠉⠙⠦⠘⢿⣿⣶⡳⣌⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⡁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣧⣤⣶⣿⣿⣿⠿⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⣳⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠁⠀⠀⠠⠀⠀⠀⠀⠺⡜⣿⣿⣿⣞⢧⡹⣿⣿⣿ ⠙⠿⠿⠛⡁⠀⠄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⠽⡝⠙⠉⠉⠀⢀⠘⠀⡰⡽⣷⣿⣿⣿⣿⣿⣿⡂⢥⢳⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠆⠀⠀⠀⢽⡧⠀⠀⠀⣇⡇⣿⣿⣿⣿⣯⠳⢹⣿⣿ ⡀⢠⣰⣄⡀⠈⠄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⢆⡂⠀⠀⠀⠀⢀⡀⠀⠈⢘⠐⢿⣾⣿⣿⣿⣿⣿⡅⢢⢫⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⠔⡀⢀⠀⠀⠁⠀⠀⠈⣨⠃⢸⣿⣿⣿⣿⡇⢈⣿⣿ ⢰⣿⣿⣿⣿⣦⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⡾⢸⣿⣿⣿⣿⣿⣿⢚⠀⠀⠀⠀⢿⣇⡈⠁⠀⠈⠂⣴⢽⣿⣿⣿⣿⣿⡁⢆⡓⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⡷⣧⠀⠈⣀⢈⢤⣸⡰⠁⠀⢸⣿⣿⣿⡿⠁⠀⣿⣿ ⡸⢿⣽⣿⣿⣿⣷⣦⣀⠐⣿⣿⣿⣿⣿⣿⡿⣮⢽⠐⣿⣿⣿⣿⣿⣟⣿⡐⠁⠀⠀⠁⠀⠀⠐⠀⠀⡀⡟⣾⣿⣿⣿⣟⢧⠂⢢⡙⢼⡹⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣧⣧⣴⣶⣿⡟⠅⠀⠀⠈⠻⣿⡿⠁⠀⢸⣿⣿ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⠻⣿⣿⣿⣿⣟⡼⢪⡅⢻⣿⣿⣿⣿⣿⣮⡷⡦⣤⢀⡄⠁⠁⠈⠀⢖⠆⣶⣿⣽⣿⣟⢮⡃⢠⢃⠖⣀⠙⢞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⠳⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⣾⣿⣿ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢷⡌⢻⣿⡟⣞⡜⣣⠆⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣖⡤⢑⣲⣿⣿⣿⣿⣿⣿⡻⣜⠆⡁⢦⣉⢞⡡⢖⡈⠐⢏⣞⡻⣟⠿⣿⢻⡟⡽⢣⠓⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡻⡄⢻⡜⣣⠞⡡⠀⠀⠈⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣧⡛⢈⡰⡘⢦⠜⣪⢕⣣⢞⡡⢆⣀⠑⠊⠙⠆⠓⠈⠁⠁⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿ ⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣯⢷⡙⢦⡙⢦⡙⠄⡞⠀⠀⠀⠙⠯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⠷⠙⡂⡔⣣⢖⡹⢎⡝⣦⣻⣼⣾⣵⣫⡔⣫⡙⣜⠢⡍⠀⣀⠀⢺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿ ⠀⠀⠀⠸⡛⣿⣿⣿⣿⣿⣿⣿⡷⣭⢣⡙⠆⠌⠀⠀⠀⠀⠀⢀⡟⠈⣉⡛⠛⠿⠿⠿⠻⠟⠛⠓⣉⡬⡴⣹⡜⣵⣳⣮⢿⣽⣾⣷⣿⣿⣿⣿⣷⣯⠵⣙⢦⡙⠀⠀⠗⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿ ⠀⠀⠀⠀⠀⠉⡻⢿⣿⣿⣿⣿⣟⡖⡣⠜⡈⡼⠀⠀⠀⠀⠀⠸⠀⠀⠘⣿⣿⣷⣶⣶⣷⣾⣿⣿⣯⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⡱⠆⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠀⠙⠀⠚⠛⠿⠿⣽⢸⠡⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣤⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠗⢀⡄⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⢀⣿⠀⡀⠀⠀⠀⠀⠀⠀ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠁⠁⠀⠐⠀⠀⠀⠰⠃⢀⣤⣦⣾⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣎⠀⠀⠀⢀⠰⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⢀⡇⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⢀⣠⣤⡔⢆⣩⣶⣾⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡄⠀⢀⡄⢸⣶⠆⠀⠀⠀⢠⠀⠀⢀⡿⠃⠞⠀⠀⠀⠀⠀⠀⠐ ⢀⡀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⢛⣭⠟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀⢿⣧⡤⠀⠀⠀⠀⢠⡿⠀⠀⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⡏⠀⠀⠀⠀⠀⣤⡜⣯⡳⠩⣞⣫⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⣽⣿⣿⣿⣿⣿⣿⣿⣿⡗⢠⣦⡀⢀⣀⠄⠀⠀⠀⣠⠟⠀⢀⠄⠀⠀⡠⠴⠎⠀⠀⠀⠀⠀⠀ ⠀⡀⡀⠀⠒⢀⣼⣻⣿⢟⣷⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⠆⠁⠀⠀⠀⠀⠁⣀⣴⣿⣆⢇⠰⢶⣶⠀⠀⠀⠀⠀⠀⣴ ⢠⣾⡇⢁⣴⣿⡞⢛⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡂⣽⡿⠃⠀⣠⣶⣶⣴⣶⣿⣿⣿⠹⠟⣸⣿⣿⠃⠀⠀⠀⠀⠀⠘⢿ ⠸⣿⣴⣿⣿⣿⢅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢼⡄⢸⡇⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣰⣶⣶ ⠀⢿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣳⢮⠸⣧⠀⣷⡹⢿⣿⣿⣿⠿⣿⣿⠿⣛⠵⢂⡠⣀⣤⣶⣾⣯⣟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢦⣤⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠁⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠉⠛⠃⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠙⢳⣄⢀⡾⠁⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠙⢿⡇⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠹⣦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠋⠛⢧⡀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠾⣧⡀⠀⠀⠹⣦⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠛⢷⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣤⣤⡤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⡆⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣠⣄⣄⣤⣤⣤⣴⡋⠀⣾⡇⢸⣧⣤⣤⣤⣤⣤⡀⠀⠀ ⠀⠙⠻⣄⠀⠠⣤⣤⣶⣾⣿⣷⣶⣲⣶⡖⢂⡼⠋⠀⠀⠀ ⠀⠀⠀⠈⠻⣦⡈⠙⢿⣿⣿⣿⣿⠟⢁⣴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠇⢠⣿⣻⣿⣿⡾⡄⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡏⢀⡾⠟⣉⣀⠻⣿⣣⠘⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡿⠀⣠⣴⡿⠛⠉⢿⣤⠉⠃⢽⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣵⠿⠋⠁⠀⠀⠀⠀⠈⠳⣦⣜⡷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⢀⡼⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀ ⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀ ⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀ ⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀ ⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢰⡇⠀ ⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀ ⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀ ⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀ ⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀ ⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄ ⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸ ⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠄ ⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⡄ ⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁ ⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣤⣄⡙⠢⣄⡀⠀⠀ ⢀⣤⡠⠖⣡⣾⣿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠻⢿⣷⣦⡙⢾⣷ ⠸⠿⠃⡾⠟⠉⠀⠀⠀⠀⠀⠀⣀⢀⡀⣀⢀⣀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⡀⢀⠀⡀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠙⠻⣾⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⣀⣀⣀⣀⣀⣄⣠⣄⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠈ ⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⢹⣿⣿⣿⣿⣿⣏⠹⣿⡉⠀⠀⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢩⡿⠋⢹⣿⣿⣿⣟⣻⡇⠈⠙⠳⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠿⣳⢦⣤⣤⣼⣿⣿⣿⣿⣿⣋⣄⣈⣻⣆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣔⣏⣄⣤⣼⣿⣿⣿⣿⣿⣥⣶⣶⡾⠟⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡟⠉⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡶⠶⠶⠶⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠶⠶⠶⠶⠦⠤⠠⣿⣿⡓⠶⠶⢶⣶⣶⣦⣤⣤⣤⣤⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢢⣸⠛⠻⣯⣿⠏⠉⠛⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⣿⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠀⠀⠀⠙⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢴⣶⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠐⠒⠒⠠⠤⠤⠀⣀⣀⣀⠀⠀⠀⠀⠀⣸⡇⢠⠖⠒⠲⣾⠈⠳⡄ ⠀⠀⠀⠀⠀⡠⠖⠙⠛⠒⠿⣋⡉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣐⠶⠋⠳⣧⠒⠒⠚⠉⡆⠀⢹ ⠀⠀⢀⡴⠋⠑⡶⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠛⠯⠭⣉⣉⡩⠗⣂⡠⠔⠒⠒⣢⠤⢀⣀⠤⠄⠒⠈⠉⠀⠀⠀⠀⢰⠀⠀⠀⠀⡇⣸⣿ ⣠⣴⡟⠀⣠⠞⠒⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⢊⡡⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⣧⣿⣿ ⣯⡀⠑⠒⠁⠀⠀⠀⠀⠀⠈⠉⠐⠒⠤⠄⣀⠴⠂⠀⠀⠀⠐⠒⠢⠤⡂⠁⠀⠀⠀⠀⠀⠀⠀⣠⣶⣖⣄⠀⠀⠀⢸⠀⠀⢀⣼⣿⣿⡿ ⢾⣿⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⣀⣀⣤⣾⣿⡏⢻⡜⡀⠀⣠⣼⣤⠞⣋⠥⢿⡿⠁ ⢸⣿⡇⠀⠸⡷⢶⣤⢄⣀⡀⠀⠀⠀⠈⠒⠂⠤⠤⣄⣀⣀⣀⣀⣠⣤⣮⣤⣤⣾⢿⣿⣿⣿⡟⣇⣿⣾⢷⣧⣾⠟⢋⠔⠋⠈⠉⠁⠀⠀ ⡿⣜⣇⣀⡤⠗⠤⢄⡉⠛⠛⠛⠻⢶⡒⠠⠤⢤⣄⢀⣹⣍⣉⣉⣉⣁⣀⠤⠔⠛⢹⣯⣽⣿⢛⣿⣿⣼⢈⠋⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀ ⠑⢌⣻⢄⡀⠀⣠⣶⣿⣽⣖⡢⠄⣀⢱⠀⠀⢾⠉⣷⠀⠀⣳⠤⠤⢿⠀⠀⠀⣴⠟⢉⣿⠈⡍⣍⢋⡿⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠓⠯⣕⠻⢷⣿⡿⠊⠁⠀⠀⢩⠃⠀⡤⠿⢿⣶⣾⣯⣏⣩⣿⠀⠀⢸⣿⡶⢾⢹⢼⡿⢃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠒⠠⢍⣑⠒⠠⠴⠯⣤⣴⣚⣒⣒⣒⣒⣶⣿⣿⡧⠐⠊⠁⠀⠀⢸⣀⣾⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⢀⣀⣀⣀⣀⣉⣉⣩⣽⣞⠠⠤⠤⠒⢊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠖⠒⠒⠒⠒⠒⢆⠀⠀⠀ ⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀ ⠀⠀⠀⢀⠇⡰⠋⠉⠉⠉⠉⠉⠉⢻⠀⠀ ⢲⡂⠒⢺⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⡃⠀⢸⠀⠙⠦⣀⣀⣀⣀⣀⣀⣸⠀⠀ ⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⡇⠀⢸⠀⠀⠀⣀⣀⡀⠀⠀⠀⢸⠀⠀ ⠀⠷⠋⢹⠁⠀⠀⡇⠀⠇⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⢸⠀⠀⢸⠁⠀⢣⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⢯⡆⠀⡼⠀⠀⠘⢤⣀⡠⠻⠀⠀
⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⢀⠾⠋⠉⠉⠉⠙⢷⣠⣔⡶⣶⣄⠀⠀ ⢸⡀⠀⠀⢀⣶⡶⣿⣿⠀⠀⠀⠀⢻⣷ ⠀⠙⠒⠚⠉⣾⠁⠀⡟⣇⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⡿⠀⠀⠀⣿⠓⠷⢶⠤⠋ ⠀⠀⠀⠀⢰⡇⠀⠀⠀⢹⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢃⠀⠀⠀⠀⡇⠀⠀⣀⡀ ⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⣿⡀⠸⠁⣇ ⡰⢳⠀⠀⠀⡗⠀⠀⠀⠀⠑⢷⣶⡯⠃ ⣧⡈⠁⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣶⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⢿⣿⣿⣿⡀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠟⠉⠁⠀⠘⢻⣿⣿⠏⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣼⣿⡆⠀⠀⢰⣾⣿⣿⠛⠋⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⣠⣤⡄⠀⠀⣀⠀⠀⢀⣾⣿⠟⠁⠀⢰⣿⣿⠀⠀⣰⣿⣿⡟⠁⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⣀⣴⣿⡷⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀ ⠀⠀⠀⢀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣷⡄⠀⢹⣿⡆⠀⢠⣶⣿⣿⣿⠇⢠⣾⣿⢆⣾⢿⣿⠇⠀⠀⢸⣿⡇⠀⢠⣿⣿⠟⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⣀⣤⣾⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀ ⠀⠀⣤⣿⡿⠟⠁⠀⠀⠀⣀⣀⣤⣴⣾⣿⡿⠟⠛⢩⣼⣿⣿⠟⠃⠀⢸⣿⣇⣤⣿⣿⣿⡇⠀⢠⣿⠟⠁⣸⡟⢸⣿⠀⠀⠀⢸⣿⠁⢀⣿⣿⠏⠀⠀⠀⠀⠀⣼⣿⠃⢀⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀ ⢀⣾⣿⠟⠁⣀⣤⣶⣶⣾⣿⠿⠙⠉⠉⠁⠀⠀⢀⣼⣿⡿⠋⠀⠀⠀⣨⣿⡿⠛⠉⣿⣿⣷⣆⣿⠏⠀⣠⣿⠃⣸⣿⡀⠀⠀⢸⡇⢀⣾⣿⠋⠀⠀⠀⠀⠀⢰⣿⣯⣾⠿⠛⢁⣀⣦⣶⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀ ⢸⣿⣿⣿⣿⡿⠟⠛⠛⠃⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⢀⣴⡾⠟⣿⡇⡀⠀⢾⣿⣷⣿⡟⠀⢀⣿⡇⢠⣿⣿⣇⠀⠀⣼⡇⣼⣿⠋⠀⠀⠀⠀⠀⣾⣿⣿⡏⠁⠀⠀⠈⠙⠿⣿⠁⠀⠀⠀⠀⠀⣶⣴⣿⠁⠀⣀⣶⡀ ⠘⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠋⠁⠀⣠⣾⠟⠋⠀⠀⢹⣿⠀⠀⠈⣉⢹⡿⠁⠀⣼⣿⠀⢨⣿⣿⣿⣷⣼⣿⣿⣿⠁⠀⠀⠀⣠⣴⡿⣿⣿⠛⠃⠀⠀⠀⠀⠀⣶⣿⣦⠀⠀⢀⣴⣿⣿⣿⢃⣠⣿⠟⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠁⣀⣴⣿⠟⠁⠀⠀⠀⠀⠀⣷⠀⠀⠀⣿⣿⠀⠀⢰⣿⣏⢀⣿⣿⠛⠛⢿⣿⣿⣿⠃⠀⢀⣴⣾⠟⠁⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⣠⣿⠟⠁⣿⣟⡿⡿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⣠⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⠀⠀⠀⢻⣿⣿⣿⡏⠀⠀⢀⣿⣿⣯⣤⣾⣿⣋⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢠⣾⠟⠁⣀⣾⣿⠑⠿⠳⢧⣱⣦⠷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠉⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣾⣿⣿⡇⠀⠀⠈⠻⠿⠛⠀⠀⠀⠸⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⡿⢶⣶⣶⣤⣤⣤⣄⣀⣼⣿⣤⣿⣯⣴⣿⣿⣿⠃⠀⠀⣰⠿⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡵⠽⠛⣁⡀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠉⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⠀⠀⠀⠀⠀⠉⠉⠛⣿⡿⣿⣿⣿⡏⢸⣿⣿⢀⣴⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠅⣶⠿⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠡⠌⢿⣿⣿⣾⠋⠁⠘⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣣⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⢠⣾⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡎⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠀⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠀⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⣆⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠘⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢤⠴⡄⣠⡔⣶⡀⢀⠂⡄⡰⢌⠀⡤⢊⡽⣳⢶⣌⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀⠀⠀⠀⠀⠀⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡐⠁⠀⠀⠀⢘⡱⠈⠀⢁⠲⣝⣮⡒⡥⢃⡾⣝⢯⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣸⣿⠀⠀⠀⠀⠀⣼⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⢠⢣⡁⢉⠢⡙⡼⣶⡻⣝⠹⠺⠭⠻⣌⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣠⣠⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣧⣄⡀⢀⣰⣿⣷⡿⢿⣷⣤⡀⠀⠀⠀⠀⠀⢀⠧⠀⠀⠀⠀⠀⠳⣜⡠⢒⡽⡹⢖⡿⠈⠀⠀⠀⠀⠀⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠤⣀⣦⣾⣿⡿⠿⠿⢿⣗⣂⠀⠀⠀⠀⢀⣀⣀⠀⠀⠈⠙⠛⠿⠟⠋⣁⠰⡐⣢⡙⢿⣿⠶⢦⣤⣤⣤⠈⢃⠀⠀⠀⠀⠀⠀⢈⡓⠡⠒⡍⣎⠘⠀⠀⠀⠀⠀⠀⠰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠢⣡⣿⣿⠟⠛⢟⠉⠀⠀⠀⠀⠙⠻⡇⠰⣴⡾⠿⠋⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣷⣿⣿⣿⣿⣿⣧⠀⠀⠈⠈⡁⠎⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠈⠀⠀⠀⠀⢀⠂⡄⣳⡿⠿⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⣐⣦⣾⠿⠧⣤⣀⠀⢀⣠⣶⠿⠋⠁⠠⠿⠛⠉⠁⠉⠁⠀⠘⣿⣇⠀⠀⠀⢀⣀⣤⡄⠀⠀⠀⠚⠐⠈⠀⠀⡀⢇⠎⡥⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢃⠀⠀⢀⡀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⡠⢃⠆⠒⠹⣆⡡⣀⣄⠀⡀⢎⣰⣤⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠀⠀⠀⠀⠉⠀⣸⡿⠋⠀⠀⣠⠁⠀⠀⣠⠿⠀⠀⠀⠀⠙⠻⣶⣦⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠨⣱⡛⢦⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠌⠐⡀⢠⣼⠋⠀⠀⠀⠀⣸⣄⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠁⠉⠙⠛⠻⣿⡿⡟⠉⠀⠀⠠⣤⣤⡄⠀⠀⣇⠀⠈⠁⠀⠀⡀⠀⠀⠀⠀⣾⠋⠀⠀⠀⣠⠁⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡙⠌⠡⢐⠲⡔ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⠃⠀⠀⠀⠀⣠⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⠆⠀⠀⠀⠀⠀⡟⠉⣿⡃⠀⠀⠀⢸⢻⡇⠠⠆⠰⣿⡄⠀⢀⣼⠋⠀⢰⡿⠁⠀⠀⠀⣠⣤⣀⣠⣤⣤⡴⠀⠀⠆⠶⣤⢾⠿⢶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣿⣴⢿⣇⠀⠀⢠⡟⣴⡀⢐⠀⣸⡿⠁⠀⣼⠃⠀⣠⡟⠁⠀⠀⠀⠘⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠢⢡⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠛⠙⢻⡤⠀⠀⠀⠀⢸⣇⠨⢀⣮⣿⣿⣾⣿⡀⠀⣾⠁⠘⡅⠀⢀⣿⠇⠀⣴⡇⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⡀⠆⢈⣉⡙⣀⣠⣤⣌⣿⣴⣿⣿⣿⣿⣏⣽⣧⣶⣿⣀⣤⣄⡀⣾⣇⣀⣼⣿⣠⣟⣉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣦⠶⠷⠟⠛⠻⠿⠛⠛⠉⠋⠋⠉⠉⠉⠉⠛⡏⠉⠉⠉⠉⠉⠉⠛⢉⣟⠉⠙⠛⠛⠛⠛⠿⠷⣶⣦⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣄⣀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠟⠛⠉⠀⠁⢀⡀⢀⣄⣤⣀⡀⠀⣤⣄⢀⣄⣀⢠⣤⡀⠰⣶⣤⣤⣀⣠⣤⣤⣾⣿⣶⣾⣶⣴⣶⣄⢀⣀⠀⠀⠉⠛⠛⠿⢦⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢋⣁⣀⣠⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣝⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀ ⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣆⣲⣬⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠐⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⣢⢁⡀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠶⡤⢀⠀⣆⠳⣞⡷⣫⢖⠡⠀⠀ ⠛⢶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠄⠃⠙⡌⠓⡀⠂⠉⠸⡳⣝⠞⡥⢊⠵⠠⡀ ⠀⠀⠀⠉⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠠⠉⠼⢀⠁⢄⠡⢠ ⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠲⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠉⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢊⠀⠀⠀⠌⠄ ⠀⢠⡘⢄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⠟⠧⠛⠘⠖⠿⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⡿⣽⣋⣉⣀⣀⠀⠀⠀⠌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⢠⠸⡜⣦ ⠈⢆⢉⠂⠀⠀⠀⠀⠌⡁⠀⢀⡀⠀⠈⠀⢀⡄⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣤⣿⡿⣿⣿⣿⣿⣿⣿⣿⠇⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡍⡖⢮⡻⢝⡶ ⢌⠢⠄⠀⠀⠀⠀⠀⠐⠨⠐⠀⠁⠀⠀⠀⠀⠀⠀⢤⣰⠊⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⢹⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣧⣿⣿⡭⣿⣿⣿⣿⠘⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⠉⠒⠱⠊⠞ ⢌⠳⡌⣄⠠⣀⢠⡐⣌⠐⣠⢠⣀⣄⠠⢀⠀⢠⣶⡿⢛⢳⣾⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢻⣿⣿⡇⠀⢸⣿⣿⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⠉⠙⢻⡧⠀⠀⠀⠈⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢣⠳⣌⡷⣜⢧⣻⢴⡫⣔⣣⡞⣌⠣⢈⠲⣤⢍⣤⣣⡾⣿⣿⣿⣿⡙⠎⡄⠻⣿⣿⣿⣿⣿⣿⣇⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣿⣿⣿⡇⠀⠀⢿⣿⣷⣄⠈⠙⠿⣿⣿⣯⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⡿⠃⠀⠀⠀⠈⠁⢠⡤⠀⠀⠀⣼⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡘⣦⢫⠵⣙⢮⡳⣝⢮⣳⢣⠟⠁⠀⠀⠙⣿⡶⢮⠛⣍⠻⡽⢶⡩⢦⠽⣆⡀⠁⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⢀⣤⣎⢙⣿⣿⡃⠀⣾⣸⣿⡏⢻⣦⡀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣯⣽⠷⠿⠋⠁⠀⠀⠀⡀⠤⠀⠀⠢⠁⠀⠀⢒⡀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠉⠎⡡⢃⡙⠬⢓⠣⠊⠜⡀⢤⢨⣳⣉⣱⣦⡛⢭⠳⢟⡣⠖⣬⢃⣙⣰⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠋⢸⣿⣿⠀⠀⢻⣿⣿⣿⠀⠻⣷⣄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⢠⠷⠈⠙⠂⠲⢩⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣄⣯⣿⣿⡿⣟⢡⠓⢮⡟⢧⡜⡘⠤⢋⠴⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠣⣿⡟⠀⠀⠀⣿⣿⣿⡇⠀⢹⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⢸⣄⠀⠠⣤⣁⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠰⣿⣿⣯⣶⣿⣌⣻⢞⠲⣛⠆⠰⣁⣌⣡⣋⣌⡉⢋⣭⡍⠀⠀⠀⠀⠀⠀⢤⣄⡀⠀⠀⠀⠄⠀⠀⢻⣿⣔⣿⡏⠀⠀⢠⡿⠻⣿⡽⠄⠀⢹⣿⣝⠿⣶⣶⠞⠋⠁⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢀⢋⠇⡀⠀⠘⣿⠤⡐⠹⢋⠛⡛⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠰⠳⢤⣷⣽⣎⢉⡙⠞⢟⠲⡌⢴⠲⣎⣿⢧⡰⡝⠛⣉⣤⣤⣴⣶⢶⣴⣤⣶⡟⠛⠻⠖⠹⡄⠀⠐⠇⣿⡿⠘⣿⠀⠀⠈⠁⠐⢻⣇⠀⠀⠈⣿⣿⠠⣿⠁⢾⠟⠛⠚⠛⠛⠻⠿⠶⠌⠛⠷⢶⣼⣎⠲⠥⠀⠀⢺⣧⠐⠀⣀⡄⢀⣈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣙⣿⣟⣿⢫⡿⢿⠿⠿⢿⠳⡼⣞⣿⣵⣎⣿⣷⣴⡿⢛⣭⣿⣶⣶⣶⣶⣦⣤⡀⠀⣀⡀⠀⣷⣄⢀⣼⡟⠀⠀⣹⣇⠀⠀⠀⠘⠋⠻⡇⠀⠀⣿⣇⣸⠁⠀⣠⣴⡶⠞⠛⠛⠿⠻⠷⣶⣤⡀⠀⢹⣷⣟⠲⡡⠄⠀⢻⣿⡙⠄⡶⣠⣜⠃⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢶⣿⣿⣿⣾⣿⣽⣾⣓⡿⣦⣙⣴⢻⢯⣽⣿⡿⠋⣩⣶⣟⣫⣥⣤⣤⣤⣤⣌⡙⠻⣿⣼⣿⡄⠘⣿⣟⣿⣄⠑⠀⠉⠋⠀⠀⠀⠀⠀⠀⡿⠀⠀⠘⣿⣿⣴⡿⠋⠁⠀⢐⣚⣛⣂⠀⠀⢨⣙⡛⣶⣬⣿⣯⣳⣭⠤⠀⢺⣿⡿⠖⣷⣶⣯⣟⠒⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢚⠠⣎⣭⣿⡟⡶⣟⣮⣿⣯⣟⠦⣻⣿⣿⣿⣿⣿⣷⣾⡿⠿⠛⠛⣋⠁⠈⠉⠉⠙⠻⣷⣾⣿⣏⠻⣦⠘⢿⣆⢻⣷⠀⠀⠀⠁⠀⠀⠀⢀⠀⠓⣧⣀⠾⠙⣿⣿⣧⣶⡾⠷⢛⠛⠛⠛⠿⠿⠷⠹⠿⣾⣝⣿⣿⣿⣣⣸⡠⠩⢟⡛⠓⡞⠰⣭⢻⢿⣶⣟⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣜⢣⣳⣾⣿⣯⢿⡽⢯⣿⣞⢷⡿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣠⣶⡿⢿⡟⠛⠛⣹⣦⣀⣀⣹⣿⣼⣿⣆⠹⣷⣌⣿⡏⠻⠇⠀⠀⠀⠀⠀⠀⠻⠆⢰⣿⠃⢀⣴⣿⣿⡟⣡⣶⠿⠋⠁⠀⠀⠀⣀⡄⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⠉⠻⠿⡟⣤⢛⡼⣿⣤⣭⡻⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⣎⣱⣾⣿⣿⣶⣯⣯⣽⣷⣿⣾⣭⣾⣽⣿⣿⣿⣿⣿⣿⡷⢿⣫⣵⠶⠟⠻⣷⣆⡉⣉⢛⠻⣿⣏⠻⣷⡝⠿⠛⢿⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣴⠟⠉⠈⣹⣿⠟⠁⠀⠀⠤⢄⣐⣚⣉⢤⣶⣤⡀⠀⢿⣿⣿⣿⣟⣿⡷⠍⢾⣷⣮⣛⡴⡟⠛⠿⣿⣼⣻⣇⠀⠀⠀⠀⠀⠀ ⠀⠐⠀⠀⠀⣰⣞⣽⣷⣿⣾⡽⣿⠿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⠟⡡⠄⢐⢢⠙⣿⣏⡉⠛⠛⠿⠿⣷⣌⢿⣦⣀⣨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠃⢀⣤⣾⣿⠧⠀⠀⠀⠤⠄⠤⣤⣟⣩⣈⠛⠛⢿⣆⠸⣿⣿⣿⣾⣟⣿⡘⢷⣚⡿⣷⣾⣵⠉⣳⣎⠙⢿⣏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⣯⢿⡽⣿⣾⣯⣵⣾⣿⢿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣳⣾⣷⢾⣿⣉⢦⣤⣍⢻⣦⡀⠀⠀⠈⠻⣷⣿⣿⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⢀⣠⡤⣌⠻⢆⡘⠒⡦⠙⢻⣿⣿⣿⣿⣿⣿⣷⣦⢻⣷⣽⢮⡽⣛⣧⣏⡽⢺⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣱⣭⣾⣿⣿⣻⣷⣯⣝⣾⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣟⣩⣟⡧⣭⢏⡛⣴⣮⡉⠹⢿⣮⣉⣲⡄⠀⠀⠈⠛⠿⣿⣿⣿⣷⣶⣤⣀⠀⢀⣤⣾⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠑⡈⢤⣤⢉⡶⢷⣷⣾⣿⣿⣿⣯⣟⣻⣻⢧⣿⣹⣿⣻⣜⣯⡷⣿⣝⣣⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⢾⣿⣽⣷⣿⣿⣯⡿⣿⣿⣿⣿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⣿⣯⣿⢷⡾⣽⣛⡧⣽⡶⠀⢛⠛⠛⢿⠘⠻⢦⣀⠀⠀⡙⠿⢿⣿⣿⣿⣷⣾⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⢋⢇⡱⢮⣶⡠⡐⠦⢂⢿⣿⣿⣿⣿⣿⣿⣿⣟⣞⡻⣷⣿⡿⡿⢿⣷⡻⠶⣍⢳⠀⠀⠀⠀⠀ ⠈⢠⣶⣏⡞⣭⣿⣭⣿⣿⣯⣳⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡽⣱⣦⢳⣯⣟⢷⡙⣿⣷⣶⣿⣶⣼⣷⣄⠀⠈⠀⠀⠰⠀⣀⣤⣤⣀⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠘⠠⡜⣲⣥⢯⡶⣜⠢⢯⣷⢶⣶⣀⣿⣿⣿⣿⣽⡿⣿⣿⣿⣶⣽⣳⣯⡿⣶⣯⠶⡍⢷⢮⡭⠁⠀⠀⠀⠀ ⠀⢐⣮⣽⣻⢿⣿⣿⡿⣟⣿⣻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠿⣷⣛⣿⣿⢻⣞⣻⣽⣿⣚⡽⢿⣦⣿⣟⣿⢶⣶⣶⣶⣬⣉⣍⣉⣹⣿⣿⣏⣉⣉⢉⣁⣀⣀⣀⣀⣀⡙⣿⡄⣤⡼⣍⠛⣦⣳⢻⢟⣊⣒⠠⠙⠋⢻⣿⣿⡿⣻⢿⣟⡿⣿⣿⣳⢿⣿⣿⣏⣽⡻⢤⡄⡉⠶⠁⠀⠀⠀⠀ ⠠⣛⣯⢳⣿⣿⣿⣿⣛⣾⣷⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣳⡿⣿⣿⣭⣿⣿⣿⣿⣿⡿⢳⣾⣯⣝⠛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⣿⣿⣯⣻⣿⣤⣾⣿⣧⡙⠽⡏⢾⡗⣎⣏⢓⡮⢃⢤⠀⢰⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⡿⢮⣷⣿⣯⣟⢷⣾⡑⠮⡅⠀⠀⠀⠀ ⢰⡽⣶⣯⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣷⣿⣿⡟⣽⣿⣿⢻⣬⣽⣿⣿⡿⠙⣿⣿⣷⣮⠵⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣶⣿⣿⣿⣿⡝⣿⣦⢿⣿⣻⣿⠶⣯⡽⢾⣍⢻⣷⣏⡂⠄⠀⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⣿⢿⣾⣷⢯⣟⡳⣮⡑⣤⣙⠀⠀⠀⠀ ⣳⢟⡷⣯⣷⣾⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⡿⣟⡷⣿⣿⣿⣿⢻⣼⣿⡿⣿⣧⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⡿⣿⣿⣿⣏⣻⣿⣻⣿⣾⣟⢿⣯⣛⠿⣽⣷⡈⠀⣄⢻⣿⣷⣿⣿⣿⣿⣿⣟⣱⢿⣯⣿⣿⡾⣝⡷⢿⡲⣍⡁⠀⠀⠀ ⢣⣿⣿⣿⢯⣿⣽⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⡞⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢚⣴⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⣽⣹⣧⠹⡍⠃⠀⠀⠀ ⡟⣍⣮⡽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⢿⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⣜⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣺⣿⡜⡇⠀⠀⠀ ⠝⣾⣭⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣯⣿⣿⣿⣿⡿⡭⢷⣛⠿⣻⣿⣿⣿⣿⣿⣿⠟⠲⠉⠒⠈⠹⢾⣿⣿⣿⡴⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢾⣽⣳⠞⡔⠁⠒⠀ ⣾⣿⣻⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠁⢺⣅⠊⠵⣩⠖⣿⣿⠫⡜⠈⠀⠀⠀⠀⠀⣼⣿⣿⣷⣼⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣳⢯⡹⢯⠙⢣⠄⠐ ⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢞⣿⢿⣿⣿⣿⣿⣷⡉⢠⢋⠰⢙⠃⠞⣸⣏⡱⢐⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠉⢹⣿⡙⣾⣿⣿⣿⡟⢩⣿⣿⠿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣯⣷⣹⡗⢮⡐⢎⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣸⣿⠤⣏⣿⣿⣿⣿⣿⣬⣜⣲⣌⣮⣴⣷⣿⣿⣦⣶⣶⣤⣤⣶⣿⠟⠋⠻⣿⡆⠀⢸⣿⣾⣿⣿⣿⠿⣹⣿⣿⣏⡷⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣯⣟⣶⣛⢧⡰⠌⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡒⣿⣿⠋⠉⠻⣿⣿⠟⠛⠛⠉⠛⢻⣿⡟⠙⠉⠛⠉⠹⣿⡀⠀⠀⠙⣁⣀⣸⣿⣿⣿⣿⡟⣼⣿⣿⢧⣦⣝⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣻⣾⣽⣾⣽⢫⣖⢁⡳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣾⣿⣤⣴⣤⣽⣿⣦⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⣶⣿⣿⣾⣿⣿⣿⣿⢿⡟⣛⢿⣷⣿⣿⣿⡟⣯⣻⡼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣻⢿⣟⣾⡻⢯⡶⣂⠔ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⠿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣯⣙⣿⠙⡻⡟⣯⣿⣻⣭⣍⣩⣯⣭⣭⣽⣽⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⡿⣹⢮⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢿⣏⣿⡿⣽⢦⣛⣤⣋ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢒⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣏⡾⣝⠶⠌ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣽⡶⣽⡺⡙ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⢤⣏⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣽⣳⡕ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⡅ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣻⣟⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣽⣿⣟⢮⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡽⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⠾⣝⣻⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣽⣿⣿⣯⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣾⢿⣷⣾⣽⣻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣤⣲⣶⣤⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣾⣵⣶⣲⣤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣶⣾⣿⣿⣿⣿⡿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠻⠿⣿⣿⣿⣿⣽⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣷⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⣾⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣶⣿⣿⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠛⠛⠛⠛⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠃⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠻⡿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⢿⣿⣿⣿⣿⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⡈⠐⠠⠐⠠⠿⣿⣯⣧⣤⣤⣤⣤⣼⣿⣿⠋⠄⡐⢈⠐⠠⢈⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣯⣶⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣽⣿⡏⠐⠠⢁⠂⡁⢂⠐⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇⡈⠐⡀⠂⠌⡐⢀⠂⢛⠛⡛⢉⠉⠄⠠⠹⣿⣿⣿⣿⣿⣿⠃⡈⠼⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⣷⣷⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⢠⣿⣿⡟⡠⢁⠂⠄⠂⠌⡁⠌⡘⢿⡿⠛⢿⡿⠛⢿⡿⠃⠄⠡⢀⠁⢂⠉⠄⡈⠄⢂⠐⠠⠈⢄⠁⡂⣌⣛⡛⠛⠋⠠⠐⡀⢂⠘⠻⠿⠿⠿⠋⢀⠂⠄⡈⠹⢿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢄⣤⣀⠀⠀⠀ ⣴⣯⣴⣬⣵⣿⣿⣶⣶⣯⣿⣿⠁⠔⠠⠈⠄⡁⠂⠔⠠⠐⠠⠐⡈⣤⡄⠡⠀⠄⡈⠄⡁⣂⠌⠠⢈⠐⠠⠈⢄⣬⣶⣿⣿⣿⣿⣿⣿⣿⠇⡈⠄⡁⠢⢐⠨⠐⠄⢂⠐⡈⠄⡈⠔⠠⢁⠂⠌⣻⣿⣿⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣾⣢⠀ ⠙⠿⠿⣿⡿⢿⣿⣿⣿⣿⣿⠇⡌⠠⠁⠌⣶⣿⣿⣮⠐⡁⢂⠡⢰⣿⣿⠂⡁⢂⠐⢠⣿⣿⣿⣧⠂⠌⡀⠃⠜⢿⠟⠛⢉⠡⢁⠠⠀⠄⢂⠐⠠⢀⠡⠂⠤⠡⠌⡀⠆⠰⠠⠐⡈⠔⠂⠌⡐⢀⠙⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⢀⣤⣌⣾⣿⣿⣿⣵⣿⣿⡿⠀⠄⠡⢈⡐⢿⣿⣿⡿⠁⡐⢰⣿⣿⣿⣿⣿⣿⡆⠈⠌⢿⣿⣿⠟⢀⠂⠄⠡⢨⣶⣶⣿⣶⣶⣶⣶⣷⣮⡄⡈⠐⡀⢂⠑⠂⢃⠒⠐⢊⠐⡁⠒⡐⢈⠐⡈⡐⢀⠂⠌⢿⣿⣟⣆⠀⠀⠀⢀⣴⣿⣿⡟⠉⠻⣿⣿⣿⣿⣿⡿ ⢺⣿⣿⡿⣿⣿⣿⣿⣿⣿⠇⡈⠄⡁⠂⡄⠂⠄⠠⠐⠠⢀⠡⢉⠩⢉⠉⢋⠁⢂⠡⠈⠄⠠⠀⠌⠠⠈⡄⠁⠆⠙⢋⠛⠙⠛⠛⠛⠛⢛⠃⠄⠡⢀⠡⣈⠡⣈⢈⠡⡈⢄⠡⡁⢌⡈⢄⡁⢌⠠⡈⠐⡈⢿⣿⣟⣄⣰⣶⣿⣿⣿⣿⣤⢈⠐⣀⢙⣿⣿⣷⠃ ⠀⠉⠉⠀⠀⠀⢈⣽⣿⡿⢈⠐⠠⢀⠡⠄⠡⠈⠄⡁⢂⠰⢀⠂⡐⠠⠈⠄⡈⠄⢂⠡⠈⠄⠡⠈⠄⠡⠄⠩⠄⠃⠄⢂⠡⠈⠄⠃⠌⢠⠈⠄⠡⠂⠔⠠⠐⠄⠢⠐⠄⠢⠐⠄⠢⠄⠢⠄⠢⠠⠁⠆⡐⠘⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣦⣠⣾⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠆⡈⠐⡀⠒⡈⠒⠑⢂⠒⠐⢂⠂⠒⡀⢃⠘⡀⢂⠘⡀⢂⠃⡘⠂⢃⠘⢂⠊⡐⢈⠂⡘⢀⠂⠡⢈⠂⠌⡀⠂⠌⡐⢁⠊⡐⢁⠊⡐⢁⠊⡐⢁⠊⡐⢂⠁⢂⠑⡀⢃⠒⠠⠁⢿⣿⣿⣿⠁⢂⠙⢿⣿⣿⣿⣿⣿⣿⠗⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠂⠄⠡⡀⢡⠁⡉⢌⠠⡁⡉⠄⡉⢄⠡⡁⢌⠠⡁⢡⠈⡄⠡⢈⠌⡠⢉⠠⡁⢌⠠⡁⢉⡈⠡⢉⡈⡁⣉⢈⠡⡉⢠⠁⡌⢠⠁⡌⢠⠁⡌⢠⠁⡌⢐⠈⡌⢠⠁⢌⠠⢈⠡⢈⢸⣿⣿⣿⡇⠂⠌⣀⣽⣿⣿⣿⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⣿⣿⠀⠃⠌⡐⠠⠂⠔⠠⠂⠔⠠⠐⠰⢀⠢⠐⠄⠢⠐⠄⠂⠔⠠⢁⠢⠐⠄⠢⠐⠄⠢⠐⠄⠢⠠⢁⠂⡐⠄⠄⠢⠐⠄⠢⠐⠄⠢⠐⠄⠢⠐⠄⠢⠐⠄⠢⠐⠠⠂⠌⠠⠂⠄⡡⢈⠸⣿⣿⣿⣿⣶⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⣿⣿⠈⡐⢠⠀⡑⠌⢂⠡⠘⡀⢃⢉⠐⢂⡐⢁⠊⠄⡑⢈⠡⠘⠠⡁⢂⢁⠊⡐⢁⠊⡐⢁⠊⡐⢁⠂⡘⠠⢈⠂⡑⢈⠂⡑⢈⠂⡑⢈⠂⡑⢈⠂⡑⠈⡄⠃⠌⠡⠘⡈⠡⢈⠐⡐⠠⢌⣿⣿⣿⣿⡻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣣⣿⣿⠐⡀⢂⠐⠠⡁⢂⠡⠌⡐⠤⠈⠤⠁⠄⢂⠡⠌⡐⠠⠡⢈⠡⠐⡈⠄⢂⠡⢂⠡⠈⠄⡂⠡⢂⠡⠄⠡⢂⠡⠐⠄⡡⠐⠠⡁⠌⠠⡁⠌⡀⠆⣈⠡⠠⠡⢈⡁⠆⡁⢂⠁⠂⠄⠡⢸⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠐⠠⢈⠐⡁⢂⠂⠒⡀⢂⠑⡀⢃⠘⡀⢂⠒⡀⢃⠒⡀⢂⠑⡐⢈⠂⡐⠂⢂⠑⢂⠐⡁⢂⠂⡘⠐⢂⠂⡑⠂⠄⢃⠒⠐⡈⠒⡀⠒⡐⢂⠐⡀⢃⠒⠠⠐⢂⠐⡀⠊⠄⡁⠂⣽⣿⣿⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠌⡐⠠⠈⠄⡃⣈⠡⢈⠄⡡⢈⠄⡡⢈⠄⡡⢈⠄⣂⠡⣈⠐⡈⢄⠡⣈⠡⡈⢌⠠⡁⢌⠠⡁⢌⡈⠄⡡⢈⠌⡈⢄⡈⢡⢈⠁⡌⢁⠄⡡⢈⠄⡡⢈⡁⢡⢈⠐⠠⢁⠂⠄⢡⣿⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠠⠁⠌⠠⠡⠄⠢⠄⠆⠰⠀⠆⠰⠀⠆⠰⠀⠆⠤⠐⡀⠆⠰⠀⠆⠤⠐⠄⠢⠐⠄⠢⠐⠄⠢⠀⠆⠰⠀⠆⠰⠠⠐⠄⠢⠐⠄⠢⠐⠄⠢⠐⠄⠢⠐⠄⠂⠌⡐⠄⡈⠐⣸⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠡⠈⠄⡁⢂⠘⡐⢂⠊⡐⢁⠊⡐⢁⠊⡐⢁⠊⡐⠒⠐⡈⠒⢁⠊⡐⢈⠂⡑⢈⠂⡑⢈⠂⡑⢈⠂⡑⢈⠂⡑⠂⡑⠊⡐⢁⠊⡐⢁⠊⡐⢁⠊⡐⢁⠊⡐⢂⠐⠠⢀⢱⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡁⢂⠐⠠⢈⠐⠠⡁⢌⠠⡁⣌⠠⡁⣌⠠⡁⢌⡈⢡⢈⢡⠈⡄⣉⠠⡁⢌⠠⡁⣌⠠⡁⣌⠠⡁⡌⢠⡁⢌⡁⡄⡡⢈⠄⡡⣈⠄⡡⣈⠄⡡⢈⠄⢂⠡⠀⠌⡐⢠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣄⠌⡐⠠⢈⠐⡀⢂⠡⠐⠠⠐⢠⠠⠐⠄⢂⠰⢀⠢⠀⠆⡐⢀⠂⠔⠠⠂⠔⠠⠐⠠⠠⠐⠄⠰⠀⠄⠂⠤⠐⡀⠆⡐⠄⠠⢂⠐⠠⠐⣀⠂⠌⡀⢂⠁⢂⣰⣿⣿⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣤⠁⠌⡐⢀⠂⠄⡁⢂⠁⡂⠄⠡⠈⠄⠂⠄⢂⠁⢂⡐⢠⠈⡂⠡⠈⠄⠡⢈⠂⢡⠈⠄⡡⠘⠠⢁⠂⠡⠐⡐⠠⡈⢐⠀⡊⠄⠡⢀⠂⡐⢀⠂⢌⣴⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢤⣶⡐⠭⡛⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢩⡞⢯⢻⡿⢿⣷⡦⡑⢌⢻⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣜⣿⣽⣿⣷⣿⣿⣷⠷⣈⡶⣼⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣴⢯⢿⣿⣿⣿⣿⣿⠯⣃⡾⢡⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣜⡾⣯⣷⣹⠿⢷⣿⣍⡼⡟⣱⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢺⣽⣻⣽⣷⣯⡟⣬⡝⣎⠗⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣛⠛⡛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣨⣿⣿⣿⣿⣽⣷⣿⣷⣻⠃⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢠⠓⣤⠒⡔⢲⠉⡌⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣽⣿⣿⣿⣿⡝⣿⣿⣿⣿⠁⣼⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢬⣛⣾⣱⣎⢷⢣⡚⡄⠆⡄⣈⢉⠉⢉⡉⠉⠙⠛⢿⠋⣠⣿⣿⣿⣿⣿⣿⣿⣯⣟⡖⣰⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⢘⣦⡝⣾⢷⣿⣿⣷⣿⣾⣴⣻⡵⣮⣻⣧⢿⡱⢢⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠁⢀⡛⢾⡽⣞⣿⣿⣿⣿⣿⣿⢷⣾⡾⣵⣋⣬⣾⢣⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⠋⠀⡠⢂⠽⣩⢻⡽⡿⠋⣃⢡⢀⠤⢢⣤⣤⣁⠙⠛⠁⠂⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡟⠁⠰⣌⡱⠩⣆⠱⢣⠘⢀⣞⡱⣎⣮⣗⣷⣾⣿⣿⣷⣶⠄⢰⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠅⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡇⢨⢑⠦⣙⢇⢦⠃⢀⡴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡇⠸⢌⢊⠵⣪⠖⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠍⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡇⠀⠠⠞⡙⠂⢠⣯⣾⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡇⣼⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡇⢀⣰⢶⠛⠀⣞⡷⣛⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠡⡞⣿⡿⣿⣿⣿⣿⣿⣿⣿⠋⡴⠀⣁⣽⣭⣧⣌⠉⠻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⠡⠊⣉⠀⠀⡾⢡⣛⣭⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⡏⢰⡹⣽⣻⣿⣿⣿⣿⣿⣿⣖⡻⠀⣴⣾⣿⣿⣾⣾⣞⢧⠀⣿⣿⣿⣿⣿⣿ ⣿⠏⠀⢠⡞⠁⡀⠳⣌⢧⣛⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⢮⣳⢯⣷⣻⣿⣽⡾⣯⡳⡽⠀⡼⣶⣿⣿⣟⡷⣟⢮⡹⡂⣿⣿⣿⣿⣿⣿ ⡿⠀⢠⡞⠀⢠⡑⡳⡜⣯⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡰⣎⣷⣻⣞⣿⣳⢯⡿⣴⡛⠔⣸⣽⣿⣿⣿⣾⢿⣛⣎⠷⢠⣿⣿⣿⣿⣿⣿ ⡇⠀⠸⠌⢐⢢⡑⢧⡻⣼⣳⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣰⢳⣝⣾⣳⣟⡾⣽⣫⢷⣣⠍⣰⣿⣿⣿⣿⣟⣾⡿⡿⣽⠊⢈⣛⡛⢛⠿⣿⣿ ⡇⠀⠠⢉⢆⠲⣙⢮⢷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣛⠆⣜⢧⣟⣾⣳⣿⢾⡽⣳⢟⡶⠃⣸⣿⣿⣿⣿⣿⣽⡷⣿⢟⣧⠋⣰⣷⣿⣷⣅⡊⢹ ⡇⠀⠀⡉⢆⡹⣌⣻⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣾⣻⢾⣳⣿⣯⣻⣵⣛⢾⡘⢁⣾⣿⣿⣿⣿⣿⣿⣻⣯⣟⡆⢰⣿⣿⢿⣻⢮⡟⢸ ⣇⠀⠀⠰⢌⡲⢥⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣽⠾⣽⣿⣿⣿⣳⢯⡶⣯⢳⡅⢸⣿⣿⣿⣿⣿⣿⣿⣿⣵⡏⢠⣿⣿⣿⣿⡽⣯⡐⢣ ⣿⡄⠀⠐⠨⢕⡯⣽⣻⢿⣿⣿⡿⣿⣻⢿⣟⣯⣟⢷⣻⣳⢯⣿⣯⣟⣷⣻⡽⣣⠆⣻⣿⣯⣿⣿⠿⣾⡽⣯⡟⢀⣿⣿⣿⣿⢿⣳⢷⣊⢸ ⣿⡇⠀⠀⠀⠈⢟⡳⢯⡿⣾⣻⣽⣳⢿⣿⣿⣻⣞⡯⣗⣯⣿⢯⣷⣻⣞⡷⣹⢆⡣⢿⣽⣿⣿⢯⣟⣷⡼⣿⠁⣿⣿⣿⣿⣿⣟⡿⣬⢇⢸ ⣿⣷⠀⠀⠀⠀⠀⠉⠳⠙⢧⢓⠮⡝⣯⢿⣽⣳⢟⣾⣽⣾⣻⣻⣾⣳⢯⡽⣓⢮⡹⣿⣟⡿⣽⣞⡿⣽⣳⠇⣘⣿⣿⣿⣟⡿⣾⡝⣧⠃⣾ ⣿⣿⡀⠀⠀⠀⠀⠀⠀⢃⠘⡘⠜⣣⠻⣜⢧⣛⢟⣿⣿⣧⢿⣿⣻⠿⡼⢧⡛⣤⣻⣧⣟⡻⣼⣛⣿⣻⢿⠀⣿⣿⣿⣟⣿⣿⢧⣻⠄⡄⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠌⡀⠛⢬⢣⢯⣿⣿⢻⡼⣻⣟⢿⡻⣝⡣⡝⢶⢯⡷⣯⢷⢧⣛⡶⢯⡞⣰⢯⣟⣾⣽⢿⣞⡯⡗⡋⣰⣿ ⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⠂⠌⠲⡉⠎⠳⣽⣳⡾⣏⠷⣍⠲⣝⢯⣾⣿⣿⣯⣿⡿⣽⡻⣜⢧⣟⡾⣽⢯⣟⡾⡝⡱⢀⣿⣿ ⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠉⠑⠉⠃⡌⠱⢎⡳⣝⢾⣻⠾⣿⣽⡳⣽⡹⣾⣽⣻⢽⣚⡮⢷⡍⢁⣼⣿⣿ ⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠊⠐⠉⠢⢍⡳⢧⡞⣽⡲⣟⣳⢯⣟⣧⢻⡜⡃⢀⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠉⠒⡙⠶⣙⢧⡻⣝⠮⡜⢣⠎⣡⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠈⠄⡐⠠⠀⠀⠈⠠⠁⠊⠑⠊⠅⠙⣀⣼⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⣦⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠊⠉⠁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠍⠁⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⢅⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠊⠀⢂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠂⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡃⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⡃⠀⠀⠀⠈⠄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢲⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⣿⣁⢈⠉⠉⣉⣉⡧⠀⠀⣼⠋⠁⠀⠘⠢⡾⠋⠉⠉⢳⠀ ⠐⠛⢻⣯⠀⢠⠋⠉⠀⠀⢸⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇ ⠀⠀⢸⡿⠀⢸⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⢴⣯⣉⣁⣀⡈⠒⠒⡀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢀⡠⠊⠀⠀ ⠈⠉⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉⠢⡠⠒⠁⠀⠀⠀⠀ ⢰⣖⠒⡀⠀⢠⣴⠒⡂⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⠈⢄⡾⠃⡜⣴⠟⢉⢥⡈⢢⢶⣯⢀⠁⠀⢰⡯⠉⡇ ⠀⠀⠈⢿⡬⢁⠌⢠⡿⠁⠆⠈⡇⢸⣿⣇⢸⠀⠀⢸⡇⠀⡇ ⠀⠀⠀⢸⡯⢻⠀⢸⡇⠀⡀⢸⠇⢸⣿⠃⢈⠀⠀⣿⡀⠀⡇ ⠀⠀⠀⣾⠁⠘⠀⢸⣧⠀⠈⠁⢀⠎⣿⠀⢺⠀⣰⡿⠀⢠⠁ ⠀⠀⠀⠛⠒⠃⠀⠈⠛⠳⠶⠖⠋⠀⢿⣄⡀⠉⠁⠀⡠⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢿⣟⣛⣭⡽⠶⠶⠶⠮⠭⠭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣯⣭⣥⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⢟⣫⣶⠿⣫⣭⣶⠿⠿⣿⣿⣿⠿⢿⣷⣶⣮⣭⣭⣭⣭⣭⣷⣶⣶⣶⣾⣽⣿⣷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣫⣾⣟⣩⣞⣫⣵⣿⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣶⣍⡻⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣵⣿⡿⠿⠛⠛⠛⠛⠿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⠿⢿⣿⣷⣼⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣚⣯⣽⣿⣿⣿⣿⢻⣿⣏⡅⠀⠀⠀⠀⠀⠠⣿⣷⣯⡛⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠐⣿⣿⣶⣽⣿⣟⣛⡻⠿⣦⡀⠀⠀ ⠀⢀⣴⣞⣯⣷⠶⣒⣛⣛⡻⢿⣷⣿⣷⣾⣶⣾⢟⣿⣿⣿⣶⣯⣟⣫⣿⣿⣿⣿⣿⣍⠀⣀⣤⣤⣬⣭⣽⣿⣿⣿⣿⣿⣿⣟⢶⡝⣦⠀ ⠀⣿⡿⣾⣿⣵⣿⣿⣿⣿⣿⣷⣾⣭⣽⣿⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡿⠿⢟⣫⣭⣭⣽⣿⣷⣿⢸⠀ ⠀⣿⡇⣿⣿⣿⡿⠿⢟⣴⣬⣛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣝⣛⢿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⢟⣿⢸⠀ ⠀⢿⣧⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣷⣮⢙⡻⠿⣿⣿⣯⣭⣾⡇⣿⣿⣟⣭⣻⣿⣿⣿⣿⣿⡿⣸⣿⠿⢿⣿⣿⡿⡁⢹⣿⣷⢿⣱⠇⠀ ⠀⠀⠻⢷⣝⣿⣿⣿⣿⣧⠉⠻⢿⣿⣿⢸⣿⣿⣷⣶⣭⣝⢛⠿⢿⣿⣿⣿⣿⣿⣯⣙⣛⣭⣾⣿⣿⣿⣿⠿⡋⣾⣿⡈⣿⣿⣿⡏⠀⠀ ⠀⠀⠀⠀⠸⣽⣿⣿⣿⣿⣷⡽⣿⣷⣆⢘⠿⣿⣿⣿⣿⣿⢸⣿⣿⣶⣶⣶⡎⣭⣭⣭⣭⡩⣭⣭⣽⣦⣰⣿⣧⢿⣿⡇⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣮⣻⣏⣿⣿⣾⣯⣍⠛⠋⠻⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡇⣿⣿⣿⣿⡟⣿⠟⠈⠉⠀⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣿⢦⣴⣦⣬⣍⡛⠛⠈⠛⠛⠛⠛⠁⠙⠛⠛⠉⠀⠀⠀⠀⢠⡆⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣮⣿⡻⣿⢏⣾⣿⢿⣿⣿⣿⣷⣶⣾⣷⣶⣄⣴⣶⣤⡤⣶⣶⡆⣾⡿⡸⣱⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣝⡻⢶⣽⣻⢿⣿⣷⣭⣝⣻⣿⡿⠿⠿⠏⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠱⣿⣃⣵⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣝⡻⢷⣮⣝⡻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢷⣮⣝⡻⢿⣷⣮⣭⣛⣻⠿⠿⣿⣶⣶⣶⣶⣿⣿⣿⠿⢿⣛⣽⣾⣿⡿⣹⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣾⣶⣭⣽⣛⣛⠿⠿⠶⢶⣶⣶⣶⣶⡿⠿⠿⢟⣛⣭⣷⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠿⠿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⢸⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣿⠯⠗⠒⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⡯⠝⠛⠒⠉⠉⠁⠀⠀⣠⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠀⠇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣼⡿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⠟⠉⣀⣀⣀⡉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣾⠋⢀⣶⡿⠓⠚⢿⣦⠤⣴⣶⣶⠾⣿⡏⢿⣿⣿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⡀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡇⠀⠀⠀⣀⣸⣿⣤⣾⡾⣶⣾⣿⡷⣿⡟⠉⠀⠀⠀⣿⡇⠘⣿⣿⣿⣿⣿⠇⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⡄⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⡧⠶⠿⠿⠽⣿⡿⣿⣅⠙⠻⠽⠋⣠⣿⠃⠀⠀⠀⠀⣿⡇⠀⢿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡸⠀⢀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠹⣿⡇⠀⠀⠀⢰⣿⣤⣬⠯⣷⣲⣶⡾⠛⠁⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⠁⠀⣸ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣴⣾⣿⣿⣿⣿⡯⠽⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⣿⠿⠛⠛⣻⣿⣿⣿⡤⢖⣫⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠈⣿⣀⣀⣀⣀⣤⣤⣤⣶⣾⣿⣿⣿⠿⠿⠛⠛⠋⠉⠀⠉⠀⣠⠞⢻⣿⣿⣿⣾⢫⢶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⠿⠿⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⡊⠀⢀⡼⣿⣿⡿⣇⢸⣿⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⣸⣿⣿ ⢀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠻⡏⠉⠛⠛⠓⠶⠶⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣀⠊⢠⣿⣿⡇⣘⣿⣭⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⡴⠚⣛⣭⣤⣤⣬⣍⣛⡓⠦⠤⠀⠙⢦⡀⠀⠀⠀⠀⠀⣇⠀⣿⠀⠀⢻⣿⡟⠋⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣡⣴⠞⠋⡽⢠⢿⡟⢯⣙⢻⣗⠦⡀⠳⣄⠉⠀⠀⠀⠀⠀⣿⠀⠙⣆⠀⠘⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⢟⣷ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠻⣷⡀⠀⢱⣘⣾⣟⣫⢟⣷⣷⡷⠞⠀⡾⠀⠀⠀⠀⠀⠀⢹⠀⠀⠈⠳⣄⣿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢉⣵⣿⣿ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠛⣦⣀⣙⡷⣴⡺⠟⠛⠁⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⣿⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⠋⠁⠐⠚⠉⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⡏⠙⢦⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⡴⠒⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⣷⡃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠘⣿⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⢁⠷⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣿⣷⡄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢻⢠⣿⣿⣿⣿⣿⣿⣇⢿⣿⡏⡖⡽⣄⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡄⠀⣾⠀⢸⣿⣿⣷⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⣯⣸⣿⣿⡼⢡⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠒⠉⠉⠀⠀⢀⠀⠀⢀⡏⠀⢸⣿⣿⣿⣷⠀⠹⣿⣿⣿⣿⣿⣿⣿⢿⣿ ⠀⠀⠀⠀⠀⠈⣿⣿⢻⣿⣿⣿⣿⣿⢏⢿⣷⢣⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⢀⣀⣀⡤⠤⠖⠚⠃⠀⠀⠈⠁⠀⢸⣻⣿⣻⣿⣃⠀⢻⣯⣯⣯⣭⡯⣭⣾⣿ ⠀⠀⠀⠀⠀⠀⠋⣿⠈⣿⣿⡏⣿⣿⣼⣾⡇⣾⣿⣿⣿⣿⣿⣿⣷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣽⣿⣾⠳⡆⠘⣷⣷⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣷⢹⣿⣳⡻⢠⢿⣿⣿⣿⣿⣿⣿⣿⠀⠉⢲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡵⣿⡀⠸⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⠸⢿⡟⡇⡼⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⡇⠻⡷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⠭⣾⣿⣿⣿⠋⣾⠗⣧⠀⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⡇⡇⢻⢹⣿⠀⢸⣿⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠸⣆⡿⣚⡩⣙⠶⣤⣄⡀⠀⠀⠀⠀⢀⣠⡤⢞⣫⣵⣫⠽⣿⣿⡿⢚⡥⣺⠜⡆⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⠻⡿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣻⠿⢮⡿⣾⡖⠚⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣄⠒⢦⠸⣿⣄⠙⣧⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣛⣷⣞⠳⣄⠘⡆⠙⢇⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣯⡝⠻⣿⣏⠉⠻⣮⣷⣝⣶⣼⡀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣇⠈⠙⢤⠈⢳⡀⠀⠹⣌⢻⠀⠙⣧⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠋⠳⢤⣄⡑⠀⠹⡄⠀⣌⠀⢳⡀⠸⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣄⠀⠂⢻⡉⠑⣦⠹⡄⠸⡄⠀⢷⡄⡇⠀⠀⡇⠀⠀⠀⠀⣀⠤⠒⠋⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣝⠀⠀⠀⢿⡶⢧⠀⠸⡇⡗⠀⢀⠃⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⣀⡀⠙⢻⣷⣦⡀⠈⠋⠈⢧⠀⠀⡇⠀⠈⠀⠔⠋⠀⠀⢀⣀⣤⣤⣤⡶⢶⣿⠿⠭⢥⢽⣁⣤⠀⠒⠿⠿⣿⣷⣆ ⠀⢀⡠⠚⠉⠉⠀⠀⠀⠀⠀⠙⢿⣿⣶⣤⣤⡘⣆⣼⣃⣴⣦⠀⠀⣀⡴⠞⣛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣿⣛⣖⠲⠦⣄⣸⡿ ⢠⠾⠒⠶⠀⠀⠀⠀⠀⡀⠀⡙⢺⣏⠛⢿⣿⣿⣿⣿⣿⣿⣿⣶⠞⡩⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠤⣍⣙⣓⠶⣴⣶⠟⠁ ⡾⠀⠂⠀⠀⠀⠀⠀⠈⠑⠉⢡⣿⣿⠛⠲⣤⣯⣿⣿⣿⣿⣿⣥⡞⠒⠒⠚⠛⠓⠠⣀⠀⠀⠀⠠⠄⠀⠠⣤⣷⣌⢙⣿⣦⡾⠋⠀⠀ ⡗⠺⠤⠛⠉⠉⠁⠐⠉⠉⣹⣿⢿⢃⣠⣾⢋⣾⣿⣿⣿⣟⠻⠏⡿⣗⣦⡀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠈⠙⠿⣿⣿⠟⠀⠀⠀⠀ ⣇⣠⠤⠀⠀⠀⠀⢀⣴⡾⢛⡽⢋⣽⣟⣵⢫⣿⣿⣯⡏⢣⠀⠄⠀⠈⠉⢙⣻⠖⢦⣄⡀⠀⠤⢙⠶⣤⡀⠈⢳⣰⡟⠁⠀⠀⠀⠀⠀ ⢿⠀⠀⠀⢀⡴⢪⠟⢩⠖⠋⢠⡾⢻⡟⢁⣿⣿⣿⡟⡀⠘⠀⣴⠀⣤⡐⠂⠈⠉⢗⣟⠿⣶⣤⡀⠲⣤⣹⣿⠞⠉⠀⠀⠀⠀⠀⠀⠀ ⠘⣧⠀⠀⠈⠀⠀⠀⠀⡀⣠⠏⣴⠏⠀⢸⣿⠟⠻⢀⠆⠀⢀⠈⢳⡸⡗⢤⡀⠉⠪⠙⢧⡀⠉⠙⠓⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢧⡀⠀⠀⢀⡴⢂⣜⡥⠚⠁⠀⠀⠀⠁⢠⡆⢸⣰⠀⠈⣧⠀⠑⢿⠀⠙⢦⠀⠀⡀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⣤⣖⣋⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⢹⠆⠀⢸⡄⠀⠈⢷⡀⠀⠑⢦⡜⢦⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣼⣾⠀⠈⢀⢳⡀⢠⡈⢻⣦⡀⠀⠙⢮⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡿⡼⠀⠄⠈⠈⣇⠀⠹⣌⠹⣿⣄⠳⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⢻⠀⠀⠀⠀⠙⠂⠀⠹⡁⡈⡻⣦⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣸⡄⠀⠀⠀⠀⠀⢰⣄⣃⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⡎⠁⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡿⠀⠀⠀⠱⠤⠤⢤⡤⣀⠀⡀⠤⠐⢦⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠋⡁⠀⢻⡇⠀⢠⢸⠀ ⠀⡶⠁⢀⡴⠾⠛⠚⠙⢇⠠⠀⢰⠋⠙⡎⠙⠾⡄ ⢠⡇⢀⠾⠁⠀⠀⠀⠀⠈⠢⠶⠾⣠⣤⠇⠀⠀⠇ ⠸⣁⢸⠀⠰⣶⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⣀⠞⠀ ⠀⠳⡘⢤⡀⠈⠀⠰⠒⠂⠀⠀⠿⠆⢀⠧⡸⠀⠀ ⢀⣄⡘⣻⠶⣾⠍⣷⣄⡴⢶⣄⣨⡤⢊⡴⠁⠀⠀ ⢸⠀⡇⠻⣶⠻⠶⠿⠎⢦⡶⢉⣈⡙⠁⠀⠀⠀⠀ ⠀⠻⣨⢚⠉⢙⢢⠀⢰⠀⢠⠎⠉⠁⣆⠀⠀⠀⠀ ⠀⠀⠸⢤⣀⡶⠞⣄⣼⣠⡜⠶⣦⡠⠛⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀ ⠀⢀⣾⡟⠒⢄⠀⠀⠀⡠⠊⣠⠔⠈⠉⢯⣂ ⠀⣾⡵⠛⠿⣭⣑⣄⣀⣠⣾⠎⠠⠠⠤⠜⡿ ⠀⠎⠓⠤⣤⢿⡿⠋⢹⠻⡹⠣⠤⠀⠠⢸⠃ ⠘⢀⣀⠰⠓⡍⢠⠀⠈⡀⠀⠢⣏⠀⠈⠁⠀ ⠀⠀⠀⡀⠸⠁⢀⠀⠀⠀⢀⠀⠈⡄⠀⠀⠀ ⠀⠀⠀⢠⡄⠀⠈⠀⠀⠀⠀⠑⡀⣿⡀⠀⠀ ⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢈⠝⠇⠀⠀ ⠀⠀⠀⠀⠃⢀⠌⠀⠀⠀⠀⠀⠘⡘⡄⠀⠀ ⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣶⠂⡇⠀⠀ ⠀⠀⠀⡔⢀⠀⠀⠀⠀⠀⠀⢰⠃⢀⡇⠀⠀ ⠀⠀⠌⠀⣴⠀⠀⠀⠀⠀⠀⡶⠀⡸⠁⠀⠀ ⠀⠸⠀⢠⠻⠀⠀⠀⠀⠀⣰⡁⡰⠁⠀⠀⠀ ⠀⡇⠀⠆⡈⠀⠀⠀⠀⢀⣿⠕⠀⠀⠀⠀⠀ ⢠⠁⡐⢀⡇⠀⠀⠀⠀⢈⢻⠀⠀⠀⠀⠀⠀ ⠘⡅⢩⣾⠁⠀⠀⠀⡠⠁⠊⠀⠀⠀⠀⠀⠀ ⠀⠇⠘⠏⠀⠀⠀⡰⢁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡀⠀⠀⠀⢐⠃⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⡀⠀⠀⢸⠀⠘⡀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⢸⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡟⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠇⠸⢿⠛⠛⠉ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⡿⡷⡶⣶⣷⡆⠀⠶⠆⠆⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠀⠐⠃⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠙⠛⠃⠀⠀⠈⠁⠀⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡀⠀⠃⠀⠀⠀ ⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣤⣴⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⢐⣺⣿⣿⣿⣿⣿⣿⣿⣻⣟⢱⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣟⣿⠛⠻⣿⣶⣦⣶⣦⣄⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠹⣽⣿⣿⣿⣿⣷⣦⣅⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⡟⢻⣿⠿⠛⣻⣿⣯⣼⡿⢹⠟⠉⣠⣾⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡃⠉⢻⣿⣶⠀⢀⡄⢴⣿⣿⡹⢫⣵⣿⣤⡾⣿⣯⡾⣯⢷⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣯⣍⡉⠉⠙⠛⣇⣸⣿⣝⣷⣆⢰⣿⠟⢸⣇⢰⣿⡟⢉⣶⡿⣫⡾⢃⡿⢠⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⡇⠀⣸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣇⡟⢭⣛⣓⠠⢀⡉⢙⣿⣿⣿⣿⣿⣿⡀⢀⣿⣻⢿⣿⣿⣯⣾⣿⣷⠟⣡⣿⣿⣿⡇⣾⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣄⣿⣷⠀⠀⠀⠀⠀ ⠀⢀⣠⣴⣿⣿⣿⣿⣿⣛⡋⠥⠤⠄⠉⣻⣟⣶⣭⣽⣿⣿⠿⣟⣿⣾⣿⣿⣵⣿⠟⢿⣿⣿⣿⠿⠁⣰⣿⣿⣿⣿⡷⣿⣷⣝⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀ ⣰⣿⣿⣿⡿⠟⠛⠋⠉⠉⠉⡀⣀⣀⣀⣈⣻⢿⣿⣿⣛⣿⣤⠀⠈⠁⠀⠉⠁⠀⠭⠌⠉⠉⠙⠲⣄⡿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠺⣿⠏⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠷⣴⣤⣀⣈⣥⣾⣟⣟⣷⣽⣿⣿⣿⠿⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣏⣿⣿⣡⣿⣛⣋⣙⣻⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣧⣀⣠⣈⣉⣚⣿⣿⣿⡛⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⠀⠀⠀⠀⠀⠀ ⣿⣿⠇⢛⣯⡭⣿⡏⢉⠉⠛⣁⠴⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣯⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀ ⠁⣿⢠⣿⣿⣴⡟⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣇⠀⠀⠀⠀⠀ ⣰⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣇⠛⢿⡄⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⠱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠊⢁⡤⠖⠒⠂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⣿⣿⣿⣿⣿⣿⣧⠈⣿⡀⠀⠀⠀ ⣿⣿⣿⢿⣇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢈⣉⡠⣤⣤⣤⣬⣽⣻⡿⢷⣦⡀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣷⡀⠀⠀ ⢿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣯⣵⡾⠋⠉⠀⠀⠀⠀⠉⠛⢷⣷⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣷⠀⠀ ⢰⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣭⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠈⢧⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀ ⢸⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⣻⡾⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢨⠈⣿⣿⣿⣿⣿⡿⢿⣿⣿⠉⠀⠰⠀ ⠘⣿⣿⣿⡇⢻⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢤⡀⠀⠀⠀⣀⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠁⠀⠀⢀⠀⢠⣤⠄⠀⠀⠀⠀⠈⢿⡆⢰⢸⣿⣿⣿⣿⣿⢻⣿⣿⠀⠀⠀⠀ ⠀⠘⢷⣽⣿⣿⠛⠻⢿⣿⣿⣶⡾⠿⢲⣶⣄⠀⠀⠈⠀⠉⠛⠲⠦⣤⣍⣭⠿⠋⠀⠀⠀⣤⣤⣶⣟⣿⣿⡟⠛⠛⠛⠛⠀⠀⠀⠀⠀⠈⣷⠸⡇⢿⣿⣿⡿⢿⠙⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠈⠙⠛⠓⠲⠿⡿⣷⣤⣀⠀⠀⠀⠀⠐⣶⡟⠁⠀⠀⣄⣤⣾⠋⠀⠻⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣿⢸⣿⣿⡟⠛⢰⠘⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠉⠻⣆⠀⠀⠀⠘⢷⡄⠀⠀⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⡇⢻⡀⠘⡆⠹⣿⣿⡄⠀ ⠀⠀⠀⠀⢻⣿⠀⠀⣄⠀⣀⣤⣤⣶⣶⣾⡿⠻⡶⣦⣈⣱⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⢿⡇⠸⣧⡀⠃⠀⣿⣿⣷⠀ ⠀⠀⠀⠀⣸⣿⠀⢀⣿⡿⠟⠉⢿⣿⣿⡿⠧⠚⠋⠁⢠⣇⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⢻⡏⠀⠇⠧⠀⠀⣿⣿⣿⠀ ⠀⠀⠀⠀⢿⣿⡀⠘⠿⣄⡀⠒⠒⠂⠀⠀⠀⠀⠀⠀⡿⠙⡆⠀⠀⠀⠀⠀⡀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣼⢸⡇⠐⠢⠀⠀⣸⣿⣿⡏⠀ ⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣿⠀⠀⠀⠀⠀⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢸⣇⡀⠀⠀⣠⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡿⠀⠀⠀⠀⠀⠀⢶⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀ ⣿⣿⣶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠈⠻⢆⢭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠈⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⣿⣿⣼⣿⣷⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⡀⢀⣄⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣝⠲⠶⢴⠖⣰⡶⠛⠉⢀⣸⡿⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣿⣿⣿⡇⢸⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢓⣶⡷⠾⠉⠀⠀⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⢸⣯⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣔⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣿⣿⣿⣿⢹⡇⣸⡏⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡟⠀⢻⡟⢿⣿⣿⣯⣿⣧⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠳⢦⣀⠀⠀⠀⣀⣀⡀⠒⣋⣥⠴⠒⠋⠉⠉⠓⠒⣒⣒⣲⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡟⠀⠀⢸⣿⡄⠙⢿⣿⣿⣿⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠿⣣⢤⣟⡉⠑⡙⠋⣁⣀⣀⣠⡴⠖⠒⠒⠋⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠘⣿⣿⣆⠀⠙⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡐⢀⠙⢿⠚⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⢸⣿⢿⡗⠀⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡰⣜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⣿⣘⣿⠀⠀⢿⣧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢧⣤⣤⣄⣀⣠⣠⣤⣤⠤⠴⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⢹⡈⢿⡄⡄⠸⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⡿⣆⠀⠙⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣘⣇⠘⠀⢻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣰⠟⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢠⠸⡄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⡾⠃⠀⡠⢀⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⣀⣷⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⡞⢷⡀⠜⠁⣸⡏⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢹⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⠋⢠⡞⠀⠈⢳⡄⣠⣿⣇⠈⣧⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠈⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣥⡞⠁⣠⠏⠀⠀⠀⢀⣽⣿⣿⣿⠀⢸⡄⠀⠈⠉⠓⠲⠶⠖⠒⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣾⡟⠀⣰⠟⣆⠀⠀⢠⠞⠁⢹⣃⡇⠀⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⣶⣀⡀⡇⠀ ⣿⣿⣿⣿⣿⣿⠟⢁⣤⣴⣾⣿⡏⠀⣼⠏⠀⢹⣄⣠⢏⡾⢡⣿⣿⡇⠀⠘⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡃⠈⢹⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣠⣤⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠟⣻⠯⢛⣛⣯⣿⣿⣯⣭⣉⢍⠉⢉⠉⠉⠉⠉⠁⠀⣀⣤⣤⡴⠤⠤⣤⣤⣄⣉⠨⢟⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣹⢧⣊⠔⠛⣋⣭⣭⣭⣭⣙⣛⡿⠿⣶⣭⡽⢿⣿⣿⢿⣿⡷⣼⣾⣟⣿⣿⢷⣤⠩⣗⠠⡑⢌⢻⡿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⢴⣽⢻⣧⣮⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⣛⣿⣯⣮⠵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣚⢿⠌⣿⣿⢿⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⢧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣼⢿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⣿⣟⣯⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣸⣿⣿⣄⠀⠀ ⠀⠀⠀⣰⣿⣿⣷⣟⢳⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡄⠀ ⠀⣠⣾⣿⢟⡽⢋⡋⣻⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣹⣿⢿⣿⡀ ⢰⣿⣷⣷⣿⣳⣿⣶⣬⣭⢋⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⢿⣇⠀⠈⠂⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠓⣉⣉⣭⣉⠑⠘⢝⢷⣽⡇ ⠈⢻⣿⣿⡿⣟⣽⣿⣿⣿⣶⣿⣦⣑⠫⡿⡿⠿⣿⣿⣿⢿⠏⣤⡀⠏⠀⠀⠀⠀⠙⡋⣀⣌⠻⡿⣿⣿⡿⠿⠻⣑⣤⣾⣯⣾⣿⣿⣿⣿⡶⢪⠃⣿⠃ ⠀⠈⠻⣿⣵⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣦⣝⣟⣩⣟⣿⣯⣗⠾⣿⣦⣀⠀⠀⠀⠀⣿⣿⣟⣩⣭⣿⣷⣶⣿⣿⡿⣿⣿⣿⡿⡿⣿⣿⠟⣡⢏⣼⠃⠀ ⠀⠀⠀⠈⠻⣿⣿⣿⡿⣛⠷⣯⣏⣹⢫⢏⠏⢻⡟⢿⣿⣿⣿⣿⣿⣿⢶⣭⣄⣢⡿⢿⣿⣿⣿⠟⣿⠙⠙⡍⡍⢳⣻⣿⣿⣷⣽⠟⣡⣾⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣙⠺⣗⣮⣿⣗⣿⣾⣄⡎⠀⢡⠃⠆⢿⠟⠓⠈⠃⠙⡿⠏⠁⠀⠹⢇⠁⠀⠀⡇⠀⣇⣿⣿⡿⢟⢯⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡙⣿⣿⣿⣯⠻⣿⣷⣄⢈⠀⠀⢸⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⠀⠀⠀⡇⢀⣿⢟⢛⡡⢪⣾⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣝⡌⢿⣮⣿⣇⠙⣿⣽⡿⢶⣤⣼⣤⣤⠤⣤⣤⣼⣴⣶⣶⡶⢾⠶⠓⡞⡟⡿⢡⠷⠃⡰⢟⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡙⢿⡟⡆⠸⣷⣷⡔⣧⠀⡇⠀⠀⠀⢸⠀⠀⠀⢸⠀⢸⠀⣰⣳⡟⡁⢁⣴⠋⣴⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡝⢧⠙⢿⡄⠹⣿⣿⣿⡀⣿⡀⠀⢀⣿⢂⠀⣀⢸⣠⣿⣷⣿⡟⡘⢠⡿⢋⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡀⢃⢨⣻⠀⠸⣿⣿⣷⣿⣷⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⢣⡟⢁⣿⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠣⠹⣷⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣰⣻⠏⣧⣾⣻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⢛⣟⢶⡈⠙⠿⢿⣿⣿⣿⣿⣿⣿⠿⠟⢋⡾⣽⡏⢰⡿⣱⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄⠩⢢⠙⠦⣄⣀⣀⣀⣀⣀⣤⡤⠤⠖⢋⣼⠟⢠⡿⣹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡆⠀⠁⢰⣶⣶⣦⣤⣶⣶⣶⣶⣶⡞⠁⠀⠀⣯⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠐⠺⠿⠿⣿⣿⠿⠿⠟⠋⠀⠀⠀⣼⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠻⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢿⣻⡷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⡿⣽⣻⢿⡽⣟⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣻⢾⣻⣯⣟⣯⣿⣻⣽⢿⡅⠀⠀⢀⣠⣴⣶⣤⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣻⢿⣽⢾⠉⠁⢻⡷⣯⡿⠁⢀⣴⣿⣻⢷⣻⡾⣷⣾⢿⣽⢾⣳⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣽⢿⡾⣯⠀⠀⠀⢻⣽⠇⢠⡾⣟⣾⡽⣟⣯⢿⣳⣯⡿⣾⣻⣟⣾⠃⠀⠀ ⠀⠀⠀⠀⠀⣠⡆⠀⣤⠀⣶⠙⡿⣽⢿⣆⠀⠀⢸⡿⠀⢼⣻⠏⠁⢿⠿⠙⠛⢯⣷⣟⣯⡷⣿⣽⣳⡀⠀ ⠀⠀⠀⠀⢾⣟⣧⠤⠺⡷⢾⠦⣧⣌⣙⢯⢷⡄⠀⠿⠀⣻⠃⠀⠀⠀⠀⠀⣠⣞⣷⢯⡿⣽⡷⣯⠷⠀⠀ ⠀⠀⠀⠀⠹⢾⠧⠀⠛⠀⠟⠀⠀⠙⠫⣿⣶⣤⡀⠀⠀⡅⠀⠀⣀⣴⢾⡟⠯⠟⠚⣛⠛⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⣤⣶⢶⣶⣶⣤⣦⣤⣀⠀⠈⠺⣷⣻⣆⠀⠀⠀⠐⠛⣉⣤⣴⣶⢿⣻⣟⣿⣻⣷⢶⡄⠀⠀ ⠀⢀⣾⣟⣷⣻⡾⣟⠗⠉⠈⠁⠛⠙⠋⠀⠀⠙⢷⣻⠇⠀⠀⠀⠛⠉⠉⠈⢉⣿⣻⢾⣳⡿⣞⣿⣽⡀⠀ ⣀⣼⣟⣾⡽⣷⣟⣿⣣⣀⣀⣠⠤⡴⣶⣦⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⠋⠟⣿⣽⣻⣽⢷⣯⣧⡀ ⠻⣟⡾⣯⣟⡷⣿⣞⣯⡿⠝⠁⣀⣴⡟⠀⠀⠀⠀⣴⡀⣽⢿⠄⠀⠀⠠⣄⡀⠀⠀⣸⡷⣯⣟⡿⣾⡽⣿ ⠀⠀⠀⢻⣯⢿⣳⣯⠗⢁⣴⣾⣻⣽⣄⠀⠀⠀⠀⢻⡃⢸⣿⣳⣦⣤⣼⣻⣽⢿⣻⣯⣟⣷⢿⣽⡷⣟⠏ ⠀⠀⠀⠈⠛⠛⠉⠁⣴⢿⣻⡾⣽⡾⣽⣻⣧⠀⠀⣸⣧⠀⢻⣷⣻⣞⣷⢯⣟⣯⣷⣟⣾⡯⠿⠾⠝⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡷⣿⢯⣟⣿⣳⢿⣻⣟⣯⣟⣇⠀⠹⣷⣻⡾⣟⣯⣟⣾⡝⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⢫⣿⣻⣞⣯⣿⣻⢾⣽⣾⣻⠀⠀⠈⠓⠿⣻⠽⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣯⣟⡷⣯⣟⣯⣷⢯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣞⣿⣽⠏⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⡀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣼⣿⣿⠁⢠⣿⡄⠈⣿⣿⣧⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀ ⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣼⣿⣧⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁ ⠀⠀⠙⢿⣿⣷⣄⡀⠀⠤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣦⣤⣤⣤⣤⣤⠤⠀⢀⣠⣾⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣿⣶⣄⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⣠⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣦⠀⠀⣾⣿⣿⣿⣿⣿⣷⠀⠀⣴⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⣸⣿⡿⠋⠀⠙⢿⣿⣇⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⢠⠟⠉⢀⣠⣶⣄⠀⠈⠻⡄⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⡀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢀⣠⣾⣿⣿⠟⠋⠀⠉⠻⣿⣿⣷⣄⡀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢢⣓⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⡿⣝⣮⢳⣍⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠉⠀⠀⠀⠀⠠⢌⣉⠉⠓⠢⣄⠀⠀⡀⢀⣠⣀⢆⣬⡱⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣾⡿⣼⢯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⣀⠩⠖⠋⠉⠁⠉⠉⠁⠐⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣯⣷⢿⣿⣿⣷⣶⣶⣤⣀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⡐⡈⢦⠱⣈⠂⡁⢀⠠⡀⢂⢀⡴⢋⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⣠⣤⣶⣧⣶⣯⣶⣦⣴⣮⠦⠉⣝⣯⣿⣿⣿⣿⣿⣦⣄⠀⠈⠻⢽⣿⣿⣿ ⠀⢠⠰⡡⢝⢢⢣⡔⢦⣱⢉⡐⡰⢢⠏⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠄⠀⠀⣀⣀⣠⣯⣅⣀⠀⠀⣠⣊⣠⣶⣿⣿⣿⣿⣿⣿⣿⣱⡞⣫⣥⡿⣿⣿⣿⣿⣿⣿⣮⢧⠀⠀⣠⢬⣫⠟ ⠈⠄⣒⡽⣎⢯⣳⣹⢦⡛⢦⢱⣱⠃⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢾⡿⢿⣿⣿⣤⣬⣙⡻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⡟⢷⣸⠷⠋⠁⠀ ⠖⠱⣈⡶⢯⡗⣯⢞⡶⡙⢎⢒⠃⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠛⣿⣿⣿⣿⣿⡞⡛⠀⠀⠀⠀ ⠴⠳⣝⢾⡹⡽⣩⢞⣰⣵⠞⡟⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⡹⠿⣿⣿⣿⢋⠩⠾⠟⢻⣷⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀ ⡬⠓⡌⢣⣝⡶⣽⢺⡱⣎⣽⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠙⢄⠀⠀⢰⡟⠿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⢠⡱⢜⡳⢯⡽⣷⡿⣟⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠱⠀⠉⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⢣⠀⠀⢠⣶⠄⣩⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⢡⢓⣬⠷⣯⣟⣷⣿⣿⡻⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡾⠁⣾⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢃⠀⠀⠙⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⣛⢾⣼⣻⣿⣿⣟⢿⣻⣷⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠶⣿⡇⢸⣿⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠂⠀⠀⠁⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠾⣟⣧⢷⡺⣭⢻⡽⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢷⣹⢻⢀⢨⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣉⡸⡀⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⠀⢿⣻⣼⢣⡟⣮⢳⣯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⢿⣾⡬⠚⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣀⠀⠀⠀⠀⠀⠀ ⣦⣝⢢⣂⢿⣳⣏⢾⡱⣏⠾⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡐⢨⠋⠀⠀⠀⠀⠈⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠛⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⡷⣞⣳⡽⣾⡽⣾⢧⡻⣜⢯⣻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑⢹⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⡿⣡⢣⡙⠵⡻⢽⣯⡗⣯⢞⡵⣇⠈⠙⠻⣷⣶⣦⣤⣀⠀⠀⣀⣤⣶⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣄⡰⠤⠀⣀⣤⡤⣾⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⠄⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⢳⠰⣇⢮⡱⡙⢎⡷⣿⣎⠿⣜⢿⡀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢏⠿⡹⠟⠻⠛⣝⢧⡘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⢣⠙⡺⢯⡳⢍⠎⣼⣳⢯⣟⡼⣫⢧⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢃⠱⠈⠂⠁⠀⠀⠀⠀⠈⠙⢟⠦⣄⣀⠀⠀⠀⠀⣀⣤⡒⠾⠛⠃⢦⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⡿⠂⠀⠀⠀ ⣧⠙⡔⠫⠜⡌⢺⢴⢫⢿⡽⣞⡵⣻⣆⠀⠀⠀⠀⠀⠀⠀⠉⠋⡝⣿⠿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠦⣉⢜⣡⠳⣌⠳⣎⢻⣎⢿⣯⣟⣷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⠀⠈⠛⠿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠓⣌⠞⡴⢫⡜⣳⣮⣗⢾⣯⣿⡿⠿⠟⢧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢿⣶⣦⣄⣀⣀⣀⣠⣞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢫⠔⣫⡕⣣⢞⣵⣯⠿⠋⠉⠀⠀⠀⠀⠀⠓⢤⡀⠀⠀⠀⠀⠀⡞⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢛⣿⣿⣿⣟⡷⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢧⢻⣴⢻⣽⡿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⢀⠀⢠⡼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣯⣟⣿⢳⢮⡵⣩⡛⡖⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⢷⣺⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣼⠏⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⢯⣟⡻⣽⢻⣮⢵⣣⢝⡹⣒⠦⣍⡹⣙⠶⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢮⣳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠟⠐⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣟⣯⣟⡞⣯⢻⡽⣞⠷⣎⡷⣭⢳⣳⣬⡒⣍⠳⢮⣜⡲⣌⢳⣒⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣸⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢶⢠⠀⢀⡸⡄⠒⢺⠀⣸⣀⡀⣦⠽⠑⠁⠀⠀⠀⠀⠀⠀⠀⣆⣀⠗⠂⠀⠀⡆⢠⠃⡠⠜⠒⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢤⠞⢳⠊⠓⠣⢸⡸⣲⠇⣘⣦⠚⢗⣻⠉⠻⡴⠂⢀⣀⠀⠀⣠⠂⠀⡇⠀⠀⠀⠀⡚⡲⢃⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠤⢼⡀⡞⢶⠦⣤⡖⠯⠭⡽⠟⡲⠀⠀⣆⠴⠊⢀⠀⠈⠅⡜⠒⠁⠀⠀⠉⢱⠀⠀⠀⠈⣑⡼⠁⢀⢠⢠⠄⢠⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠢⢄⢳⣁⣀⠆⠃⣇⡇⠜⠍⢳⡄⢰⢃⡈⡩⣲⠾⡃⢀⠀⠘⠤⢁⣠⠃⢠⢼⣇⣰⢃⣼⠀⠀⠀⣩⡾⠦⣆⠷⣅⠜⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⢦⠀⠈⠒⡥⣽⢁⠌⢹⢶⡤⡧⣾⠀⠀⠙⣾⣤⠖⠿⡿⣄⡗⢴⢣⡌⢲⣩⠚⠸⣌⣍⠹⣸⣚⡙⢷⣤⠞⠡⢄⣀⡳⣎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢄⣣⡈⠦⡜⣸⡹⣰⠃⡀⢱⣛⣰⣑⢽⣧⠀⢰⣿⡇⠰⠋⠑⡜⡗⡞⠋⠂⠘⢦⠳⣠⠿⠦⣼⢩⣤⢊⡾⠋⠀⠀⠀⠋⠀⢨⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢁⠇⠀⡏⠀⠈⢾⡄⠙⣤⠃⣟⠀⠋⣿⣅⡾⢻⢀⡀⡆⣰⣥⣟⢱⣞⣀⠀⣨⠧⣯⡀⠀⢸⣈⣷⡟⠀⢀⢦⠀⠀⠀⢠⠏⠀⠀⡀⣷⠀⠀⠀⠀ ⠤⢲⠚⢒⢻⠙⢶⣴⢺⠉⠒⡧⠔⠛⠲⢤⣸⣿⠁⣼⡶⠿⠿⣽⣓⣸⢿⣓⡶⣚⢧⡷⣿⢫⣦⣸⣿⠏⢹⡴⠋⠸⡄⠀⠀⡞⠀⢰⣰⢣⠊⠀⣰⡠⠀ ⠀⠈⡄⠀⢭⡇⡀⠉⠻⣇⠀⡇⠀⠀⠀⣀⡝⢿⡆⣿⢁⢀⡴⠋⣏⣏⡼⠋⡷⣇⡝⣇⣿⡜⠋⣿⣿⡆⣼⡝⡄⣠⢹⠀⣸⠁⠀⠀⠀⠛⣄⣸⡖⠊⠀ ⠐⠴⣅⡆⠘⡎⢢⠀⠀⢹⣎⣷⠀⠀⣀⡕⠻⢚⣿⣿⡉⠉⠳⣄⣰⠟⠑⢶⠁⠹⢴⠁⡇⣠⣴⠿⣏⣾⡇⢹⡃⡗⢸⣷⢃⣠⠔⠋⠀⢠⠃⠀⠑⠹⠀ ⠀⢤⢎⣈⡲⠵⣈⠉⠓⣾⠙⣾⣇⠀⠀⠛⣆⡇⢻⣿⡇⠀⣠⡾⠛⢶⡆⠈⣇⣰⠏⢰⣿⢏⡏⢠⣏⣼⠞⠉⠉⠱⣿⢿⡭⣄⠀⠀⢠⠏⠀⠀⠀⠀⠀ ⠐⠚⠒⠂⠼⣄⠀⠉⠢⣼⡀⠈⢻⣆⠠⡄⠳⡇⢸⣿⣧⣾⡟⠀⠀⢸⡇⠀⣸⠋⠀⣼⡏⢾⠛⣿⢹⡏⠀⠀⢀⡼⠃⢘⠂⢨⠀⢀⡞⠀⢀⠄⢀⠆⡀ ⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠳⣄⠀⣿⣆⠸⡠⠜⣆⣿⣿⠏⠀⠀⠀⢸⡇⢰⠇⠀⢀⣿⠁⣿⢰⡇⣼⠁⠀⢠⡞⠁⠀⠸⣚⣮⠵⠟⠓⠦⣸⠀⡤⠼⠓ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣈⠳⣜⢿⣯⠀⠀⢈⣿⡿⠦⣤⣀⠀⢸⣷⡏⠀⠀⣸⣿⡾⠋⣿⢁⡟⠀⣰⣯⣤⠶⠞⣋⠽⢓⣒⡡⠤⠒⠛⠳⢧⡀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠳⣿⣷⡀⢸⣿⡇⠀⠀⠉⠛⢾⣿⠀⠀⠀⣿⡟⠁⣸⣿⣾⣿⣿⠟⢉⣠⣴⠞⠋⠉⠉⠉⠂⠀⠀⠀⠀⠈⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣾⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⢸⡟⢀⣼⡿⠋⣼⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀⠀⠀⣿⡀⠀⣿⣷⡿⠋⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⢿⡇⣸⣿⠟⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⣸⣷⣿⡇⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⢿⣿⣦⣀⣾⣿⢯⣿⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣮⣿⣿⣿⡿⠁⣸⡟⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡟⠀⢠⣿⠃⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣠⣾⣿⣤⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠿⠛⠻⣿⣿⠿⠿⠿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⡾⠛⠳⠶⣤⣀⣠⣤⣤⣴⡟⠁⠀⠙⣷⠟⠋⠉⠉⢿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠁⠀⠀⠀⠀⠉⠀⠀⠀⡿⠀⢠⣟⣿⠿⠳⢦⣤⡴⣼⣇⠀⠀⠀⠀ ⠀⠀⠀⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣽⣏⠀⠀⢸⣷⡄⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠓⢾⡟⠛⢁⣼⣟⠀⠀⠀⠀ ⠀⢀⣼⣇⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⣿⣿⣥⣽⢤⠀⠀⠀ ⣀⣈⣷⣏⣁⠀⠀⢀⠀⠉⠙⠻⣶⣾⣳⣶⠟⠉⠁⢀⠀⠀⠀⠶⢻⡟⠒⠒⠀ ⠀⠀⠸⣇⣀⠀⠀⠛⠉⠂⠀⢀⡿⣉⣉⢿⡄⠀⠒⠉⠋⠀⠀⠠⣼⠧⢤⠀⠀ ⠀⠐⠛⠻⣍⣀⡀⠀⠀⢀⣠⠞⠙⠧⠼⠈⠳⣄⡀⠀⠀⠀⣠⣴⣟⡀⠀⠀⠀ ⠀⠀⣠⠴⠛⢿⣭⠿⠿⢯⡅⠀⠀⠀⠀⠀⠀⣠⣭⣩⣭⣭⣿⣋⠈⠙⠂⠀⠀ ⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⣿⠶⠶⠶⠤⠶⣾⠇⠀⠘⣧⠀⠀⢹⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣇⠀⠀⣰⠾⠋⠀⠀⠀⠀⠀⣧⡀⠀⠀⢿⣄⣤⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡀⠀⠀⠀ ⠀⢠⣾⣿⠟⠉⢉⣉⣉⠛⢦⣀⡴⠛⣉⣉⡉⠙⠻⣿⣦⡀⠀ ⢀⣿⡿⠁⣠⣾⣿⡿⠿⠿⣶⣍⣴⠿⠿⢿⣿⣷⡀⠙⣿⣧⡀ ⢸⣿⡇⢀⣿⣿⠋⠀⢀⣤⣄⡉⣁⣤⡀⠀⠹⣿⣿⡀⢹⣿⡇ ⢻⣿⡇⢸⣿⣯⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⢹⣿⡇⠠⣿⡇ ⠸⣿⡇⠈⣿⣿⡀⠀⢿⣿⣿⣿⣿⣿⣿⠃⠀⣾⣿⠃⢰⣿⡏ ⠀⢻⣿⡄⠘⣿⣷⣄⠈⠻⢿⣿⡿⠟⠁⢀⣾⣿⠋⢠⣿⡟⠁ ⠀⠀⠻⣿⣆⠈⠻⣿⣷⣄⠀⠈⠀⣠⣶⣿⠟⠁⣰⣿⡟⠀⠀ ⠀⠀⠀⠉⠿⣷⣤⡈⠙⠿⣿⣿⣿⠿⠋⣁⣴⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠻⣿⣶⣄⡈⠉⣀⣤⣾⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⋆˚࿔ 𝐧𝐚𝐦𝐞 𝜗𝜚˚⋆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡾⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠄⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⣠⣾⣿⣿⠿⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣦⣤⣤⣄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣸⡟⣾⡿⠀⠀⠀⠘⣿⣿⣿⣿⣦⡀⠀⠀⣠⣾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⠁⣿⣷⡀⠀⣀⣼⣿⣿⣿⣿⣿⣷⡀⣼⣿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⡃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣦⣤⣤⣾⣿⣿⣿⣿⠿⣿⣿⡏⣿⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣨⣿⣿⡀⠻⣿⣿⣿⣿⣿⣿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣼⣿⠟⢠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣤⣤⣼⣿⡉⠻⣷⣄⡈⠛⢿⣿⣿⣿⣷⣤⣿⣿⠇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣡⣴⣿⣿⣿⣁⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀ ⢾⣟⠁⠀⠉⠉⠀⠀⠈⠛⢿⣿⡿⠿⠷⠾⠿⡿⠟⠉⠀⠀⠀⠙⠿⠷⣿⣿⣧⣷⣶⣿⣿⣿⠟⠋⠙⠛⠿⣶⡿⠟⠋⢻⣷⡄⠀⠀ ⠘⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣶⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣼⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⠙⢷⣤⣤⣤⣤⡶⠿⠿⠟⠛⠋⠉⠉⠁⢴⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣦⡀ ⠀⢀⣿⠅⠀⠀⠀⡀⠀⠀⠀⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿ ⠀⠈⢿⣶⣶⣶⠟⠻⣧⡀⠈⣿⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⢸⣿⠃⠀⠀⠀⠀⠀⢰⣾⠿⠿⠛⠃ ⠀⠀⠀⠉⠁⠀⠀⠀⠙⠿⡾⠟⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⣿⣿⠀⢀⣴⣷⣄⠀⠀⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠃⠀⠀⢠⣤⣴⣶⣶⣤⣤⣤⣀⣀⣀⡀⠀⡀⠀⠀⠘⢷⣜⠛⠻⠛⠁⠈⠻⠷⡶⠿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⣴⣿⠀⠈⠉⠉⠉⠙⠛⠛⠛⣿⣟⠃⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⢀⣤⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣀⠀⠀⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⢅⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠄⠂⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⣄⠀⠀⠀⠀⢐⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⢀⠊⠁⠀⠨⠀⠀⠀⠀⢰⠏⢆⠀⢀⠌⠀⠀⠀⡘⠸⠀⠀⠀⡐⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠎⠀⠀⠀⠁⠀⠀⠀⠠⣻⠀⢈⠗⠁⠀⡂⠀⠨⠀⠀⠑⠂⠊⠀⠀⠡⢀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠀⠀⠀⠅⠀⠀⠠⠁⠁⠁⠡⠂⠀⠀⢰⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢐⠀⠀⠠⠂⢐⠀⠀⡐⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⢀⠔⠀⠀⢨⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡠⠤⠤⢔⠂⠁⠀⠀⠀⠈⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⡶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢶⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀ ⠀⣠⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣄⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡆ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿ ⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣄⣀⡀⠀⠀⣀⣀⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣷⣶⣶⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀ ⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣦⣬⣍⣉⣙⣛⣿⣿⣇⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣸⣿⣿⣟⣋⣉⣉⣥⣴⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣟⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⠻⠿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠿⠿⠛⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⢛⣿⣿⣦⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣿⣷⣤⡀⠀⠀⠈⠙⠛⠿⠿⠿⣿⣿⣧⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⠛⠛⠁⠀⠀⠀⣠⣾⣿⠿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣤⣠⣤⣤⣶⣿⡿⢿⣿⣇⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢰⣿⡿⢿⣿⣶⣦⣤⣤⣤⣤⣶⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⠿⠻⠛⠋⠉⠀⠈⢻⣿⣦⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⣰⣿⡿⠁⠀⠈⠙⠛⠟⠟⠻⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⣰⡿⠀⣀⣀⡀⠀⢀⣀⣀⡀⢻⣧⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣷⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠰⠛⠻⣿⣿⣿⣿⣿⠟⠛⠇⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⢠⣿⣷⣤⣿⣿⣿⣥⣾⣿⡆⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠈⠻⠿⠿⢻⣿⡿⠿⠿⠟⠁⠀⢸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣶⣾⣾⣿⣿⣿⣷⣶⣶⣶⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣍⣉⠉⠁⣀⠈⠉⣉⣉⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠶⠶⠶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠏⢉⡱⠶⠶⠶⣄⠙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠯⡍⠴⠏⠉⠀⠀⠀⠀⠈⣧⠀⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢷⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣶⠶⠶⠶⠶⠶⢶⣷⣤⣼⣇⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⠿⠋⡠⠤⠤⠤⢤⣈⠉⠉⣻⠿⣿⣷⡟⢦⡀⠀⠀⠀⠀⢠⡄⠀⠀⣀⠀⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀ ⣰⣿⠿⠉⣠⠞⠁⠀⠀⠀⠀⠉⠈⠉⠙⠲⢾⡿⣿⣧⡝⠆⠀⠀⠀⠲⡇⠀⣀⠻⣦⣿⡿⠾⠿⣋⢉⣉⣉⣉⣉⣉⣻⣿⣶⣄⠀⠀ ⢹⣿⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣍⣿⡇⠀⣿⡇⠀⡄⢀⠀⢿⠀⣿⡏⢁⠀⠞⠉⠉⠉⠉⠉⠉⠉⠙⢿⣿⣿⣷⣄ ⢸⣿⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣍⠹⢿⣧⣤⡌⢣⢀⡀⢾⠃⠘⣧⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢹⣿ ⠘⣿⣦⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⠰⠋⠹⠋⠀⠘⠈⠀⠈⣠⣖⠉⣄⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿ ⠀⢹⣿⣧⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⢀⡀⠀⠀⠀⠀⠀⠀⣉⣀⣀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣼⣿ ⠀⠀⠙⢿⣿⣤⠈⠳⣤⣤⣴⢛⡿⣦⣤⠄⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⠃⠀⠀⠀⠀⠀⠀⢀⣠⣴⠇⣼⣿⠿ ⠀⠀⠀⠈⠙⢿⣷⣄⣀⣬⣿⣿⠷⣿⡟⠒⠒⠒⠐⠂⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⣤⢤⡄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣠⣾⣿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⠟⢁⡴⢦⣩⠏⠀⠀⢰⡆⠀⠀⠁⠘⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⠋⠉⠉⠉⠛⠋⢡⣴⣿⠿⠿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⡠⠋⠀⠈⠁⠀⢀⡴⠋⠁⠀⠐⠀⠀⠀⠀⠀⣴⡴⠀⣤⣿⣭⡿⢷⡾⠿⠿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠿⣤⠎⠀⠀⠀⠀⠀⣠⣾⠟⠀⢦⡴⠀⡆⡀⢆⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠳⣼⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠟⢀⡿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⡇⠟⠹⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠉⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣿⡇⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡤⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣁⣴⣿⣧⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣇⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢫⣾⣿⡟⠋⣿⣧⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⣬⣽⠛⣦⠤⣤⣼⣿⣿⣿⣤⣿⡿⠃⠀⠀⠈⠻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣤⠟⢩⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣤⣤⣿⡿⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡏⠁⠁⠀⠀⠘⠋⢁⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣛⣯⣻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡀⠄⡀⠀⡈⢻⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢯⣞⣽⣿⣿⡟⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠐⡀⠂⠄⢁⠀⠠⠙⣎⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣏⢾⣹⣿⣿⠁⠀⠀⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠄⡁⠠⠁⠌⢈⡶⠀⠁⡘⡜⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢮⣳⢻⣿⡇⠀⠀⠀⢰⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠄⠀⠐⠘⡆⢀⠈⠐⡀⢐⠰⢹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢧⣋⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠈⠀⠀⢂⠀⢂⠐⡀⠐⡀⡄⠌⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢧⡹⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⢂⠀⠀⠀⠄⠀⠀⠌⡀⠂⠄⠐⢀⠸⡀⢹⣿⣿⣿⣿⣿ ⣿⣿⣿⣎⠽⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⣀⣀⣠⠤⡤⠆⠀⠐⡀⠐⠠⠀⠀⠀⠠⠀⠀⠐⡀⢁⠂⠀⠀⠄⠐⠘⢿⣿⣿⣿⣿ ⣿⣿⣿⣜⠳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣮⠃⠀⠠⢀⠁⠂⠀⠄⢀⠡⠀⠀⠂⢀⠂⠄⠀⠂⠀⠁⢀⠃⠙⢿⣿⣿ ⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⢂⠠⠀⠀⢰⣿⡀⠀⠀⠄⠐⠠⢈⠀⠀⢡⠀⠐⠀⢨⣐⣀⠙⠻ ⣤⣤⣤⡤⢤⡖⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣉⠛⠛⠻⠁⢀⠀⠠⠀⠀⠀⠛⣋⣉⠀⠀⠀⠀⢂⠄⠠⠁⠀⢆⠁⠀⠀⠻⣿⣿⣿ ⣿⣿⣿⡜⡱⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠙⠛⠉⢛⠇⢀⡆⠀⠀⠀⢀⡛⠙⠋⠉⠀⠀⠈⠀⡌⢄⠃⢬⠡⢊⠠⠀⠀⠀⠈⠻⣿ ⣿⣿⡷⣍⢳⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢃⣒⣒⣸⣶⡃⡸⠀⠀⠀⢠⣾⣶⣧⣐⣚⡀⢀⡔⢠⢘⠢⡱⠎⠐⢨⠀⠈⢄⠀⠀⠀⠈ ⣿⣿⣿⡘⢆⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣌⡻⣿⣿⣿⣧⠃⣠⢴⣱⣿⣿⣿⣿⣿⣿⢇⣾⠇⠤⠋⡼⠱⡈⠀⠂⠀⢀⠀⠀⠐⣦⣀ ⣿⣿⡷⣉⠎⣞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣧⠲⣯⣼⣿⣿⣿⣿⣿⣿⣿⡾⢋⡈⢠⢊⡕⠣⠀⠁⠄⠡⠀⠀⢆⠀⢹⣿ ⣿⣿⢣⡃⠞⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣻⣿⣿⣿⣿⣜⢷⢎⣿⣿⣿⣿⣿⣿⡿⠟⠩⠐⠊⠂⡐⠁⠀⢈⠐⠀⠡⠀⠘⣷⢘⣿ ⣿⣿⢧⡹⢍⠆⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢂⠀⠀⠀⠠⠈⠄⠀⢁⠀⢹⣻⣿ ⣹⣜⢣⠎⡭⠀⠀⠀⠀⡐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣯⣿⣿⣿⣿⣿⣭⣿⣿⣿⠟⠀⠀⠀⠐⠀⠂⡀⠀⠀⠌⠠⠀⠀⠀⠈⢿⣿ ⣿⣿⣯⠘⠀⠀⠀⠀⠀⢀⠐⡀⠀⠀⠀⠂⢀⠐⠠⣀⠈⠻⣿⣿⣿⣾⣿⣿⣿⣿⠟⠁⢀⡤⠀⠀⠈⠄⠁⠀⠀⠀⠀⠂⡁⠀⠀⠀⠘⢿ ⣿⣿⠇⠀⠀⠀⠀⠀⠐⠀⠀⣀⡀⠀⠀⠐⠀⣹⠲⣤⣈⠐⠈⠻⣿⣿⣿⡿⠟⠁⢀⢖⣽⣾⡄⠀⢈⠀⠀⠀⠀⠂⠀⠀⠠⠁⠀⠀⠀⠀ ⠟⠁⠀⠀⠀⠀⠀⠐⠀⢀⣤⣶⣍⠀⠀⡈⠀⡜⣳⢇⡾⣀⠂⠄⠈⠉⠉⠀⡀⠀⡎⣾⣿⣿⡇⠀⢀⠀⢀⣷⣦⣄⣀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣷⣚⡷⡀⠀⠄⠉⢧⣛⡖⢡⡘⢦⡡⠀⢀⠀⠀⣸⢰⣿⣿⣻⡇⠀⠀⠀⢸⣿⣬⣟⡿⣻⠿⡜⢆⠀⠀⠤ ⠀⠀⠀⣀⠀⢆⣡⣾⣿⣿⣿⣿⣯⢷⡇⠀⢀⠸⡈⡷⣉⠦⡙⢦⢹⣁⢀⡀⠀⡿⣼⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣷⣯⣽⢠⡄⠀⠀ ⠀⠒⠹⠄⢋⣴⣿⣿⣿⣿⣿⣿⣟⠾⡇⠀⠀⠐⡇⡓⣌⠲⣙⣾⣾⣯⡸⡇⠀⡏⣿⣿⣿⣿⡇⠀⠀⠈⢼⣿⣿⣿⣿⣿⣿⣿⣼⡷⠀⠁ ⠀⠀⠀⢈⢹⣫⣿⣿⣿⣿⡿⡿⣼⣻⡇⠀⠀⠀⡁⠵⣨⣿⣿⣿⣿⡟⣹⡷⠀⢧⡙⣿⣿⣿⡧⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡷⣿⠀⠀ ⠀⠀⠀⠀⢂⠹⣯⣿⢿⡻⣽⣳⢯⣷⠁⠀⠀⠀⡉⣦⡻⣿⣿⣿⣿⢿⣙⣽⠜⢋⣛⡻⢾⣽⣛⠀⠠⠀⢻⣿⣿⣿⣿⣿⣿⣻⢿⣏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠋⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⣹⣀⣀⣤⣀⣀⡜⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠋⠀⠀⠀⠀⠀⠀⠀⠉⠳⡔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣀⡀⠀⣀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠓⠃⠀⠧⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣩⢯⡁⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠷⠦⢄⣀⣀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⡠⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠒⠢⠄⠒⠃⠀⠀⠀⠀⠀⠀⠸⠤⠤⠴⠊⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠉⠘⢰⠖⠒⢤⡤⠔⠒⠪⠥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠉⠒⠤⣀⣀⣀⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
MAKING DOT ART REQUESTS!! this doesn't cost anything! contact me through the socials below! x/twitter: loganzuu discord: logays ⠀⠀⢀⢠⢴⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⡟⡵⢉⢝⣹⡏⠳⢄⠀⠀⠀⣀⣔⣤⣼⣿⣷⠳⢄⠀ ⢰⡇⢸⣞⡵⠛⡿⣯⡀⠀⢇⡠⢊⡴⠿⠫⠟⣸⣷⣻⠈⡆ ⢸⠐⠸⣟⣠⢆⢉⣽⢽⠈⡞⠀⠈⢀⣠⠆⡀⠩⢟⢪⠈⡇ ⠈⡆⢇⡿⣿⣿⡋⠷⢿⡅⡇⠀⠀⢀⣵⢖⣡⠶⠷⠎⡰⠁ ⠀⠘⡌⠢⡗⡿⠁⣴⢵⠆⠁⢀⣴⠟⠑⠟⠁⠁⢀⡔⠁⠀ ⠀⠀⠈⠣⠙⢄⣮⡾⡟⠀⢠⡞⠂⢠⣶⡶⢂⣴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠟⠃⣴⠕⠀⠀⠋⢀⡽⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢠⠑⡍⡀⠀⠀⡴⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢈⠁⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡦⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⣶⢺⡝⣿⣿⠄⠀⠀⠀ ⠀⠀⠀⠀⢰⡿⣝⣮⢟⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣿⣿⢿⣏⡿⡼⣏⡾⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⢠⣿⣽⡹⣞⢯⡳⣭⢳⡝⣯⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣿⣟⣯⢿⡹⣞⣵⢻⡼⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⣾⡟⣧⠿⣜⣯⢽⣚⣧⢿⣭⡟⣾⡽⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣝⣞⣳⣛⡾⣭⡗⣯⡞⣷⣻⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⢘⣿⢿⡼⣿⣻⡼⣟⡿⣼⢿⣼⣻⡿⣿⣿⣼⣻⣿⣤⡀⠀⠀⠀⠀⠀⢀⣼⣿⢻⣧⣼⣧⣿⣼⣣⡿⣤⢿⣸⢧⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⢸⣯⣏⡟⣷⢯⢿⣽⣻⣽⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣴⣶⣿⣹⣾⣿⣾⣿⣿⡿⣿⣧⢻⡽⣮⢳⣟⡿⣿⣿⣿⣷⠀⠀ ⠀⠀⠸⣿⡜⣾⡱⣏⢿⡺⣕⣫⣾⣯⣿⣿⣿⣷⣿⢮⣽⣟⣻⣿⣷⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣽⣻⡜⣧⣟⢧⠿⣜⣻⣽⣿⣿⣿⡆⠀ ⠀⠀⠀⣯⣟⢶⡹⣎⠷⣹⢮⡵⢿⣿⣿⣿⢯⣿⡾⣿⣟⣿⣿⣿⡟⠛⢛⣿⣶⣯⣞⣳⢯⢯⣟⣳⣧⡿⣽⢞⣯⢻⡭⣗⢯⣟⣿⣿⡧⠀ ⠀⠀⠀⢻⣞⣷⡹⣎⠿⣥⡛⣾⡹⢿⣿⣯⣿⣟⣹⢾⠏⣿⢿⣿⡇⠀⣾⢿⣿⣝⠿⣫⣿⣳⣾⣿⢷⣻⡽⣞⣧⡿⣵⣛⣮⠽⣞⣿⣷⠀ ⠀⠀⠀⢸⣯⣶⣿⣬⣷⣶⡽⠶⠿⢿⢿⣏⠷⣎⢞⠒⣮⣟⣾⢯⡟⠀⣿⣿⣷⡸⣿⡿⡧⢷⣿⣿⣦⡈⠉⠙⠚⠽⠷⣿⣞⣿⣼⡽⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣯⠞⡽⡜⣮⢱⣎⡬⢷⡻⠇⢸⣯⢷⡻⣝⣧⠶⣯⢟⣿⣇⠿⣞⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡯⣝⢮⡝⣱⡙⢦⠳⡜⣼⢣⢿⠃⠘⣧⣿⠭⠮⢱⣾⡹⣿⣟⡼⢟⡺⣏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣝⢮⠳⣍⠶⣙⠦⢭⠇⢧⣲⣍⢮⡏⠀⠀⢻⣧⣶⢤⡢⣄⠭⢴⢫⣜⢫⠵⣩⠗⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣟⢳⠭⣞⡹⣲⡹⡬⣓⡙⣞⢣⣵⢚⡻⠀⠀⠀⠘⣯⢞⡭⠗⣮⢫⡝⣲⢬⢣⡛⣬⢛⡴⢺⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⡓⢮⢇⡻⢔⢣⢏⡵⢳⣋⠟⡸⣍⢦⡟⠁⠀⠀⠀⠀⠸⣮⢧⣛⠗⣃⠝⡲⡍⢶⢩⠖⡭⡚⡵⣊⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⣱⢫⡓⢭⠚⣌⢮⢓⡜⢧⣘⢣⡳⢎⣷⠁⠀⠀⠀⠀⠀⠀⠹⣮⡙⡞⣭⢳⡱⣙⢎⢧⡚⡵⣙⠲⣍⢎⡳⡄⠀⠀⠀⠀ ⠀⠀⠀⣠⢟⡲⢇⢧⡙⢦⣙⣱⢋⡜⡫⢆⢧⢣⠽⣭⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⣵⡹⢆⢧⠳⣍⠞⣦⡙⢶⣉⠷⣘⠮⣱⠹⢆⠀⠀⠀ ⠀⢀⡴⣛⢮⡱⣋⠦⣝⡢⢱⡕⣪⢜⡱⣏⢮⣝⣺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢫⡞⣹⢬⣛⡴⣙⢦⡹⡜⡱⢎⡵⢛⡹⡦⡀⠀ ⢠⡎⢳⠉⠒⠃⠉⠈⠀⠀⠀⡞⢱⡎⡗⣮⢳⣮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣭⠓⣧⠓⣮⡝⣮⠁⠉⠁⠛⠊⢣⠓⣽⣵⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣣⡝⡾⣱⢮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⡧⢯⡝⣎⢷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣛⡵⣫⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢣⡞⣝⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣞⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡼⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠟⠛⠛⠛⠛⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣤⣤⣠⣠⣠⣶⣶⣷⣆⣘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⢿⣿⣿⠟⡟⠉⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠣⠬⢴⣫⣤⣽⣖⠈⠀⢡⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠄⣼⣾⣿⣿⣿⡆⠄⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡚⠹⠿⠛⣒⣨⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⣿⣿⣿⠿⠋⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇⠈⠉⠛⠉⠀⠀⠀⣸⣿⣷⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢾⣿⣿⣶⠄⠀⠀⠀⢀⣴⣿⣿⡟⣒⣫⠵⠦⣄⡀⠀ ⠀⠀⠀⠀⢠⠔⠊⠉⠐⠢⠿⣿⣿⣴⣽⣶⣴⣺⣷⣿⡿⠯⣅⣀⣀⡀⠉⠀⠉⠓ ⠀⠀⠀⡰⣁⣤⣶⡖⣚⡻⠽⠟⠛⠛⠉⡏⠉⠉⠉⠒⠓⠒⠛⠻⠶⢯⣯⣽⣇⠜ ⠀⠀⢠⢳⣿⠟⠉⢁⣀⠤⠤⠠⣒⢒⣺⣻⣽⠉⢳⠖⣶⣦⢄⢤⠤⣀⡀⠀⣇⠴ ⠀⠀⡞⠙⠯⣶⢎⡉⠦⠖⠚⠛⠉⠉⠉⠀⠀⠉⠉⠉⠛⠛⠚⠳⠿⢶⣿⣽⣀⠠ ⠀⠀⣿⡗⠤⡝⢁⣀⠠⠤⠤⠖⠒⠒⠊⠉⠁⠐⠒⠒⠒⠶⠦⠤⣠⣀⣈⡭⠤⠔ ⠀⠀⣇⡈⠒⠲⡟⠁⠀⠀⠠⠤⠠⠤⠐⠒⠒⠤⠤⠤⠤⠄⣀⣀⡀⠘⢹⣤⡤⢴ ⠀⠀⢷⣯⣻⢶⣶⣤⣆⠤⠤⠤⠤⠄⠀⠠⠤⠤⠤⠤⠤⢄⣀⣀⣀⣩⡷⠿⠟⠻ ⠀⢀⠆⠈⠙⠻⢿⣆⢀⣀⡠⠤⠤⠤⠤⠤⣀⣀⣀⣀⣀⣀⣀⡀⠀⣸⡀⠀⠀⢰ ⠀⣼⠀⠀⡀⠀⢸⠇⠠⠄⠤⠤⠀⠠⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡬⠅⠀⠀⠀ ⢀⡇⠀⠀⠫⡰⡗⠤⠄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⡀⡇⠀⠀⠀⠀ ⢸⠁⠀⠈⠀⣹⣗⢖⠒⠤⠤⠤⠄⠀⠀⠀⣀⣀⡀⣀⣀⣀⣈⣀⢠⡟⠀⠀⠀⢠ ⢸⠀⠀⠀⠀⣹⢈⠑⠂⠤⠤⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠁⠀⠀⠀⢸ ⠀⠀⠀⠀⢡⣧⣄⠈⠑⠒⠀⠤⠤⠄⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣿⠀⠀⠀⠀⡈ ⠀⡄⠀⠀⢸⡏⠣⢌⡑⠒⠠⠤⠤⢀⣀⣀⣀⣀⣀⣀⣀⢀⡀⣀⣿⠀⠀⠀⢠⡇ ⠀⡇⠀⢀⣜⣟⡢⢄⣉⠐⠒⠒⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⡟⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⣻⢿⣏⡒⠬⢉⡐⠒⠢⠤⠤⠤⠄⠀⠀⠀⠀⠀⢀⡤⡇⠀⠀⢀⡇⠀ ⠀⠘⣀⣼⣿⣷⣅⡻⡶⣦⣍⡁⠀⠒⠂⠐⠒⠒⠒⠒⠤⠔⣀⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⣿⣿⣿⣿⣟⢿⣶⣤⣍⡛⠙⠻⠶⠖⠚⡉⢩⡤⣕⣿⣷⣿⡁⠙⣿⠟⠁⠀ ⠀⠀⢸⣿⣿⣿⣿⣤⣜⢿⡿⡿⣿⢿⣷⢶⣶⢾⣿⣿⣋⢫⣽⣿⣷⣨⠇⠀⠀⠀ ⠀⠀⠀⣿⣿⣯⢹⣿⣿⣾⣿⣄⣿⣿⣿⣥⡾⣆⣘⡛⢻⣿⣷⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣭⡝⠚⡛⣋⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢯⢛⠿⢻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⡉⠉⠟⠆⠀⣨⡀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⣧⠙⠀⠁⠀⠀⠜⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⣀⣘⣮⣆⣣⣰⡌⣇⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣫⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⠀⠀ ⠀⣼⣠⣤⠃⢙⣦⣀ ⢬⣿⡥⠌⢣⡞⠀⠀ ⠀⠹⠀⠀⠀⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⢠⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⢸⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡟⠀ ⠘⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⠀⠀ ⠀⢿⣿⣿⠀⠀⠀⢀⣴⣾⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠀ ⠀⠈⢿⣧⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣴⣶⣿⡿⠁⠀ ⠀⠀⠀⠹⣆⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⢈⣨⣦⣄⡀⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⠁⢀⣠⠶⠋⠁⠈⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⡴⢻⠀⠀⢀⣠⠴⠊⠉⠀⣠⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣾⣴⣾⠔⠚⠍⠀⢂⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠔⠚⠉⠀⣀⢤⠚⢷⣾⡉⠂⠀⣈⣶⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⠤⠖⠒⠋⠉⠁⣀⡤⠤⠒⠒⢊⡉⠀⠈⠻⣶⡿⣯⡴⣪⣵⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠞⠉⠀⠀⠀⠀⠀⢰⠋⠀⢀⡀⣴⣄⠈⠻⣾⣶⡄⠀⠉⠋⠀⠙⠮⠅⣀⣀⡠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠃⠀⠀⠀⠀⠀⠀⠀⣈⡉⢻⣾⣿⣾⡿⣿⣷⡀⠉⠁⢀⣠⠆⠀⠀⣀⡠⣤⣰⡤⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⢻⣟⣮⣹⠾⠬⠓⣖⠚⢉⠇⣤⡾⠛⣋⣉⣉⡠⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣧⠾⢇⠀⠀⠻⠿⠃⠎⣸⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢇⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢀⠚⣧⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣆⢹⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡴⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠯⣏⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡤⠊⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⠈⠛⠦⣄⣀⠀⠀⠀⠀⠀⠀⣀⡴⢺⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠉⠛⠒⠲⠶⣖⠋⣩⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣶⣾⣿⣷⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣟⠯⠓⣉⣩⣭⣝⣻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠗⢡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⢠⣿⣿⣿⣿⣿⠿⢿⣿⣀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣿⣿⠋⠀⠀⠀⣨⣩⠉⠀⢹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⡏⣀⣀⣀⣀⢧⣿⠂⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⠗⡤⢤⣀⡉⠊⡱⢋⣉⣉⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡝⣿⣿⠀⠈⠙⠿⠃⠀⡇⠽⠛⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⡀⠀⣀⠤⠾⣄⡹⣄⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣋⢹⣿⣿⣷⡾⢄⠀⠀⠀⠀⢈⣶⣿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⣸⣿⣿⣿⣿⣿⡏⢻⣿⣿⣇⠈⠡⢄⣀⠐⢉⣿⣿⣴⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⢻⣿⣿⣿⠀⠀⠻⣿⣿⣷⣤⣄⣠⣴⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠔⠒⠒⠉⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠉⠛⢿⣿⡿⠛⠋⠘⣿⣿⠿⢯⠛⠂⠤⢄⡀⠀⠀⠀⠀ ⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡇⠀ ⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⢣⠒⠲⠤⣀⡀⠀⡀⣀⠤⠒⠂⠸⡀⠀⢱⠀⠀⠀⠀⠀⠀⠙⣄ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⢣⡀⠀⠈⠀⠈⠀⠃⠀⠀⠀⠰⠧⠀⠚⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠲⠻⠷⠒⠞⠂⠸⠣⠲⠖⠖⠀⠀⠻⠻⠿⠼⠟⠿⠧⠿⠃⠀ 🚩🚩 Jai Shree Ram 🚩🚩⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣠⣤⣄⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⣋⠽⢟⣛⣫⣭⣭⣭⣭⣙⡉⡉⡉⠉⠉⠉⠉⠉⠁⠈⣁⣭⠬⢵⣶⠶⠤⣤⣄⣉⡨⠝⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢻⢯⣌⠅⠚⢋⣉⣭⣭⣭⣉⡙⠛⠿⢶⡬⣭⠿⢿⣻⣷⢟⣿⡴⢰⣛⣋⣭⣿⣶⣠⠨⣕⠢⠁⢂⡙⡝⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣵⣿⣯⢆⣴⣴⣶⣿⣿⣿⣿⣿⣿⣷⣬⣑⢳⣯⣦⣉⠤⣯⠕⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣦⡈⣻⡇⢳⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣏⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣭⣶⡾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣷⣜⣷⡿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣧⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⢀⣼⣿⠿⡣⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⡇⠀⠀ ⠀⢰⣿⣿⡵⣻⢶⣾⣭⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠁⠀⠀⠀⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⣛⠋⠙⠍⢯⢷⣌⢿⡄⠀ ⢠⣿⣿⡿⣰⣿⣿⣿⣿⣿⣿⣯⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠃⠀⢠⠏⠉⠀⠀⠀⠛⠅⠀⠀⢹⣿⣿⣿⣿⣿⡿⠟⣋⣾⣿⣿⣿⣿⣿⣿⣦⣄⠳⡹⡞⣷⠀ ⢸⣿⢿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⣻⣿⣟⣫⣽⣿⡳⠼⠿⣦⡀⠀⠀⠀⠀⠘⣴⣿⡿⠐⣓⣾⣯⣭⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⣵⣻⡄ ⢸⣿⣌⢼⣿⣿⣿⣿⣿⣿⣿⣯⣈⣻⠛⡿⡿⡻⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⡂⢠⣴⣾⣿⣿⣶⣿⣿⣿⢿⣿⡟⣿⢻⢻⣉⣿⣯⣽⣿⣿⣿⣿⣿⣿⡄⠋⣿⡇ ⠈⢿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣽⡦⣇⡇⢪⠋⢽⡿⡹⢹⣿⢿⠟⠻⢻⣿⣿⢿⠋⠉⢿⣿⠟⠉⠟⡇⠀⡇⢡⣬⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣸⡇ ⠀⠘⣿⣧⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣄⢠⠇⠀⠸⡏⠁⠀⠀⠀⠉⠇⠀⠀⠀⠀⡡⠀⠀⠀⡇⠀⣰⣿⣿⣅⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⣬⣿⠀ ⠀⠀⠈⢿⣦⡈⣽⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡟⣧⣤⣤⣧⣤⣤⣤⣄⣤⣧⣤⣤⢤⣤⣶⡶⡶⣶⠷⢿⣽⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡹⢹⡇⠀ ⠀⠀⠀⠀⠙⢿⣿⣾⡞⠷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣸⣿⣿⣹⣁⣏⢸⣵⣸⣏⡏⡇⣆⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⠋⡴⣁⠞⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣝⢦⡙⠛⢿⣿⣿⣿⣿⣿⣯⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⢻⣽⣾⣿⣿⣧⣿⣿⣿⣾⡿⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⢾⣷⣤⡛⣍⠻⣿⣿⣿⣿⣷⣿⣟⢻⣻⣿⠿⡿⣿⣿⣿⣿⢿⣿⠟⠏⢁⣧⣷⣿⣿⣯⣿⣿⣿⡿⡿⣿⣯⣿⣿⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡷⣭⢿⣿⣮⡳⡌⢻⡻⣿⣿⣿⣻⡻⣿⣾⣤⡁⢁⡿⢸⣸⣸⣸⣤⣾⣾⣿⣪⣿⣿⣿⠟⢉⡥⢊⣾⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣮⣆⠻⣿⣷⣱⡀⢻⣧⢹⠻⢿⠿⢿⠿⠿⠿⠿⢿⠿⠿⠿⢿⠿⢿⠛⠛⡟⡟⡻⢃⠴⠋⡠⢟⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣈⠻⣧⢷⠀⢿⣾⣄⢸⡄⠸⡆⠀⠀⠀⡞⠀⠀⠀⢸⠀⢸⠀⣤⣥⡵⡃⠀⣠⠞⣠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣮⠳⡌⠻⣧⠈⢻⣿⣾⣧⢰⣇⠀⠀⢠⣯⣄⠀⡀⣸⢀⣾⣼⣿⡟⣰⢁⣾⢋⣴⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡆⠰⡀⣹⡆⠈⢻⣿⣿⣾⣿⣇⣰⣿⣿⣾⣶⣷⣿⣼⣿⣿⡟⣰⢃⡾⠁⣾⣵⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⠁⡌⣿⡄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⢫⡟⠀⣾⡟⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⢘⢿⢦⡈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⢫⣿⠀⣼⢏⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠩⣣⠛⢆⠀⠀⠉⠋⠉⠉⠉⠉⠉⢁⣠⠔⢡⡿⠃⣼⢏⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠑⠀⣉⡛⠓⢒⣋⣉⣉⣉⣩⣀⡤⠔⠋⠀⣼⢃⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠤⠽⣿⣿⣷⣿⡿⠟⠕⠊⠀⠀⠀⣰⣷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠶⠶⠶⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⡀⠤⠤⠐⠒⠒⠒⠒⠒⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠤⢒⡩⠵⠒⠂⠉⠉⠁⠀⠀⠀⠀⠉⠉⠑⠲⠤⣉⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠮⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣑⠢⢄⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢍⡲⢄⣠⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⣀⡠⠤⠄⣒⣂⠀⠀⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢔⣂⢭⣥⣶⣶⡿⠟⠉⣿⠋⢸⣽⣷⣶⡦⠭⣑⡂⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣔⡁⢤⣰⣯⡶⠋⢁⣴⣿⣿⣿⣿⡧⠤⠤⠤⠀⠸⣿⠋⠁⢀⣀⣴⣿⡓⠒⠬⢑⡢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀ ⠀⠠⡎⣵⣶⡙⠿⣿⣿⣿⣿⣿⣿⣿⠋⢹⣿⣷⡶⣶⣶⣤⡀⠁⠀⠀⠀⠀⢀⣤⣤⣬⣍⡉⠻⢷⣶⣬⣕⡂⠠⢄⡀⠀⠀⠈⢆⠀⠀⠀ ⠀⠀⠉⠪⢿⣿⣶⣶⣶⣿⣿⣿⣿⡟⣠⣿⠋⠀⠀⢀⣈⠙⡟⠀⠀⠠⠤⠼⡟⠋⠉⠉⠙⠻⣷⣿⣿⣿⣇⣼⡍⣶⣦⣭⣔⣂⠄⠣⡀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣼⡏⠀⠀⠀⣿⡿⠆⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠹⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⢦ ⠀⠀⠀⠀⠀⠋⠁⠠⣴⣿⣿⣇⢯⠸⡈⣆⠀⠀⠀⠫⠝⢀⠀⠀⠀⠀⠀⠀⠸⣛⡖⠀⠀⠀⢀⡏⢲⡿⠋⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠻⡫⡇⠮⡑⠒⠀⠀⠐⠋⠀⣠⠀⠀⠀⠘⠦⠄⠀⠀⠀⢤⡊⠀⡮⢣⠎⣠⣿⣿⡛⠛⠻⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⢼⢠⠉⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠱⡼⠉⣉⠿⢿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣰⠋⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠀⠀⠀⠀⠠⠤⠤⠤⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⢯⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇⢷⠻⣶⣤⣀⣀⣀⣤⣴⠞⠋⢀⣞⡼⢩⢷⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠋⠃⢇⠘⡄⠈⠻⣿⣿⠿⠋⠀⠀⠀⣨⠞⠀⣜⠞⢣⠉⠦⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠀⠀⠘⢆⠘⡄⠀⠙⠃⠀⠀⠀⣠⠖⠁⠀⢠⠏⠀⡌⠀⠀⡘⠀⠉⠲⢮⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡆⡆⠀⠈⢢⠈⠲⠄⣀⣀⠤⠊⠁⠀⢀⠔⠁⠀⢠⠁⠀⢀⠃⠀⠀⠀⠀⣸⠣⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠁⣿⣿⣿⣿⣿⣿⣿⣿⣧⠇⠀⠀⠀⢑⡴⡏⣉⣟⣄⢀⡠⠞⠁⠀⠀⣠⠃⠀⠀⣸⠀⠀⠀⠀⢀⠃⠀⠀⠉⠢⢄⠀ ⠀⠀⢀⠔⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⢠⠪⢕⠯⢤⣀⣉⡳⡀⠀⠀⠀⣰⠃⠀⢠⢒⣓⣒⠤⢤⣀⡜⠀⠀⠀⠀⠀⠀⠉ ⠀⢀⠎⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⢧⢰⠋⠙⠛⡛⠋⠉⠁⢀⡨⣆⢀⡾⠁⠀⠀⡄⣾⣿⣿⣿⣷⣶⢹⠀⠀⠀⠀⠀⠀⡄ ⠀⡜⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⢀⣀⠀⡿⠤⡷⣊⢵⡪⠞⠉⠀⠀⠀⠀⡇⠿⢿⣿⣿⣿⡏⡎⠀⠀⠀⠀⠀⡜⠀ ⡜⠀⠀⢠⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠉⡏⠀⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣶⣭⠴⡁⠀⠀⠀⢀⣰⡁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠲⢶⡶⠶⢺⠗⠒⢺⡖⠒⣒⠶⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣭⣄⣀⢀⡷⠀⠀⠀⠀⠀⠈⠳⣼⠀⠀⠀⣧⠞⠋⠀⠀⠀⠀⢸⣇⣤⡤⠶⠿⠶⢤⣤⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣶⣟⡋⠉⠀⠀⠈⢙⣿⣇⠀⠀⠀⠀⠀⠀⢀⠏⢑⣦⡚⠙⡆⠀⠀⠀⠀⠀⢹⣿⣧⠀⡀⠀⠀⠀⢨⣽⣻⣦⣄⠀⠀ ⠀⠀⠀⣴⡿⠟⠛⠻⣦⠀⡄⢠⣧⡟⣿⣿⣦⠀⠀⠀⠀⠀⢈⠷⠋⠀⠙⢷⣷⠀⠀⠀⠀⣠⣿⣿⠙⢿⡵⣀⣶⣶⠏⠉⠀⠈⢻⠇⠀ ⠀⠀⠀⠋⠀⠀⠀⠀⠻⣿⣿⣿⠏⢰⡏⢻⢿⠳⣤⡀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠃⣀⣤⣾⠟⡿⢹⡧⠘⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⡰⣾⡇⠈⠈⠃⠈⢿⡓⠲⣤⠀⠀⠀⠀⣴⡞⠛⠿⠋⠋⠀⠁⢸⡗⣂⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⣿⣿⡇⠀⠀⠀⠀⢀⣴⡶⣾⣷⣄⣠⣼⣿⣶⣤⣀⡀⠀⠀⠀⣸⣧⣿⣀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⣿⣿⣇⠀⣀⡴⠾⣽⣿⣶⣿⠯⣿⣿⣿⣿⣿⣿⣎⠛⢳⣆⠀⣸⣿⡿⠛⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠈⢻⣷⣏⣭⡴⠚⠛⢾⣿⣷⣿⣿⣿⣿⣿⣿⡿⠋⠛⢦⡨⣷⣿⠟⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢹⣯⡾⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⢻⣿⠏⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠛⣿⡀⠀⠀⠀⠀⠀⠻⣿⣿⠟⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠹⣷⣀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⡼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠦⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ MADE BY VEE vv.meilleur on ig dawg
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣏⣟⡻⣟⣿⣿⣦⢀⠀⠀⠀⠀⠀⣘⡯⡜⡠⠃⠀⡀⠈⢇⡰⢁⠈⢀⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣮⡽⣞⣳⣻⢿⣷⣄⠀⠀⠤⡘⣽⢚⡵⡱⢄⡰⠘⡤⣈⣵⣿⣷⡟⠄⡀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣞⣳⢯⣟⣿⣿⣾⣄⠳⣘⡧⠛⠚⠳⣭⡇⢀⡻⢁⡼⢃⡿⣏⠩⠡⠁⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣀⠔⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣟⣾⣳⡿⣿⣿⣝⣳⣽⡹⣏⠷⣄⢳⡎⣴⠋⠀⣽⣻⠅⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⣴⠊⢀⢄⠔⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡒⢦⡀⠈⠑⠲⣌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣓⣽⡯⣋⣿⡁⣿⣦⡴⣻⣥⣴⠎⣄⢀⢀⡀ ⠀⠀⠀⠀⠀⢀⠔⠀⡠⠚⢁⠆⣠⠊⢀⡨⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠓⢤⡀⠈⠓⢭⣻⣿⣿⣿⣿⣿⣿⣿⣛⣭⢷⣻⡽⣽⣿⣭⡵⢾⣏⢳⡘⢜⢢⡃⠂⠀ ⠀⠀⠀⠀⠀⠊⡠⠈⡔⢠⠇⢠⠁⣠⠎⠀⠀⠀⢠⡾⠁⠀⡄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠱⡄⠘⠢⠤⡀⠙⢾⡻⣿⣿⣿⣿⣿⣿⣞⣯⢷⣿⣿⣿⣿⠇⢸⣏⡧⢄⢸⣷⣿⣦⣄ ⠀⠀⠀⠀⢀⠜⠀⡘⢠⠃⢠⢃⢞⡝⠀⠀⠀⡴⢃⠇⠀⡀⠘⣄⠀⠈⠑⢦⣀⠀⠀⠀⠀⠈⢢⡀⠀⠉⠲⣌⠳⣜⣹⠻⣿⣿⣿⣿⣾⣿⣳⣿⣿⣿⣇⢸⡷⡽⣎⣀⣿⣿⣿⠟ ⠀⠀⠀⠀⡜⠀⢀⠃⡟⢀⣇⠟⣸⠀⠀⠀⣸⢠⠟⢸⠀⠻⡀⢿⣄⠀⠀⠀⠣⣿⣄⠀⠀⠀⠀⠻⣄⠘⠤⠘⢧⡸⣇⢧⠀⡘⠻⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠿⠃⠀ ⠀⠀⠀⠀⠀⠀⠆⡸⠀⣼⠇⢀⡇⠀⢀⣼⡷⠃⠀⢸⣧⠀⠱⡸⣏⠳⡀⠀⠀⠀⠛⣟⠦⣄⠀⠀⠈⠣⣀⠀⠂⠙⣿⣞⢧⠠⢡⢀⠈⠹⣯⣙⠛⣿⣿⣾⡛⠋⠉⠡⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡘⢠⠃⢠⡏⠀⢸⠀⠀⢸⠏⠃⠀⠀⢸⣻⡄⠀⠀⢻⣧⠹⣦⠀⠀⠀⠀⠙⠮⣝⡳⠲⠤⢌⡃⠠⠀⠀⠛⣿⣎⢡⠎⠌⣐⡸⢟⣧⣿⣿⣿⣿⡄⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⢁⡇⠀⡼⠀⠠⠀⠀⢠⡟⠁⠀⠀⠀⢸⣧⢧⠀⠀⠘⣿⣆⠛⠷⡄⢠⡀⠀⠀⠈⠙⠛⠓⠶⠴⢤⣱⣄⣂⣈⣿⣤⣾⠾⣉⠄⣹⡞⢿⣿⣿⣿⣷⡀⣴⣿⣿⡇⠀ ⠀⠀⠀⠀⢀⠎⡀⢰⢃⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⡼⢸⡞⣆⠀⠀⢹⢿⣧⠀⠙⢦⠙⢶⣄⡀⠀⠀⠀⠀⠀⠠⠤⢤⣀⣠⣤⣞⣳⣴⠴⢚⡧⠘⣯⢿⣿⣿⣿⣧⣿⣿⡷⡆⠀ ⠀⠀⠀⠀⠀⡰⠀⣾⣏⠀⠀⠀⠀⣼⠀⠀⠀⠀⢸⡇⠠⢷⡸⡆⠀⠈⡆⠹⣷⡀⠀⠙⢦⣈⣻⣿⠶⡶⠶⢚⡒⢡⡀⢄⠠⢀⠄⠠⣀⣶⣿⣘⡰⠘⢯⣿⣿⣿⣿⣿⣿⣟⣧⠀ ⠀⠀⠀⠀⢀⣃⠼⣽⠃⠀⠀⠀⣠⣿⠀⠐⠀⠀⣾⣄⣀⣉⣧⣹⣄⠀⢣⠀⠈⢻⣄⡤⠖⠋⠳⢤⣀⢀⣰⠃⠼⢦⣴⣬⣤⣧⣾⣾⠿⠧⠿⢿⣽⣷⢦⡽⣿⣿⣿⣿⣿⣿⣽⡆ ⠀⠀⠀⠀⣠⠏⡼⢡⠀⠀⠀⢰⣿⣿⢠⢁⣴⠂⡟⠀⠀⠉⠉⢻⡹⣆⠈⣇⠀⠀⠈⠑⠦⣄⣠⢒⣭⣿⣷⣮⣶⣶⣶⣾⣯⠷⠋⠤⣤⣀⡀⠀⠈⠻⣟⢶⡜⣿⣿⣿⣿⣿⣷⢿ ⠀⠀⠀⡜⢁⡼⢁⠇⠀⠀⢀⠏⣾⣿⠈⣟⣦⣸⢻⣄⣀⣦⣤⡀⠙⣽⣄⠘⢆⠀⠀⠀⠀⠀⡸⠿⢷⣦⣬⣙⣿⣿⠙⡻⣧⣌⡱⢦⣤⣈⡉⠙⠂⠀⠈⢣⡙⢿⣿⣿⣿⣿⣿⣻ ⠀⠀⣜⠤⠎⡠⠃⠀⠀⢀⢂⣼⣿⡟⢨⠇⣼⣿⣿⣿⣿⡿⣿⣿⣷⠬⠻⣦⡈⠣⡀⠀⠀⠀⠀⠀⠀⣉⢻⣧⣾⡥⠚⠀⠀⠉⡏⠓⣲⣯⢽⣳⣄⠀⠄⠀⠹⣆⢻⣿⣿⣿⣿⣿ ⠀⠚⠀⠀⡴⠁⠀⢀⠀⣶⣾⣿⣿⡇⠋⢸⣿⣯⡀⠈⠻⣍⠛⢻⡿⠀⠀⠈⠛⠷⣌⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⡼⢋⡾⣇⢌⣩⡙⠦⣄⠀⠘⣧⣿⣿⣿⣿⣿ ⠀⠀⠀⠘⠀⢀⡠⢶⡿⣋⡾⢉⣾⠀⠀⣽⣿⣄⠉⠒⠤⠬⠽⠋⠁⠀⠀⠀⠀⠀⠈⠉⠛⠷⠶⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⣗⣫⣴⡏⠄⣻⢈⡇⢹⡀⢿⣦⡀⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣠⠔⣋⡼⠋⢴⡟⣰⣿⠇⢀⡾⣽⢿⣌⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣡⣼⣷⣾⣤⣤⣿⣂⡽⠈⣧⣿⡾⢧⣿⣿⣿⣿⣻⣿ ⠀⢀⠞⠁⠘⣟⠠⢁⣏⡾⣽⢃⡴⣯⢰⡟⣺⣟⣧⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿ ⠐⣼⠀⡐⠀⠙⢢⣸⡿⣷⡟⠉⣰⣿⣼⡇⠸⢿⣶⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⠇⠀⠀⠀⠀⣠⠎⣹⣹⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿ ⠀⠈⠳⢦⣀⣀⣀⡨⠿⢳⡆⢠⠟⡾⣿⡇⠀⢼⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠘⠛⢿⣿⣩⣭⠷⠋⠀⠀⠀⠀⣀⠞⠙⣶⠾⠟⠛⠋⢁⡺⡽⣉⣿⠿⢿⣿⣿⣿⣿⣿⣿⢿⣽⣿ ⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡇⡏⢰⠃⡟⣷⢠⣿⣿⣿⡟⢻⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⢨⣷⣶⣴⣮⣯⣵⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣯⣿ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠃⠠⣀⣾⣧⢿⣾⣿⣿⣿⣡⣯⣿⣿⣿⣿⣟⠲⠤⣄⡀⠀⠀⠀⠀⠀⢀⡴⠚⠁⢀⢠⠞⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢠⣶⣿⣿⡟⣿⡶⠶⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣷⣿⣿⣏⠑⠢⠤⠤⠔⠋⠀⢄⣰⣾⠏⡾⡅⣳⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣻⢽⡺⣝⢯⣿⣻⣿⣿ ⠀⠀⢀⣾⣿⣿⣿⡷⣿⢻⣶⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣷⣥⣐⠀⠂⣤⣷⣾⣿⡟⢸⠁⣷⠉⣿⣿⣟⣷⢿⡿⣽⣷⣿⣿⣿⣷⡿⣽⢶⣧⠿⠊⠁ ⠀⠀⣸⣟⣿⣿⣿⣷⡻⣟⡼⢻⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⡇⢾⠀⢻⣷⡘⠿⣾⡽⣯⣟⣳⣟⡾⣽⣿⣿⡿⠟⠋⡡⠄⠀⠀ ⠀⢠⡟⢫⣿⢿⣿⢿⣷⣝⢷⣄⠙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣄⠀⠹⢭⡓⠌⠙⠳⣯⣷⣾⣿⡿⢟⡡⠔⠊⠁⠀⠀⠀⠀ ⠀⠌⠀⣿⡽⣿⣿⣟⣿⣻⣿⣿⣷⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢴⣸⢧⣹⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⢻⣧⣤⣄⣌⣁⣀⠀⣹⡿⣋⠵⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣘⢧⣟⡿⣿⣾⣟⣷⣛⣶⡻⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢋⣴⣿⣿⢲⣿⣿⡟⣹⢛⣿⣿⡻⢿⣿⣿⣟⡼⢣⡀⢿⣿⣿⣿⡿⡟⣟⠉⠁⠀⠀⠀⠀⣤⣠⣦⣀⠀⠀⠀ ⠀⠀⡼⣳⣞⡿⣿⣳⡟⣾⡱⢏⡷⣭⢻⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣼⣿⡿⢯⣛⡏⢷⢺⣯⣟⣯⣥⣇⣹⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⡦⠀⠀🌊
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣛⣉⣙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠋⠁⠀⠀⠀⠑⣿⣆⠀⢠⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⡴⠋⠑⣄⢤⡤⠧⣤⣬⣦⢤⣵⣤⣀⣠⢴⣶⡶⠶⠿⠿⣶⣶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣘⣤⠿⠛⠛⠅⠀⠀⠀⠈⠉⠙⢿⣧⡀⠀⣀⣀⣀⠀⠙⢿⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⣲⡟⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡿⡍⠁⠀⠙⡗⠀⠈⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠊⣷⠋⠰⠒⠄⠀⠀⠀⠀⠀⠀⠀⡖⡆⠀⠀⠀⠀⠈⢇⢧⠀⠀⠀⠁⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⣾⣛⠀⠀⢀⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣯⠇⡴⣫⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⠀⠀⠀⠀⠀⡇⡟⠃⠀⠀⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⡎⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣯⣷⣷⠀⠀⠀⠀⡇⡧⠤⠶⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⢱⠃⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⡟⡷⣷⣯⡇⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡤⣞⣉⡍⢏⡼⠀⠘⠷⠃⠁⣀⣀⣀⠀⠀⠀⠀⣇⢿⣿⡿⢼⡾⠁⠀⠀⠀⣿⣒⡲⠶⠦⠀⠀⠀⠀⠀ ⠉⢁⠖⠉⢀⡜⣷⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠛⠉⠙⠉⠉⠀⠀⠀⠀⣾⠳⢤⣄⠑⠦⡀⠀⠀⠀⠀ ⠀⣎⡤⢺⠋⠀⠘⡧⡀⠀⠸⠤⠞⢧⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡜⢹⡧⢄⡘⢌⠑⠦⣳⡀⠀ ⠘⠁⢠⠃⠀⡠⠔⠉⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠡⠖⡡⠊⣿⠀⠀⠈⠳⠀⠀⠁⠀⠀ ⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠈⣷⣍⠛⠛⠭⠭⠭⠭⠟⢋⡥⠞⠁⠀⠀⠉⠀⠀⣷⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠢⣝⠒⠒⠒⠒⡉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡏⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢆⡀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠘⣼⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣽⠇⠓⠤⠥⠭⠭⠭⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡤⠊⢱⡘⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣿⡶⣒⣶⡀⠀⠀⣠⡶⠶⠒⠒⠖⠋⠀⠀⠀⡀⠀⠀⠀⣀⠔⠻⡼⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣼⠃⠚⢁⣼⡇⠀⢰⣇⡒⠒⠂⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠁⠀⠀⣸⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠈⣝⠇⠀⠀⢳⡄⠉⠁⠀⠀⠀⢀⡴⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠧⣀⣀⡠⠶⠋⠁⠀⠀⠀⠀⠉⠉⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⣉⠩⠥⠦⠀⠀⠀⠀⠈⢈⠁⠒⠤⡈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠺⡀⡰⠭⠤⠤⣴⠀⠀⠀⠀⠀⠀⠘⠅⣀⣀⡙⡤⠊⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⢓⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⠎⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⢀⠀⠀⢀⡠⠊⠀⠀⠀⣀⣾⣷⡠⠔ ..⡀⡀⠀⠀⠀⠙⠢⡀⡠⠤⣸⠀⠀⠀ ⠀⠀⠀⢏⢆⠀⠀⠀⠑⠢⠼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠈⠀⠀⠀⢀⡴⡱⠁⠀⠀ ⠀⠀⠀⠈⢦⡑⢄⡀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⢀⡀⡔⢋⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠣⠌⣑⡎⠐⠒⠚⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠑⠀⣉⣉⠥⠤⠚⠁⠀⠀⠀⠀⠀ ⣀⣀⣀⣠⠤⠤⢄⠒⢊⡯⣙⣛⣛⣛⣯⡲⢤⠄⢀⡀⠀⠠⠤⠔⢞⣗⣛⡋⣉⣉⣏⣉⠐⡢⠤⠤⠤⠄⢀⡀ ⠀⠉⠁⠈⠀⠉⡩⠝⠋⣹⣁⡤⠒⠀⠉⢉⣋⠕⠘⠂⠐⠂⠲⣹⠉⠉⠀⠒⡤⣀⣏⡁⠒⢌⠉⠉⠉⠉⠁⠀ ⠀⠀⠀⠀⡴⠊⡩⠒⢩⡎⠁⡠⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⢦⠀⣑⡌⠑⢅⣉⢢⡀⠀⠀⠀ ⠀⠀⠀⡾⠋⠁⠀⢠⠋⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠘⡄⠀⠀⠉⠻⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠓⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠴⣿⣷⡀⠀⢠⣾⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣷⣿⢷⣿⣷⡀⠀⠀⢀⣤⣤⣌⠙⠧⣀⣸⣏⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀⢀⣩⡝⠛⠉⠁⠀⠀⠀⠀⠉⠙⠻⣦⣄⠀⣀⣀⣠⣴⣶⣿⣛⣿⣿⣯⣽⣿⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣇⢠⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⠛⠛⠿⠷⣿⣿⣿⣷⡿⠟⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⢰⣿⠁⠘⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⠋⠙⠋⠁⠀⣸⡏⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢠⣴⢦⡄⢀⣀⠀⠀ ⠈⢿⣤⣀⣀⣀⣰⡟⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠛⡇⠀⠀⠸⣧⠈⠿⠋⣹⡇⠀ ⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⢘⡟⠀⠀⠀⠀⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠇⠀⠀⠀⢿⣦⡀⠀⠙⠷⠶⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠆⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣠⣤⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠿⠿⠿⠿⢿⣧⣀⢽⡍⠻⢶⡄⠀ ⠀⠀⠀⠀⠀⣴⠟⠋⣵⡀⣼⡿⣷⣴⣶⠿⠀⠘⠛⠛⠛⠿⠿⣶⣤⣀⢠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠿⠎⢻⡆ ⠀⠀⠀⠀⢸⣏⠻⠇⠈⠁⠈⣴⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠰⠦⣸⡇ ⠀⠀⠀⠀⠀⢻⣦⡀⠠⣶⡶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⣠⡿⠁ ⠀⠀⠀⠀⠀⣀⣭⣧⣤⣤⣤⣼⣿⣶⣤⣀⣀⣀⠀⢀⣀⣀⣠⣴⣿⣯⣼⣿⣷⣶⣤⣤⣤⣤⣤⣶⣾⣿⣿⣶⣶⣾⣯⣤⡀ ⠀⠀⠀⠀⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠛⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀
⠀⢸⡒⠀⠄⠀⠀⠀⡀⢀⠀⠀⠠⠀⠀⠀⠀⢀⢴⣀⠀⠀⢀⠑⠻⣿⡷⣤⠚⠀⣀⡀⠉⢰⢓⠀⠀⢀⠀⠀⠍⡘⣿⣿⣿⣿⣿⡛⢏⢿ ⠀⠀⡁⠀⠐⠁⠈⡇⢻⡗⠄⠀⠀⠀⠁⠀⠀⢸⢭⠋⠈⠀⠀⣀⣠⡇⡘⠹⣆⡀⠃⠄⢒⣸⠈⠀⠀⢨⣿⣷⣢⣽⣿⣿⠿⠯⠳⡩⠌⠈ ⠀⣠⠤⠂⢴⠲⢎⡵⠚⠊⠁⠀⢀⠀⠀⠀⠀⠀⠀⢇⠲⠄⡞⠻⠙⠀⠁⠱⢊⠴⣡⠞⣼⢿⡧⢀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⣱⠍⠤ ⣰⣿⣷⣭⡆⡁⢈⠣⣀⠠⠀⣀⣬⢀⠀⠀⠀⢀⠇⠂⣌⡐⡈⠄⡀⣄⡠⡘⠁⠀⠀⠀⢀⡟⠁⢢⡲⡝⡉⠻⣿⣿⣿⣧⡀⢀⡳⣽⣿⡷ ⠿⣿⣿⢫⣑⠀⠂⠀⠀⠁⠓⡌⠀⠀⠂⠀⠀⠀⠠⠁⠊⠳⡰⠐⢄⣻⣷⡈⠀⠀⠀⠀⠘⠳⠀⠈⠛⢃⡀⢀⣽⣿⡟⠁⠙⣯⢖⡻⢿⡝ ⣝⣷⢿⠁⠀⢹⠠⢀⠠⢀⠱⢤⠃⠀⢀⢠⣁⡀⠀⠀⠀⠀⠁⠈⠐⠿⠿⠇⠂⠀⠀⣤⣀⣠⡤⠀⣀⣘⣼⣿⣿⣿⠛⠲⣞⣿⣯⡔⠡⠀ ⠉⢻⣏⢦⡰⣡⠀⡄⢂⠈⣐⢣⠈⡐⢎⣿⣿⣿⣧⣿⡜⡔⠁⠑⣐⡀⠠⡀⠀⠀⠀⠿⢛⡿⣄⡋⠀⢹⣿⣿⣿⣧⣭⣱⢾⣿⣿⣿⣴⣡ ⠀⢨⠩⣆⡽⣷⣿⣾⣦⡱⣾⣯⣷⣻⡝⡦⣏⣿⣿⣿⣿⣇⣀⣰⣿⣿⡶⠂⠀⠀⣵⣡⣢⣟⣽⣿⣶⣾⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿ ⠀⢸⣿⣿⣾⣿⣿⣿⣷⣿⣻⣿⣿⣿⣿⠻⣝⣻⢿⣿⣿⣯⣿⣷⣾⢿⣷⡄⠀⠺⣾⣿⠁⠈⢻⠿⢿⣿⣿⣿⡿⢿⡹⢲⢱⣯⣿⡿⣟⣿ ⡆⢢⢙⡿⣻⠻⣿⢿⡹⢲⢉⠻⠍⠃⢏⡳⠦⣝⣎⠡⣃⢳⣙⠾⣭⠛⡹⣧⡀⢄⣼⣿⣶⠒⠁⠀⢀⡯⣟⣼⡳⣌⠰⣁⠻⡞⢭⣳⣿⣿ ⡛⠆⢿⠡⡁⠘⠤⢣⡑⢣⠌⡐⢈⠀⠠⢑⡸⢼⣾⡷⢬⠻⢯⡾⢍⠡⡍⠀⢸⣿⡏⠉⠙⢦⣤⡶⣏⠲⡝⣿⢻⣮⡵⣎⣷⣿⣾⣷⣿⣿ ⢆⡉⠶⠳⠤⢳⡌⡷⣭⣳⣿⡼⢂⠈⡀⠤⠉⠃⠙⢲⡀⢡⠒⡈⠌⣲⣿⣶⣿⣿⠷⠀⠀⠙⣢⢽⣾⣱⡌⣧⠛⡼⠓⡭⢾⣿⣿⣿⣿⣿ ⣦⡐⡄⠀⠀⠀⠐⠈⠉⠉⠢⢙⣦⣳⠜⠀⠀⠀⠀⢡⠛⠄⠃⣜⣴⣳⣿⣿⣷⢯⠁⠀⠀⠀⡿⠛⠿⣽⣹⡤⠓⠰⡡⠘⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⣦⣀⠀⡀⠀⢀⡀⡉⠞⣿⡷⡤⣄⣠⢐⣦⣯⣰⢬⡾⣿⣿⢿⣿⢧⣏⡀⠀⠀⡰⡅⠉⠀⠈⣳⣷⣍⣴⢡⣹⣼⡿⠛⢻⠿⢿ ⡟⡛⢿⣿⣿⡿⣈⠐⢌⠲⡰⠁⡘⣼⣿⡷⣿⣿⣞⣽⣻⣽⣿⣽⣻⣞⢿⣾⣿⣻⣿⣷⣜⣆⡙⡄⠀⠠⣼⣿⣿⣿⣿⣿⣿⣧⣀⣠⡀⢠ ⣷⣜⣻⢿⣿⣷⢦⡰⣌⣳⣴⣷⣾⣿⣽⣿⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣯⣿⣧⢟⣿⣯⣟⠿⣿⣿⣿⣿⣿⠿⡙⢯⢻⡿⣿⣿⣿⣿⣿ ⣿⣿⣷⣯⣼⣌⢣⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣽⣻⣿⢿⣿⣿⢿⣿⣿⣾⣿⣿⣿⣶⣭⣻⣿⡯⡑⠉⡐⢆⣻⣿⢿⡿⣿⢿ ⣿⣟⡻⢿⣿⣿⣶⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣴⡀⢈⠲⢡⠎⡱⢨⡑⣫ ⣷⠯⣜⠢⢏⢿⣳⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢆⡘⠢⢿⣶⣷⣿⣧ ⡜⡹⢤⠳⣌⠒⢯⡻⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠄⠁⠀⡹⣿⣿⣿ ⠐⡁⠎⠑⠠⠉⠢⠹⢌⣿⣿⣿⣿⡿⠉⠐⠈⠁⠉⠛⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣬⣶⣽⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⡀⠁⢨⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⢭⢁⡻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠁⡀⠀⠀⡐⣿⣿⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠜⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⠂⠀⡐⠀⠠⠀⠁⠀⢻⡟⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⡟⣿⣻⢿⣿ ⠊⡅⠂⠀⠀⠁⠐⣀⠂⠼⣧⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⡥⢚⢥⢫⢟⡼ ⠀⠀⠁⠈⠀⠂⡱⢠⠎⣠⠍⠙⠙⠻⠿⣿⣿⣷⣤⠀⠀⠀⢀⢀⣀⣤⣤⣤⣄⣤⣠⣬⣟⡛⠋⠀⠋⠉⠹⣿⣿⣿⠃⠀⠀⠀⠀⠉⠈⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠅⣻⡯⢿⣿⣵⣿⣽⣻⠆⠀⠀⠈⠻⡿⣟⠿⠻⠟⠻⠻⠟⠻⠛⠷⡀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠙⡷⣮⣿⣿⢯⠷⡟⠄⠀⠀⠀⢣⠝⣾⣿⡿⣿⣷⣬⣖⣢⡄⠈⠁⠀⠀⢀⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠐⠓⠋⠉⠐⠈⠀⠀⠀⠀⠢⠐⠫⣜⣶⣜⢿⢿⣸⢟⠳⠂⠀⠀⠀⢰⣿⣿⣑⢢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⠈⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⡿⡿⢁⠰⢁⠠⠀⠀⠀ ⠀⠀⠀⠀⢠⢀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⢲⡏⠁⠀⡘⢌⠲⠡⢄⡀ ⠀⠀⠀⠀⠈⠉⠁⠊⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⠯⠵⠳⠀⠀⠀⠀⠠⠈⢁⠂⡑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⠴⠃⠄⡀⠀⠀⢀⠁⢆⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠐⢰⠜⠁⠒⠤⢈⠄⠒⡠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣧⣴⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠑⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡗⠀⠀⠈⠄⠠⠀⠢⡐⠠⢄⡨⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢋⠀⠀⠀⠀⠘⡐⢄⠀⠀⠀⠀⠓⠊⠔⡤⠀ ⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠂⠀⠠⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠞⡡⠀⠀⢀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⢠⢎⣿⣏⢿⣿⣿⣿⣿⣿⣿⡿⣿⣻⢷⡟⠉⠂⠀⠄⢂⠀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠂⠀⢠⠀⢈⣿⣿⣿⢪⡟⣽⢫⣗⣻⠼⣝⣳⡏⠋⠀⠀⠀⠌⠐⠀⡀⠀⡜⣢⠑⢂⠀⠂⠠⢀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⢀⠖⠁⣄⢃⢆⠸⣾⣿⣿⣿⡇⢞⡵⣫⢞⡵⣫⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⢄⣾⡑⢆⡉⠆⡌⢂⠡⠀⠈⠐⠤⠀⠀ ⢁⠂⠁⡀⠀⠀⠀⠈⠶⣀⠚⣼⣈⣿⣿⣿⡛⢸⡇⢺⠰⡉⢞⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣡⠚⡤⣉⠞⣠⠃⠄⡁⠂⠄⠠⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢛⣼⣿⣿⣿⣿⡔⢨⣇⠧⢁⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠴⣡⢫⡔⣣⠚⡄⢡⠒⢠⢃⣼⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣏⣿⣿⣿⡎⡔⢿⣮⠛⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⢀⣾⢏⡼⡑⢦⢳⡸⢡⠎⡰⢡⢎⡵⠟⠋⢁⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣼⣿⣿⣿⣿⡤⡛⠀⠀⠀⠀⠈⠊⡢⣀⠢⠀⠀⣰⣿⢏⡎⡴⣩⢏⠖⣡⢃⢞⣱⢿⣫⠀⡽⢲⡀⠎⡔ ⠀⠀⠀⠀⠀⠀⠀⠀⠌⢠⠀⣟⣾⣿⣿⠉⠠⢶⣿⣦⢄⠀⠀⠠⡁⠌⣦⡉⢓⣼⣿⢏⡎⢴⢣⡓⢮⡙⢦⣹⡾⣡⢴⡠⢄⠙⡹⣓⡖⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠘⡗⣾⣿⠟⣠⣾⣿⣿⢧⣆⠓⢬⡐⡈⢖⡠⢩⣾⣿⡟⡬⢜⢣⠧⣙⠦⣙⢮⣏⣾⣿⡖⣍⠚⡀⢃⠳⡘⢧ ⠀⠀⠀⠀⠀⡀⠀⢄⠂⠌⠐⢯⣿⣑⠻⢿⣟⣿⡏⡾⠀⠀⠑⣙⠩⢐⣱⣿⣿⡟⡼⣐⢋⠦⡛⢴⡹⣼⢻⣼⣾⡟⣽⣴⡁⢧⠈⣣⣙⠢ ⠀⠀⠀⠀⠀⠀⠀⠃⡘⠀⠀⢺⣇⡛⢢⣼⣸⠿⠀⠁⠀⠀⣸⣿⢳⣦⣿⣿⡿⣙⠦⡡⢏⢲⡙⢦⣳⠃⠉⣉⣀⡂⢸⡾⡳⣌⠳⠀⢀⢃ ⠀⠀⠀⠀⠀⠀⠠⠡⠀⠀⠀⢺⣿⢃⣧⢧⠫⡕⠀⠀⠀⣰⣿⡏⡼⣹⢿⡿⡱⣍⠲⣡⢋⢦⡙⡶⡝⣉⢧⠻⢭⠇⣾⣽⣷⡹⣯⣵⠀⢐ ⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⣹⢯⢟⢞⡄⡘⠀⠀⠀⣰⠿⣽⢐⡳⢧⣧⡟⡱⢌⠳⣄⢋⢦⡹⢼⠏⣒⢺⠨⣹⠀⣶⣾⣶⣷⣱⡿⣌⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢣⢧⡛⠁⠀⠀⠀⣰⢭⡻⠇⣎⣝⡳⣾⢭⡑⣎⠱⣌⠚⡴⣩⢿⠐⡄⠣⢐⣣⠀⣷⣻⣿⣟⣧⢱⣎⢧ ⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⣼⠟⡭⣎⠅⠀⠀⠀⢠⢇⡧⣻⠕⣪⢞⣵⣿⢆⠳⣌⠳⣌⡙⢶⣩⣷⡅⢨⠑⢸⢆⡄⣿⣿⣟⣾⣽⣷⣾⣻ ⠀⠀⠀⠀⣏⡎⠀⠀⠀⢰⡿⣶⣀⠁⠀⠀⠀⠀⡏⡜⣶⡹⢨⣷⣻⣮⣿⢎⠳⣌⠳⣰⡙⢦⢳⣧⣛⡄⢏⣻⠂⡥⢹⣫⣿⣾⣿⡽⣷⣻ ⠀⠀⠀⠀⣼⠁⠀⠀⠀⣾⡳⡬⠸⠂⠀⠀⠀⠘⡘⣜⡧⡇⣏⢾⡱⢯⣿⢎⡳⡌⣇⢧⡚⣥⢯⣇⢽⠮⡌⢯⡙⡾⣞⣷⣿⢯⣿⣿⣳⢳ ⠀⠀⠀⠀⠀⠀⠀⠠⢹⣿⠱⢁⠉⠀⠀⠀⠀⠈⠱⣎⠷⢑⣮⢳⣽⣿⢿⣏⠶⣙⠴⣪⢕⡞⣮⣇⣎⡎⣁⠄⠴⢅⡟⣾⢯⡟⣞⣷⢯⣶
⡟⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠛⠿⢷⣶⣦⣄⠀⠀⣠⣴⣶⡾⠿⠛⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠙⢿⣷⣾⡿⠋⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⢠⣶⡾⠿⠿⢷⣶⡄⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣆⣤⣤⣤⣀⢰⣿⠋⠀⠀⠀⠀⠙⣿⡆⣀⣤⣤⣤⣰⣿⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⣀⣠⣴⣾⠿⠟⠛⢿⣿⠟⠋⠉⠙⠻⣿⣿⣤⣤⣀⣀⣤⣤⣿⣿⠟⠋⠉⠙⠻⣿⡿⠛⠻⠿⣷⣦⣄⣀⡀⠀⠀⠀ ⡇⠀⠻⣿⡟⠛⠉⠁⠀⠀⠀⣿⡏⠀⠀⠀⠀⣾⡟⠋⠉⠙⢿⡿⠋⠉⠙⢻⣷⡀⠀⠀⠀⢹⣿⠀⠀⠀⠈⠉⠛⢻⣿⠟⠀⠀ ⡇⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⢻⣷⡀⣠⣤⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣄⢀⣾⡿⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀ ⡇⠀⠀⠀⢹⣷⠀⠀⠀⣀⣴⣶⣿⣿⡿⠉⠁⠉⠀⠀⣀⣴⣶⣶⣦⣀⠀⠀⠉⠉⠉⢿⣿⣿⣶⣦⣀⠀⠀⠀⣾⡏⠀⠀⠀⠀ ⡇⠀⠀⠀⠈⢿⣷⣄⣸⡿⠋⠀⠀⣿⣇⠀⠀⠀⢀⣼⡿⠋⠁⠈⠙⢿⣧⡀⠀⠀⠀⣸⣿⠀⠀⠙⢿⣇⣠⣾⡿⠁⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⣩⣿⣿⡇⠀⠀⠀⢸⣿⡷⠀⠀⢸⣿⡁⠀⠀⠀⠀⢈⣿⡇⠀⠀⢾⣿⡇⠀⠀⠀⢸⣿⣿⣍⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⢀⣾⡿⠋⢹⣷⣄⠀⠀⣿⡏⠀⠀⠀⠈⢻⣷⣄⡀⢀⣠⣾⡟⠁⠀⠀⠀⢹⣿⠀⠀⣠⣾⡟⠙⢿⣷⡀⠀⠀⠀⠀ ⡇⠀⠀⠀⣸⡿⠀⠀⠀⠉⠻⠿⣿⣿⣷⣀⣀⣀⠀⠀⠉⠻⠿⠿⠟⠉⠀⠀⣀⣀⣀⣾⣿⣿⠿⠟⠉⠀⠀⠀⢿⣇⠀⠀⠀⠀ ⡇⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⣼⡿⠁⠙⠻⢿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⠋⠈⢿⣷⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀ ⡇⠀⣾⣿⣷⣤⣀⡀⠀⠀⠀⣿⣇⠀⠀⠀⠀⢿⣧⣄⣀⣠⣾⣷⣄⣀⣠⣼⡿⠁⠀⠀⠀⣸⣿⠀⠀⠀⢀⣀⣤⣾⣿⣷⠀⠀ ⡇⠀⠀⠀⠉⠉⠻⢿⣶⣶⣴⣾⣿⣦⣄⣀⣠⣴⣿⣿⠛⠛⠉⠉⠛⠛⣿⣿⣦⣄⣀⣠⣴⣿⣷⣦⣶⣶⡿⠟⠉⠉⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿⠋⠛⠛⠛⠋⠸⣿⣄⠀⠀⠀⠀⣠⣿⠇⠙⠛⠛⠛⠛⣿⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠘⠿⣷⣶⣶⣾⠿⠃⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⣠⣾⡟⢻⣷⣄⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣀⣴⣶⡾⠿⠟⠋⠀⠀⠙⠻⠿⢷⣶⣦⣀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⢤⡴⣽⣶⢶⡿⣖⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣽⣾⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣾⣿⢟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡖⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣻⣟⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣿⣿⣿⣿⡟⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡿⡻⣿⣿⠋⠰⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣇⣿⣿⠀⠀⡘⡘⢅⠘⠛⢋⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣻⣿⡀⠀⠜⡰⢈⠌⡱⣣⢙⡯⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣄⡘⠄⡓⠖⣢⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢋⠞⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⡵⠛⠀⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣾⣿⣿⠋⡄⡇⢰⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⣾⣿⣿⣿⠇⠀⢘⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⠀⠀⢮⠘⠀⠡⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠦⣄⠄⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⠀⠜⣼⠀⠁⠀⢢⡠⣿⣿⠿⣿⡿⣿⣿⣿⡟⢬⠑⣜⣦⠢⠀⠀⠀⠀⠀ ⠀⠈⠏⠉⡟⡛⢿⣮⠘⣼⠀⠀⠄⠀⠳⣩⡆⠚⡷⢮⡵⣛⡟⢾⣄⠣⢼⣇⢣⠐⡀⠀⠀⠀ ⠀⠀⠁⡸⣍⠷⡾⡄⣷⡈⠀⠀⠘⠀⠀⢸⠇⢰⡹⢧⣻⣽⡸⣡⠯⣓⢞⡇⢎⠥⡁⠀⠀⠀ ⠀⡈⢠⡛⣬⢻⠃⣷⣿⣟⡀⢀⠀⠡⠀⡌⡆⠲⣝⢯⡖⣿⡱⢆⠯⡽⣯⡼⣊⠾⠁⠀⠀⠀ ⢀⠃⢬⢳⡹⣾⠀⣿⣿⣿⣧⠸⠀⠀⢆⢱⠃⢴⣛⡼⣳⣯⣳⡜⢦⡳⣟⠃⠙⠀⠀⠀⠀⠀ ⠰⢀⡏⢶⣹⡇⠀⣿⣿⣿⣿⣷⡀⠀⢰⢘⡀⡗⣎⢷⣣⡷⢭⡻⣷⣿⣯⠢⣄⠀⠀⠀⠀⠀ ⡂⢼⡘⣧⣿⢠⡀⣡⣿⣿⠟⠛⣆⠀⢤⢷⠀⣽⣚⡬⢧⡹⢶⡹⡜⡽⣌⢫⣎⠀⠀⠀⠀⠀ ⡏⣶⠹⡜⣥⢫⢵⡳⣯⢿⠐⠔⠮⠗⢸⢂⢥⣞⣵⣻⣎⠳⢧⢻⣙⣩⡜⠉⠈⠣⡀⠀⠀⠀ ⠹⠶⠯⠜⢶⣫⣾⣵⣻⣦⢔⡨⣿⢳⢧⢗⣠⡀⢰⢏⣾⣛⣷⣻⣽⣻⣴⣳⣤⣀⠘⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢏⠐⢹⠋⠀⠃⠰⠀⠿⡚⠷⠫⡖⡽⣺⣷⣛⣮⣿⠾⢾⢶⣿⡌⡄⠀ ⠀⠀⠀⠀⠀⠠⢐⠖⠁⡰⠅⠠⠄⠀⠤⡃⠀⠳⠒⠌⠓⡲⣏⡿⣽⢯⣿⢀⡒⠯⠀⠛⢠⠀ ⠀⠀⠀⡀⠁⡠⠅⠠⠘⠄⠀⠀⠀⠀⠄⠣⢀⠀⢣⢀⠣⡕⢮⣝⣯⣗⣻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠌⠀⠀⠀⠀⠀⠀⠐⠄⢠⠊⠀⠀⠀⠀⠈⠲⢀⠯⣜⢣⡞⡾⣵⢯⡄⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢫⠂⠀⠀⠀⠀⠀⠀⠀⢎⡲⣍⠾⣩⡗⣯⢞⡷⡀⠀⠀⠀⠀⠀ ⠀⠃⠀⠀⠀⠀⠀⠀⠀⠤⣹⠀⠀⠀⠀⠀⠀⢠⢉⠶⡱⣎⢻⡵⣻⢼⣛⣞⢷⡀⠀⠀⠀⠀ ⠐⡀⠀⠀⠀⠀⠀⢀⡐⣣⢟⣆⠰⣀⠆⡄⢃⠦⣙⠮⡵⣹⢺⡜⣧⢿⣹⡞⣧⠷⠀⠀⠀⠀ ⠀⢣⢄⠠⡀⡄⡔⣦⣝⣳⢯⣿⣢⠑⡮⠜⣭⠲⣍⠾⣱⢣⡗⣯⡽⣞⣷⣻⣭⣛⢇⠀⠀⠀ ⠀⠈⢮⣱⠳⣜⡳⣵⠾⣭⢷⣻⣷⣍⠲⡙⢦⠻⣬⢻⡵⣛⣾⢳⡯⣟⣶⣛⣮⡽⣾⠀⠀⠀ ⠀⠀⠀⡍⢻⡓⠿⢾⢻⠽⣯⣟⣿⣿⣷⣭⣂⠟⣼⣣⠿⣽⣚⣯⢷⣻⢾⡽⣞⣷⣳⣆⠀⠀ ⠀⠀⠀⢰⠀⠈⠙⢌⠣⣝⢲⢯⡿⣿⣿⣿⡉⢟⠲⣭⣟⣳⡟⣞⣯⢯⡿⣽⣻⣞⣿⣿⡄⠀ ⠀⠀⠀⠀⢂⠀⠀⠀⠒⡈⢏⠾⣽⣿⣿⣿⣷⡀⠱⣔⢭⣳⢻⡽⣞⢯⣽⣳⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠀⠈⢕⣢⢤⣀⣰⣌⣷⣯⣿⣿⣿⣻⡌⠒⢯⢷⣾⣧⣿⣼⣿⣾⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠈⢷⡽⣿⣿⣿⣿⣿⣿⣿⣿⡃⠟⠄⠈⢳⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠔⠂⠐⠀⠉⠈⠁⠉⠉⠉⠀⠐⠐⠂⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡀⠀⠀⠀ ⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⢀⣠⡶⠿⠛⠁⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢆⠀⠀⠉⠻⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀ ⠀⢀⠄⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣀⠠⠒⠁⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠁⠢⠄⡀⠀⠀⠉⠉⠀⠐⠀⠀⠀⠀⠀⠰⡀⠀ ⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⣨⣴⣤⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⣤⣬⣅⡢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀ ⠰⠁⠀⠀⠀⠀⠀⠀⡴⠊⠀⣰⡿⠋⢻⣿⣿⠣⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢺⣿⣿⠋⠙⣷⡄⠈⠓⣄⠀⠀⠀⠀⠀⠀⠈⠆ ⠐⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⢹⣽⣶⣾⣿⣿⣦⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣼⣿⣿⣷⣾⣽⣠⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠁ ⠆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡾⠸⣿⣿⡿⢿⣿⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠸⣿⡿⢿⣿⣿⠉⡟⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢸ ⡃⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠐⢤⣹⣯⣷⡾⠃⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠹⢷⣮⣽⣁⡴⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠄⠀⠉⠉⠁⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠉⠉⠁⡀⠠⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄ ⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆ ⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀ ⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢄⠠⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀ ⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀ ⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⢀⡠⣄⣠⢠⣀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠉⠒⠄⠃⠒⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠢⠄⠤⠀⣀⣀⣀⣀⣀⣀⠠⠄⠤⠔⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣠⢤⡀⢁⡀⠀⠢⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⡖⢺⡇⠀⢀⠀⣹⡇⢸⡇⠀⠀⠀⠘⠥⣨⠇⣘⡃⠀⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣄⠀⣸⡿⢸⡇⠀⠹⣾⣉⢀⣬⣇⠀⠀⠀⠈⠛⣩⠓⠹⠂⠀⠣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠙⠉⠀⠈⠋⠀⠀⠉⠉⠉⠈⠚⠀⠀⠀⠀⠙⠋⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⢿⣿⣿⣿⣶⣤⡠⠿⠿⠿⠿⢿⣟⡿⡿⠿⠿⠟⠿⠭⠍⠍⡣⢐⠈⠁⠁⠄⡐⠄⠐⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠠⠞⠋⠉⠁⠈⠉⠛⣿⣿⣿⣷⣄⠀⠀⠀⢸⣟⣷⡇⠀⠀⠀⠀⠀⠀⢂⣁⠒⠀⠀⠀⢀⠡⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢀⣀⠄⣇⠒⡄⠄⠠⠀⠂⠄⠡⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠧⠀⠀⢸⣿⣿⡇⠀⠀⣤⣵⡌⠉⠤⢊⠰⠈⠀⠀⡀⢁⣐⠀⠀⠀⠀⠀⠀ ⢀⣤⣶⣶⣶⣶⣶⣤⣤⣀⣀⣀⣀⣴⣿⣿⣿⡿⠉⠨⠀⠀⢸⣿⣿⡇⠀⠀⣿⢧⡀⠀⢒⠠⢡⠀⠀⠀⡉⢀⢂⠀⠀⠀⠀⠀⠀ ⠈⠁⠀⠀⠈⠙⢿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠻⡚⡵⢀⢪⢐⠢⠀⠀⠀⢈⠁⢢⠀⠀⠀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡀⠀⠀⠑⠌⣃⠆⡂⠀⠀⠀⠀⡀⡌⠄⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠻⣿⣿⣿⣿⣷⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠪⠖⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠁⠀⠈⠻⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⡋⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣤⣄⡀⠀⠀⠀⢀⣠⣤⣿⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⠿⡼⠋⠁⠀⠀⠀⠀⠀⣀⣂⡀⠤⠤⠤⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠚⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠅⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠐⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⣶⡶⠶⠷⣶⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠏⠁⠀⣶⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡄⠀⢶⠗⠀⠀⠀⠙⢃⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⣁⡙⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣟⡛⢁⣘⣟⣋⣠⣄⣀⡀⠀⠀⣶⣶⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠟⠉⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⠛⣿⣿⣿⣿⣿⡟⠻⠿⠀⠀⢀⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣠⣿⣿⣿⣿⡿⠀⣤⣾⣧⣤⠼⢧⣿⣿⡟⠛⠉⠉⠙⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⡿⣻⣿⣿⣿⣿⢻⣿⡇⠾⠟⠻⠿⢩⣤⣶⡟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣾⣿⣿⣿⣿⡿⠿⢿⣤⡶⡦⠀⠀⠈⠉⠉⠀⢀⣸⠇⠀⢰⣾⣿⣿⣿⣿⣿⡇⠀ ⠀⢀⣴⣿⣿⣿⡿⠛⠛⠋⢩⣿⠁⠀⠀⠉⠀⠀⠀⠀⢀⣤⡀⠀⣼⣿⣦⢰⣾⣿⣿⣿⣿⣿⣿⣷⠀ ⣰⣿⣿⣵⣆⡀⠀⢀⠀⠀⠀⠀⢠⡄⢀⣠⣄⣄⣀⠀⠘⠛⠁⠀⠻⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⠀⢶⡀⠀⠀⣰⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠙⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢠⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⢀⡀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠙⣻⣀⠛⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⣼⣿⣉⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⢈⣉⣉⡛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠿⠿⠿⠛⣏⣁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣢⣤⣐⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣶⣦⣤⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⣿⣶⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⢟⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣾⣿⣿⣿⣷⣻⡽⣽⢲⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⡭⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣯⣿⣿⣿⣿⣿⣿⣳⢱⡞⡔⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⢥⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡜⣥⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠿⠟⣟⢏⣿⣿⢿⣿⣿⣿⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⢱⡞⠛⠛⢈⣹⣿⢻⣿⣿⣿⣿⣿⣟⣢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀⣰⣤⣿⣻⣿⢿⣿⣿⣿⣿⣿⠛⡄⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢿⣿⡿⢳⣶⠿⣻⢟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⡿⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⡿⠥⠚⠀⢋⠏⡰⢏⡷⣾⣟⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⣟⡿⢿⣿⣿⣿⣿⠿⠿⣿⣇⠇⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣤⣀⣤⣤⣤⣤⣤⣤⣶⣶⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣀⡄⡇⡤⢋⣴⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⡿⣻⢿⡾⠵⣎⠻⡹⣿⣿⣿⣿⣷⣴⣴⣬⡿⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣁⣥⣶⣿⣿⣿⣿⣿⣿⣽⣧⣿⣿⡿⣳⣞⣴⣛⡿⢧⠘⣂⣿⣿⣿⣿⣿⣿⡟⡄⠘⡆⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣿⣾⠛⢸⣶⣾⣽⣿⣿⣿⣷⣸⣉⣿⣩⠗⣺⣨⣾⣿⣿⣿⣿⣿⣿⣿⣿⠤⢹⡀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⠚⠡⢊⣿⣾⣽⣿⣿⣟⣿⣿⣷⣯⣝⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣔⣁⣥⣾⠿⣿⣿⣯⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢸⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣶⣞⢿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⢳⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⣇⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡘⡄ ⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡮⡏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣔⠭⡚⣝⠽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣹⡎⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⣰⠾⢋⠭⣰⡿⢷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢶⣧⡿⠆⠀⠀⠀⢀⣠⣴⠷⣋⣵⡺⠗⣯⣞⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠌⣾⡟⠇⠀⢀⣤⣾⣟⣻⡼⣼⡾⢕⡣⣶⢋⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣰⣏⡆⢇⡶⣿⢏⡹⣹⣷⣏⢿⣹⢉⣿⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡱⣟⢸⣷⣿⡿⣱⣾⡵⣿⣴⣻⣽⣶⣿⣺⠥⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣾⢥⡿⡿⣿⣿⣿⣷⣧⣿⡿⣻⠿⣯⣭⣭⣽⡭⢖⡪⢔⡂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡽⣧⣾⣷⡯⣿⣽⡻⣽⣳⣾⣷⣏⣾⣻⣿⣾⡻⣷⢿⣪⢝⡲⣕⣬⣀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⢹⣽⣽⣧⣷⡿⣷⣿⣑⣶⣿⣯⢷⣿⣿⣿⣟⣝⠾⣕⡫⠗⣶⣴⠺⡸⣝⢢⣑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣣⢬⠏⣞⣿⣿⣿⣿⡿⣿⣿⣿⣿⣮⣿⣿⣿⣭⡗⣽⣚⣻⡿⣭⣾⢽⡼⡻⣵⠮⣃⠶⣁⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢾⢡⡿⣡⡿⢟⡿⣻⣿⣧⡿⠉⠀⠙⣿⣿⣿⣿⣷⣿⣽⣿⣻⣿⢭⣭⡯⣗⠏⠮⣕⡫⢏⣶⢥⡂⠀⡀⠀⠀⠀⠀ ⠀⣀⢀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡾⣿⣺⣅⡻⣇⣾⣿⣿⣿⣿⣯⣽⡈⣽⣽⣿⣾⣛⣫⢾⢋⣉⣉⠛⢿⡻⠷⠿⠛⠿⣯⣽⣷⣒⡮⣝⢱⣢⣕⠂⢤⠆ ⠷⣾⣿⡿⣷⣶⣾⣯⣴⣐⣠⢤⡄⠄⡸⢿⣹⣿⣷⣿⣿⣿⣿⣷⣳⡉⠛⠉⡇⠈⠋⣰⣿⣻⣿⣾⣯⣯⣯⢵⣆⢣⡇⠀⠀⠀⠀⠉⠈⠈⠛⠋⠓⠚⠙⠛⠊⠀ ⠀⠀⠈⠋⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣟⢦⠠⣭⢆⣴⡟⣿⣷⣿⣻⢯⣹⣿⣾⣿⣸⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠚⠹⡿⣿⣿⣿⣿⣿⡿⡿⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣿⣿⣿⡿⣯⣟⢷⣿⢞⡽⣽⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠹⡻⣿⣿⣿⣯⡽⣷⣿⣻⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣷⣻⣷⢻⣾⡿⣝⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠫⢻⢷⣿⣿⢯⣟⡿⣿⣿⣿⣿⣟⣿⣯⣿⢾⣿⣿⣿⣷⣿⣿⢹⣷⣿⢿⣟⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢟⢿⣾⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠾⣿⣿⣿⣽⣟⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠟⡻⠿⣿⣿⣿⣿⣿⢿⣿⣽⣶⢯⣿⣿⣿⣟⣾⣭⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣾⢿⣹⣾⣿⠟⣹⣿⢯⢶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⣿⣿⣟⣿⣾⢻⣼⣿⠿⠋⠁⠀⣿⣿⢯⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣹⣎⣿⠿⠁⠀⠀⠀⠀⣿⣿⣏⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣻⣼⠯⠋⠁⠀⠀⠀⠀⠀⠀⣿⣿⣻⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⡿⡷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣷⡿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⢟⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⣸⣭⣿⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡟⢰⣿⣿⣿⣿⣾⣾⡝⠿⡿⣿⣿⣿⣿⣿⡿⠿⡛⣛⣋⣩⣭⣽⠀⢿ ⣿⢁⣿⣿⡿⣾⣿⣿⢿⣷⡤⠈⡙⠁⠉⠭⣤⣄⠀⠈⢿⣿⣿⣿⣿⡆⠘ ⡟⢰⣿⣿⣿⣦⣴⠿⢀⠀⠀⠐⠧⠇⢠⣄⣙⣿⡗⠀⠀⣿⣿⣿⣟⣿⠀ ⣿⣶⣾⣯⣬⢉⠷⠚⠛⠩⠀⠀⣴⣶⡄⠻⣿⣻⣟⠀⣘⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⠟⠁⠾⠂⢀⣀⠀⠐⢰⣿⣿⣷⠀⢺⣿⣟⣛⡛⠋⢉⡁⢲⣿⣿ ⣿⣿⠏⠀⠀⠀⠀⠉⢩⣿⢠⣿⣿⣿⣿⣆⢺⣿⣿⣯⣷⣶⣿⣿⣧⡝⣿ ⣿⣿⡀⠀⠀⠀⠀⢀⣾⢏⣾⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣧⠀⠀⠀⠀⠈⡉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⣿⣿⣿⣿⣿⣿⢸ ⣿⣿⣿⣧⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⢸ ⣿⣿⣿⣿⣦⠀⡄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⣿⣿⢸ ⣿⣿⣿⣿⣿⣧⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⢸ ⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣺
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀ ⢀⠄⠂⠈⠀⠀⢣⠀⠀⠀⠊⠁⠀⢸ ⠀⠀⠀⠠⠖⠒⠁⠀⠀⠀⠀⠀⠀⠄ ⠀⠀⡊⠀⠀⠀⠀⠀⢀⡄⠀⠀⠌⠀ ⠀⠀⡅⠀⠀⠀⠀⢠⠃⠀⠀⡂⠀⠀ ⠀⠀⠑⠄⡀⢀⠘⠀⠀⠀⠀⡁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⡂⡀⡀ ⠀⠀⠀⠐⡀⠀⠀⡂⠀⠀⠀⠅⠀⢈ ⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠈⢂⡌ ⠀⠀⡤⠂⡂⠀⠀⠐⡀⠀⠀⢄⠀⠀ ⠀⠀⢇⡰⠁⠀⠀⠀⠂⠀⠀⠠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠂⠀ ⠀⠀⠀⠀⡀⠀⠀⢀⠅⠀⠀⠀⢈⠀ ⠀⠀⠀⢇⡠⠔⠂⠁⠀⠀⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣀⣴⣷⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⡄⢀⣀⣤⣶⢿⠏⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡟⣿⣿⣿⡟⡇⢸⠀⢿⣿⣿⡟⣰⠃⣾⣿⣿⣿⣿⣿⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡟⠛⠿⣿⡇⠈⢷⠝⢷⣧⠀⠀⢸⣽⡟⢰⠃⠀⢿⣿⣿⣿⡿⣿⡿⠟⢛⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⢧⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠙⢦⡀⠈⣷⠀⠀⠀⠙⠙⢧⠀⢸⠿⠀⠀⠀⠀⡞⣾⠟⠁⠀⠀⠀⠐⣿⣿⣿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⡀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠓⠒⠒⠒⠶⣼⣆⠀⠀⠀⠀⠈⢧⣿⠀⠀⠀⠀⠀⢻⠏⠀⠀⠀⠀⣠⣶⣽⣁⣀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢦⣀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⢀⣴⠽⠂⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⡀⠀⠀⠈⢹⡀⠀⠀⠀⢠⠇⠀⢀⡤⠒⠋⠉⠀⠀⠀⠉⢉⣛⡺⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠓⠦⡀⠀⠀⠀⠙⢦⡀⠀⠐⠛⣲⣶⠶⠤⠤⣄⣀⣀⣀⣀⠀⠀⠀⠉⠂⠀⠀⠀⠃⠀⢀⡴⠋⠔⠚⠓⠒⠒⠲⠦⢤⣀⠀⠀⠀⠀⠉⠙⠻⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢶⢄⡀⠀⠀⠙⣆⠀⢀⡿⠀⢀⡤⠖⠊⠉⠉⢉⡭⠝⠓⠒⠂⢀⣀⡤⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⡶⣒⠻⠿⣿⣷⣮⢷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠙⣦⡀⠀⠈⢣⣟⣤⡶⠋⠀⠀⠀⢀⡔⠉⠀⠀⢀⡤⠞⠉⠀⠀⠀⢀⡆⠀⠀⢀⠐⠒⠦⢤⣀⠀⠀⠀⠀⠀⠉⢻⣷⣤⣤⣙⢿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡇⠙⣄⠀⠀⢿⡟⠀⠀⠀⠀⣠⡏⠀⠀⣀⣴⡟⠁⠀⠀⠀⠀⠀⡞⠀⠀⠀⠈⢆⠀⠀⠀⠈⠙⠢⡤⣄⣠⢤⣀⡉⠻⣏⠻⣷⣽⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⡀⢸⣧⠀⣼⢀⡔⠀⣠⣾⣿⠃⢠⣾⣾⣿⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠘⢦⠈⠙⠛⠿⣿⣿⣧⠘⣇⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣇⠀⣿⣧⣧⡟⣴⡾⠟⢩⡿⠰⣳⠟⠁⣿⡀⠀⠀⠀⢀⢀⠏⢣⠀⡀⠀⠀⠀⢸⡹⢆⢂⠀⠀⠀⠀⢧⠀⠀⠀⡘⠻⡎⠓⣼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⠀⣿⣿⣿⣿⡏⠀⠀⠀⣇⡼⠃⠀⠀⣿⣇⠀⠀⠀⡌⡾⠀⠸⡄⢷⠀⢀⠀⢸⠿⠮⣷⣄⠀⠀⢳⠘⣧⠀⠀⢾⣄⢸⣶⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣧⢻⣿⣿⣿⠃⠀⠀⣠⣿⣷⣶⣤⣀⠸⣾⠀⢀⢰⣷⠁⠀⠀⢻⡸⡆⢸⠀⣼⠀⠀⠀⠙⢮⠀⠈⣇⠹⣆⡀⠈⢻⣧⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣿⣿⣿⠀⠐⢿⠟⢉⡍⠛⠛⠲⣝⠻⡆⢸⢸⡏⠀⠀⠀⠀⢧⣿⢸⣸⠃⠀⠀⠀⠀⠈⢷⡀⢸⡆⢸⣯⣆⠀⣯⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⣿⣹⠀⠀⣶⠀⠏⠀⣾⣿⣶⡌⢷⠹⣾⣻⠁⠀⠀⠀⠀⢸⣻⣿⣥⡤⠤⠤⣤⡀⠀⠈⣧⣾⡇⣸⣿⣾⡆⣸⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⡛⢿⠀⠀⢿⡎⡆⠀⣿⣿⣿⠇⠘⡄⢹⣿⠀⠀⠀⠀⠀⠈⢋⣤⣖⣟⡛⠛⣟⠻⣷⣤⣿⡟⢀⣿⣿⢻⣿⡏⣀⣀⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⢿⣦⣤⣌⠛⢽⣦⣀⣉⣁⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢱⣿⣿⣿⣇⢸⡀⠘⠛⠿⠁⣸⣿⣿⡼⠿⣛⡽⠚⠉⢉⡽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣑⣿⣿⣿⡿⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠈⠻⠿⠟⠁⡈⠀⣴⠏⠀⣰⢿⣿⣿⠡⠞⠉⠀⢀⠴⠒⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⡿⢋⡼⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣴⣚⣠⡾⠋⠀⢰⣧⠾⠖⣿⠠⠤⠖⠊⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣉⣠⡞⢡⣾⢷⣤⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠧⣭⠛⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡖⡆⠸⣿⡟⠀⣸⣿⣿⡆⠀⠙⠢⡀⠀⠀⣀⣋⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠧⠇⢸⣿⡇⣾⣿⣿⣿⣿⠀⠀⠀⢸⣦⣾⠳⠬⣙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣶⣶⣶⣿⣿⠇⣾⢋⣙⣿⣿⡀⣀⣀⡼⣅⢟⢦⣀⣀⡴⡻⠀⠀⠀⠀⣀⡠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣼⣿⠸⣄⣽⣿⣇⢧⣸⠁⠈⠻⣵⣲⣶⣯⠵⠖⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠹⡟⠉⠉⠉⠀⠈⣷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠙⢿⣯⡉⠁⠀⠀⠀⠀⣠⠜⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣳⣤⣙⣛⠒⠒⠒⠚⠉⢁⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠋⠀⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣲⡄ ⠀⠹⢆⢌⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⢡⡘⡟⠀ ⠀⠀⠐⣄⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⣠⠊⠀⠀ ⠀⠀⠀⠸⡁⣄⠀⠀⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⣠⣂⠞⠀⠀⠀ ⠀⠀⠀⠀⠹⠛⠳⠢⡀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢀⠄⠝⠉⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⡀⠀⠘⢄⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡠⠃⠀⡀⡛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⡁⠂⢄⠀⢠⣌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣡⠦⢀⠠⠐⢁⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⣆⠀⠈⠶⠎⡓⠈⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⠁⠈⡜⠞⠉⢀⢀⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡅⠓⢆⢄⠀⠧⠠⣦⡈⢢⠀⠀⠄⠀⠀⠂⠀⢄⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠁⠉⠐⠀⣀⡠⠁⢼⡆⠸⠁⣠⠰⠃⢉⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢾⢑⠄⡀⠀⠒⠀⡈⠱⣄⠀⡮⠀⠀⣀⣠⣤⣀⠀⠱⡀⠀⠀⠀⢀⡜⠀⣀⣤⣔⣤⠀⠀⢲⠁⡠⢞⢁⠀⠊⠀⢀⢠⡆⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠻⠼⣆⡄⠀⠀⠐⢄⠀⡌⠠⢶⠋⠁⠀⠹⣷⠀⠙⢄⠀⢠⠊⠀⢘⡟⠀⠀⠈⢻⠃⢀⡀⠠⠎⠀⠀⡀⠦⠻⠛⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡂⠀⠠⠄⡀⠁⠂⢀⡆⢴⣿⠂⠦⠀⠀⠀⠈⡿⠄⠀⠀⠀⠇⠀⠀⢺⡇⠀⠀⠀⢘⠂⠻⣿⠀⡢⢀⣉⢀⡀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⣀⡀⠀⢀⡁⠹⣧⠀⠰⡀⠀⠀⠀⠹⣤⣼⣷⠃⢶⢿⣶⠚⠀⠀⠀⢀⡜⠀⢰⠟⠠⠄⠀⣀⣠⡄⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣠⣦⡀⠀⠧⠤⠤⠉⠉⣁⡄⡶⠀⠹⣆⠀⠙⢄⠀⠀⠀⠈⠹⣜⠀⣘⡞⠁⠀⠀⠀⡠⠊⠀⢠⡟⠀⠸⠆⢮⠁⠈⠐⠒⢲⠃⠀⢀⣔⣄⠀⠀⠀⠀ ⠀⠀⣀⠀⠛⣿⡿⠞⠁⠘⢦⡀⠀⠀⠈⠀⠠⠀⠀⢹⣶⡄⠀⠑⢆⡀⠀⠀⢉⣞⣄⠀⠀⠀⡠⠋⠀⡀⣾⡞⠀⠀⠀⠀⠀⠀⠀⡀⡤⢃⡀⠘⢻⣯⡷⠋⠀⠀⠀ ⢀⣠⣿⣦⣤⣯⣇⡤⡤⣾⣄⡙⢣⠜⣛⡘⠓⠓⣴⠈⠚⢿⣶⡀⠀⠈⣂⠘⠻⣯⣯⠃⡠⡂⠀⢠⣼⡿⠛⠁⠸⡌⠛⡫⢌⣓⠲⠉⡀⣬⡷⣤⣤⣿⣇⣤⢴⣧⣀ ⠈⠹⣼⠛⠉⢻⡿⠛⠓⢿⡟⠨⣅⠨⠀⠸⠋⠀⢡⠼⠆⡲⠫⢣⡀⣼⣷⢧⣤⣻⣧⣤⣷⣷⣄⡠⡟⠓⡅⠟⢦⠁⠈⠙⠄⠀⠦⡧⠈⢻⡟⠛⠙⣿⠛⠛⢺⣿⠋ ⠀⠀⠀⠀⠀⢸⣷⠀⠀⠈⠁⠀⣷⠒⢀⢄⣠⣴⢃⡸⡘⢠⣆⡅⠉⢣⡟⠚⠻⣽⡟⠉⠛⣿⠉⠀⢠⣷⠨⣄⢆⢳⣦⣄⢀⠈⢻⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠀ ⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠛⢦⠂⣩⡾⡵⠋⠌⠁⣼⡿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢩⣿⣄⠁⣄⠻⢽⣆⣀⡷⠚⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣽⡀⠀⠀⠀⠀⠀⠈⠻⡟⢋⣀⣋⣱⡿⡿⠗⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⡀⠀⠀⠑⠻⢿⣿⣅⣥⣈⣉⡟⠁⠀⠀⠀⠀⠀⠀⣸⣟⣧⠀⠀⠀⠀ ⠀⠀⠀⠘⠟⢻⣹⠋⠁⠀⠀⠀⠀⠀⠠⢻⠏⡺⠋⠙⠁⠀⠀⠀⢠⣠⡅⣠⢃⣿⣟⣷⡠⣱⢤⠀⠀⠀⠀⠈⠈⠛⠌⢷⢢⠀⠀⠀⠀⠀⠀⠻⠛⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣧⡌⠀⠀⠀⠀⢠⡄⡜⠀⢹⠉⣴⠛⠛⣼⢻⡕⢠⡄⠉⠀⠈⠂⠐⠀⠀⠀⠀⠀⣦⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠉⠉⠁⠀⠀⢀⠀⢀⡤⢀⢑⡧⠖⠁⠀⠀⠐⠋⠀⠀⠉⠲⢮⡘⡲⡀⢀⢀⡀⠀⠀⠈⠀⠈⢂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣛⡉⡄⣄⣄⣀⣠⠌⣽⠿⠾⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣄⣢⣤⣠⠤⠤⠆⡨⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠘⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠐⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀ ⢺⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀ ⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠰⡠⡄⠀⠀⠄⠆⠀⠀⡀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣼⣿⢋⣿⢻⠟⢻⠟⣿⡟⡟⢺⠧⡼⠽⣏⣿⣿⠟⢿⣏⠙⣿⣿⣦⣷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣿⣧⣤⣮⣼⣹⣇⣇⣸⢦⣧⣤⣿⣼⣿⣧⣾⣿⣿⣿⣿⣿⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣽⠀⠀⠀⠀⠀⠀⠀⢀⢆⡄⠀⠀⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⡄⠀⠀⠀⠀⠀⢠⢫⢌⡀⠀⠀⠀⠀⠋⠙⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡛⢻⣿⠋⠉⡟⣉⣿⠷⢿⣿⣿⣽⡿⠿⣿⣿⡇⢻⣧⠀⠀⠀⠠⡰⢫⠋⠈⠀⠀⢀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠋⢩⡿⠃⠀⣉⣿⡟⠀⣸⠁⣼⡏⢀⣀⣹⣿⣷⡇⠀⣼⢻⣿⣨⣿⠀⠀⡴⠿⡕⠠⠀⠀⠀⣠⠿⠉⠁⢀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣿⣿⢿⡏⣹⣯⣴⣿⣷⣿⣶⣣⠏⢀⣴⢃⡼⡟⣸⣿⣿⣿⣿⣿⣟⠀⡏⢸⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⢀⡴⡇⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⢸⣆⣨⣿⡿⣿⣿⣿⣿⡿⠛⣽⠷⠋⠞⠀⢻⡿⣿⠟⡏⢹⡿⢹⠃⣾⣿⣿⡇⠇⠀⠀⠀⠀⠀⣠⠞⢀⠏⣴⣫⠭⢥⣤⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣿⣿⣇⢸⣿⡀⢹⡷⣹⣗⡭⣸⠁⠀⠀⠀⠀⠀⠀⠈⠻⠂⠴⠗⣹⣡⡎⠀⣿⢻⣿⣿⢸⠀⠀⠀⢀⡼⢁⡴⣡⣾⣏⢹⠰⡯⣤⡅⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣿⠸⡞⢿⣦⣵⣄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢿⣿⠀⣸⣿⢸⣿⣿⡟⡇⠀⢠⠎⣠⢊⣼⣟⢱⡏⠈⠀⢳⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣸⣿⣿⡆⢻⡀⢻⣿⡍⠁⠂⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⣾⣿⣼⣿⣿⣿⣿⣿⣷⢻⠐⢁⡜⣵⡿⣻⣿⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣿⣿⣿⣷⡀⡻⣾⣿⣿⣄⠀⠀⠀⠀⢯⠛⠁⠉⡹⠀⠀⠀⢠⣾⣿⣿⢁⣿⢿⣿⣿⡿⣿⣿⡄⢀⣾⢿⠇⢹⢿⠀⣇⣀⣀⠠⠄⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⣿⣿⣿⣿⣷⢳⡘⣿⣿⣿⣷⣄⡀⠀⠈⠓⠒⠚⠀⠀⣠⣶⣿⣿⣿⣿⢸⣿⣸⣿⣿⣿⡏⢿⣧⠐⠁⠀⠀⢸⢸⡸⣫⢶⠒⣢⣤⣤⠤ ⣿⣄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣼⣿⣿⣿⡟⣿⣿⣧⣻⣿⣿⣿⣿⣯⠓⠠⣄⣀⣠⠔⢋⣼⣿⣿⣿⣿⣿⡞⢻⣿⣿⣿⣿⣧⠘⣿⡀⠀⠀⠀⡼⣫⣾⡷⢸⠘⡷⠶⡎⠀ ⠹⣿⣯⣷⡀⢠⠀⠀⠀⠀⠀⠀⠀⢸⣳⣿⣿⣿⣿⡇⣿⣿⡜⢻⣿⡟⣿⣿⣿⠀⠀⠀⠨⠤⠒⠉⢸⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⡆⣿⣷⡀⠠⣫⢾⣿⢹⡇⠀⠀⠙⠀⠀⠀ ⠂⠈⢿⣿⣿⡴⣧⡀⠀⠀⠀⠀⠀⣾⣿⣿⡿⣿⣿⡇⣿⡏⢇⢘⣿⣇⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠸⢿⣏⣼⣿⣿⡀⠘⣿⣯⠽⡝⣿⣿⣸⡟⢧⡞⠑⢿⢹⠘⡇⠀⠀⠐⠀⠀⠀ ⠀⠐⠀⢻⠛⠋⠐⣅⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠿⠇⣿⡧⢸⡆⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡅⢲⣿⣿⣿⣿⣿⣿⡿⣷⠘⣿⡄⠈⢸⠀⣇⣀⣠⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⣴⣿⣿⣿⠋⠁⠀⠉⢻⣿⠀⣼⣿⣿⣿⣿⠿⢖⡒⠢⢄⠀⢀⡠⢴⣲⣶⣿⣿⣿⣿⡇⠈⣿⣿⡤⠋⠙⢻⣿⣿⣇⠈⢿⡄⣼⠔⡩⢶⠒⣒⣖⡒⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣾⣿⣿⢿⣯⠀⢠⡀⠀⠸⡿⢀⣿⢹⣿⠏⠻⡦⣀⡈⠉⠙⠓⠛⠛⢿⣿⠿⢋⢸⡏⣧⣿⠀⣿⣿⠀⠀⣵⠋⣿⣿⣿⣄⠈⣿⡖⢉⡅⠘⠘⡷⢶⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⣾⠃⢣⡀⢳⠀⣿⠃⢸⣻⣿⡿⠈⠁⠈⠢⣉⠱⣶⣒⡒⢚⣉⠥⠀⠸⣼⢷⠘⣿⡆⢹⣿⡄⣸⡇⡔⢿⣿⣿⢻⣎⠈⢿⣌⠂⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡇⣿⠀⢰⡱⡈⣠⡏⠀⡏⣏⣾⢧⡇⠀⠀⠀⠈⠑⢬⠑⠤⠀⠀⠀⠀⠀⠹⣿⣆⢸⣻⠈⡏⣧⢛⡜⠀⢸⣿⣷⡁⢹⣆⠀⢻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⢀⡴⣿⣿⣿⡿⣹⣿⣇⣿⠘⡄⠃⠘⣾⠃⢸⣰⢏⡼⡿⠁⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠘⢯⣦⣧⣧⢱⣸⠉⠀⠀⢸⡿⣿⣿⣄⠹⣦⠀⠹⣧⠠⠀⠀⠀⠀ ⠈⠳⣄⡴⠋⣼⣿⣿⣿⠁⡼⣿⢹⡟⠀⠀⠀⢠⡿⣻⣿⣾⠛⠋⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣏⢿⣧⠀⠀⣼⡇⣿⢿⣿⣦⠘⣧⠀⠹⣧⠀⠀⠀⠀ ⢀⣴⣋⢹⣾⣿⣿⣿⠇⢠⠇⣿⢸⡇⠀⠀⢠⣿⣇⡏⢱⠏⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⣷⢸⡝⣿⡆⡰⠁⣷⢹⡘⣿⣿⣷⡘⣷⡀⠙⣧⠀⠀⠀ ⠋⠁⢹⣿⣿⢫⣟⡿⠀⡸⠀⣿⢸⡇⠀⠀⣼⣿⣸⠀⡾⢷⣶⣶⣦⣄⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣠⣴⣶⣶⣾⡇⣧⣿⡿⡇⠀⣿⢸⡇⢿⡿⢿⣿⣞⣷⡀⠘⡆⠀⠀ ⠀⢠⣿⣿⣯⡿⣹⠁⢠⡇⢰⡏⢸⡇⠀⢰⢻⣿⣿⢸⡇⠘⣿⣿⣿⣿⣿⣷⣄⠀⣿⣿⣿⣿⣿⣿⡇⢀⣴⣿⣿⣿⣿⣿⡇⢱⢸⣿⣿⢸⠀⢻⡼⣿⠸⡇⠈⣏⢿⣿⣽⡄⠘⡄⠀ ⢠⣿⣿⡿⣱⢠⡇⠀⡼⠀⢸⡇⢸⡿⡄⡼⢸⣿⢻⣸⣇⠀⠸⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⡏⠀⢸⢼⣿⣿⠀⠀⢸⡇⣿⠀⢱⠀⢹⡄⢻⣻⣷⡀⢳⠀ ⣮⡏⣿⢳⠃⣾⠃⢠⠃⠀⣼⡇⢸⡇⠙⢧⣸⣿⣿⣿⡼⡄⠀⠉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠀⠀⣾⣼⣿⣿⢀⠀⢸⡇⢻⡄⠠⣧⠀⣷⠀⡿⡼⣷⠈⡆ ⡙⢰⠇⡎⢠⡝⢀⣾⣠⣤⣿⣥⣼⣗⣦⡈⢿⣿⣿⣿⣷⡙⠢⠄⠀⠉⠉⣉⣉⣉⣉⣉⣉⣉⡉⣉⣉⣉⣉⠉⠉⠁⠀⣀⡾⢻⣿⣿⣇⠞⣀⣸⣧⣸⣧⣀⣻⡄⢸⣇⢹⠹⡼⣇⠃ ⠇⡼⢸⠁⢸⢁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢦⠀⠀⠀⠀⠀⠉⢟⠛⠃⠙⠟⠘⠛⠛⠉⠁⠀⠀⠀⠈⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⢸⢸⠘⡆⢻⢻⡀ ⠀⡇⡏⠀⠘⣸⠃⠀⠈⢹⠉⢻⢧⠠⠬⠭⢍⣛⢻⡟⢿⣏⠉⠱⡀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⢿⠟⠛⣉⣉⣁⢸⠛⠙⡏⠙⡇⡆⢸⠀⠀⡇⠀⡆⡇ ⠀⡇⡇⠀⢰⡇⢠⠀⠀⠘⠀⠀⢸⠀⠀⠀⠀⠀⠙⡇⠀⠈⠉⠀⠈⠂⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⡔⠉⠀⠀⠀⢸⠀⠀⠇⠀⡇⢳⢸⠀⠄⠇⠀⡇⡏ ⠀⡇⢹⠀⢸⣇⢸⡀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⡄⠀⡘⠀⠀⠀⢸⠘⣰⢰⠀⠀⠧⠁
⣿⣟⡿⣻⢏⠿⣭⢛⡜⣣⢛⡬⢳⡹⣌⠧⣙⢦⣙⣽⣽⣽⡿⡿⢿⠿⡿⢿⢿⡿⣿⣿⣽⣟⡟⣻⢛⡟⠛⢦⣠⣼⣿⣿⢿⣻⠿⣿⢷⡶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡞⣵⢫⢞⡳⢮⡹⡜⡥⢏⡜⢧⡱⢪⣵⣽⣾⣟⢯⡿⣞⡻⢯⡝⡿⢭⣻⢮⣽⢳⢮⣻⣽⣿⣿⣦⣇⡀⠀⣿⣿⢿⣹⣿⣿⢿⡿⣶⣷⣧⣙⠻⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⡹⢎⣧⢫⣜⢣⢳⡙⣜⢣⠞⣥⣳⣿⣿⣿⣝⡹⢖⣳⣌⢏⡳⣙⢞⣣⢻⡝⣞⡻⢯⣟⣽⣻⣽⣿⣿⣿⣶⣿⣿⣿⣟⣿⡯⣎⢗⡳⣎⡟⣿⣯⣓⢬⡛⣶⡄⠀⠀⠀⠀⠀⠀⡟ ⣷⢫⠟⡼⣓⢎⡻⢦⡹⡌⢇⣾⣿⣻⣟⣮⠷⣎⢻⣉⠶⡘⢬⠱⡩⠞⡴⣋⠽⣞⡽⣫⣞⣿⡿⣽⣾⣿⣿⣧⣿⣿⣽⣿⣿⠳⣍⡞⣱⢫⡜⣧⡛⣿⣶⣱⢎⣻⣦⣄⠀⠀⢠⡟⠀ ⢧⡛⣎⠳⣍⢮⢱⠣⣕⣾⣿⣻⣿⡻⣍⢎⠳⣌⢳⣌⠲⣉⠦⠳⣌⢳⡱⣍⢞⡹⢞⡵⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⡛⡴⡙⢦⢣⡝⡲⣝⠶⣹⠻⣷⡖⢭⣿⣿⣶⣏⡄⠀ ⢧⡹⣌⠳⣜⡊⣇⣿⣿⣿⣿⡝⣣⡓⢎⡬⢓⡎⡷⠏⡑⠀⠀⢀⣾⢇⡱⢎⣎⣳⣽⡿⠋⠉⠉⠉⠉⠉⠙⠛⠛⢿⣿⢣⢣⡝⣰⠹⡘⠦⡜⡱⢎⡻⡴⣛⠼⣻⣧⡛⣿⣿⣿⣿⡄ ⣇⠳⣌⠳⣬⣵⣿⣿⣟⣳⣿⠟⣥⡙⠲⣌⢣⠟⠰⠀⠄⡀⠲⢻⣞⢣⠎⣧⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢣⢣⠳⡌⣥⢣⡙⢦⡙⠴⣋⠴⠳⣍⡞⣥⢻⣷⣩⢿⣷⢫⣷ ⢬⠳⣌⠳⣼⣿⣿⣿⠺⣾⢫⡝⡢⢍⠳⡄⡛⡈⠄⡑⠐⡀⣶⠿⣱⢏⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢏⢧⢋⠖⡱⢂⠣⢜⢢⡉⢖⣡⢋⠳⣬⢓⣮⢣⠽⣷⡯⣿⣟⣼ ⢇⡟⡸⢇⣷⣿⠟⣼⣟⣣⢧⡸⢃⡟⠤⣃⢃⠸⡀⢀⢃⣼⡟⢣⢇⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡜⡜⢇⡼⢃⠟⡸⣀⠇⡸⣀⢄⡛⢤⢃⢿⡠⢟⡼⢻⣧⢿⣿⣼ ⢎⡼⠱⢎⣿⣿⡿⣸⢧⡓⢦⣍⢣⠜⡱⠌⣌⠒⣄⡶⣟⠣⣜⣥⣿⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡗⢮⡙⣎⠴⣋⠬⡱⢄⠢⡁⡔⢢⢘⠢⡝⣢⡝⡳⡞⣭⢿⣯⣿⣿ ⢎⡼⡙⣾⣟⣬⣿⡓⣮⡙⢶⡘⢮⡘⣅⠫⣄⠟⣌⠳⣌⡳⣹⡿⢁⡤⣾⠟⢷⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡿⣜⢣⡝⣤⠓⣌⠲⣡⠊⠔⡡⠀⠀⠈⠦⣑⢣⠞⡵⣛⠴⣻⣯⢿⣿ ⢎⢲⢹⣿⣿⣽⣷⡙⢦⣙⢮⡙⢦⡙⢦⣛⢬⣛⡬⣛⢬⢳⡿⡵⠋⣰⠟⠀⢤⠙⢿⣦⠀⠀⠀⠀⠀⠀⣸⡷⣩⠶⣘⢦⡙⡤⢓⡤⢃⡘⠰⠀⢀⠠⡑⡌⢎⡽⡸⣥⢻⡱⣿⡿⣿ ⢎⢣⣿⣯⣿⣟⠦⣝⢣⠞⣦⡙⢦⡝⣣⢎⡳⡜⢶⣩⢮⣿⡟⠀⣱⡟⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⢥⡛⣬⠲⡱⢌⡣⢜⡡⢆⡡⢍⠢⢆⡱⠸⣌⠶⣱⢣⡳⣍⢿⣟⣿ ⢎⢶⣿⢳⣿⣭⠞⣬⢣⡛⣴⢩⡳⡜⣥⢯⣱⢫⡳⣜⣿⡏⡐⢠⡿⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠐⣿⡟⡼⡱⢆⡛⡴⣉⠖⣡⠒⡥⢒⡉⢖⡡⢜⡱⢌⡳⣌⢧⠳⣎⣻⣯⡿ ⢎⣾⡟⣷⣿⣧⡟⢦⢧⡹⢆⡳⢵⡹⢦⡳⣬⢳⠵⣺⣿⠇⣀⣿⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢨⡿⣏⡵⣋⢮⡱⡒⡍⢎⢥⢋⡔⢣⠜⡢⠜⢢⠝⡬⢳⢜⣪⠳⣥⢻⣷⡇ ⣾⡿⣝⢮⣿⣾⣽⢣⢯⡝⢮⡱⢯⡝⣧⢻⡜⣏⡞⣵⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⣿⡷⡸⢇⢮⡱⢅⡫⢜⣊⠶⣈⢇⡚⡅⢎⡱⢎⣱⢋⣎⠶⣛⡴⢫⣷⠃ ⣿⡳⣹⢎⣿⣸⣧⣛⣮⣝⡣⣝⣣⠿⣜⣧⣛⢾⡹⣼⣿⡟⠛⠿⣿⣿⣦⣄⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣿⡷⣙⡏⢶⡩⢎⡱⢎⡲⢍⠶⣌⠲⣉⠦⡱⢎⡜⣣⢎⡳⢭⣚⢭⡟⠀ ⣟⣱⣿⠮⣽⡹⣯⢷⡺⣜⡳⣌⣷⢻⣝⡶⣏⣯⠷⣽⣿⡛⠀⠀⣿⢸⣿⣿⢳⡀⡏⠀⠀⠀⠀⠀⠀⠀⢿⣏⢧⣛⠦⡝⣎⡒⢧⡱⢎⠳⣌⠳⡜⣲⡙⢮⡜⡥⢯⡜⣳⣚⢾⡃⠀ ⣾⣿⣿⡝⣾⡱⢿⣳⣏⠷⣝⢦⢻⣟⣮⡽⣞⣭⢟⡾⣿⣇⠀⠀⣿⠈⣿⠟⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠷⣭⠞⣽⢲⡝⢦⡓⡭⢳⣌⢳⡱⢦⡹⢦⡹⣎⢳⡜⣧⡝⣾⠀⠀ ⣿⣿⣿⡟⣶⣹⢻⣿⣞⡽⣫⢾⡻⣿⡾⣽⣹⢮⡻⣼⣿⣿⡀⠀⢹⠀⠀⠀⣜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡜⡯⢞⣧⣛⢧⡹⡜⣥⠚⣦⠳⡥⣛⠶⣹⢬⢳⡹⢶⣙⣟⢶⣦ ⣿⢏⡿⣿⣶⢭⡳⣿⣿⣞⡭⢿⣱⢻⣿⢧⣛⡾⣵⢫⣿⡟⠋⠙⠚⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣯⢽⡹⢶⡁⣎⠷⣩⢖⡹⢆⡻⢴⡩⢞⡱⣎⠷⣙⢧⣻⣼⡷⠋ ⡜⡢⡕⡸⢿⣾⣱⣿⣿⣾⣿⢻⣧⢏⣿⣯⣟⡼⣣⢟⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠹⣿⢮⣝⡳⣿⣭⣛⢦⠯⣜⣣⠝⣦⢏⡳⡽⣸⠽⣹⢞⣽⢻⡻⣽ ⡜⢥⡓⣍⠚⣿⣷⣿⣿⣿⣎⣯⣷⢺⡜⣻⣿⣵⢯⡞⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣥⠀⠀⠀⠀⠀⠹⣿⣮⢳⣯⢿⣞⢮⡝⡶⢭⡞⡵⣎⢗⡳⡝⡾⣱⣏⣞⡳⣽⣚ ⡜⡥⣚⠴⣉⢆⡛⠿⣿⣿⣿⣾⣿⣷⣚⡥⢿⣿⣿⣾⣶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣞⣯⢿⣾⡜⣝⣳⠺⣵⡹⣎⡳⣽⣵⣳⣞⣼⣽⠶⠋ ⡜⢲⢱⠊⡕⢪⡜⢱⡌⢻⡟⣬⠛⣿⣶⣿⣼⣿⣿⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⣷⢻⣷⡞⣯⣿⣿⣼⢲⠛⣶⠙⣶⢹⡆⣯⠛⣿⣯⡄⠀⠀ ⢣⠏⡶⣉⡓⢮⢱⢣⡝⢦⡓⡼⢬⡙⠿⣿⣿⣿⣿⠿⠛⣆⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢴⡆⠘⢷⡉⢿⣷⣽⣯⠛⠿⣷⣯⣿⣬⣓⣾⣩⣞⣵⣫⣿⡷⠄ ⣭⢚⡥⢣⡝⢎⡥⢳⡸⣑⢮⠱⡎⣍⢳⡡⢏⡛⣿⡆⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣼⡍⠉⠉⢹⡏⠉⠉⠉⠀⠀⣾⠇⠀⠈⠻⣖⡆⠙⢿⣧⣼⠟⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀ ⣎⢳⡜⣣⠞⡱⢎⢧⡱⡍⠶⣙⠼⣌⠳⣜⢣⡝⡼⣧⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⢿⡇⠀⠀⢸⡇⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠈⢁⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⢧⡹⣆⢯⡱⣋⠶⡱⣍⠳⣍⡞⢬⠳⣌⡳⣜⡱⢻⣆⠀⠀⠀⠀⠀⠉⠓⣤⣄⠘⣷⡀⠀⠈⢃⠀⠀⠀⣼⡟⠀⠀⢀⣀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⣬⠳⣽⣷⡱⣍⢞⡱⢎⡳⡜⣿⣎⡳⣍⠶⣥⢫⡝⣻⢦⣄⠀⠀⠀⠀⠀⡟⠉⠻⢿⣷⣤⣄⣀⣀⣤⣼⣯⣤⣶⢾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡻⢬⡳⣹⣿⣷⡜⢮⣙⢮⡱⡹⡜⣿⣿⣎⣳⣬⠳⡜⣥⢣⡛⢷⢦⣀⠀⢸⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⢇⡷⣹⡏⠻⢿⣷⣜⡶⣩⢳⡹⣜⠻⣯⡉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⣿⠀⠀⣰⠆⢀⠀⠀⣀⠤⣦⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣶⢯⣧⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⢦⠀⠈⠳⠊⠀⣀⡴⠃⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠐⠀⡀⠄⠁⢀⠀⠄⠂⠀⠄⠀⠈⠀⠀⢐⣠⣁⡀⠀⠀⣦⣶⠶⣦⡄⠀⠁⡀⠄⠂⠀⠐⠀⠀⠂⠀⠁⠀⠈⣿⣿⠿⢿⠿⣿⢿⡻⣛⢯⡛⣭⢻⣿⣜⢳⡣⢞⣣⠗⣞⣿⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣾⠃⡜⢠⢃⠘⣿⡇⠌⡡⢂⠅⠢⢁⢊⡐⢨⣽⡏⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠙⣿⣌⢈⠡⣌⣄⠢⡘⢠⠊⡐⣢⣿⡌⡈⠼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠈⠀⠄⠀⢀⠠⠀⢀⠠⠀⠂⠀⡀⠁⢀⢨⡿⠋⠉⣿⡆⣼⠏⠀⠀⠈⢿⡄⠐⠀⠀⡀⠐⠀⠈⠀⠄⠈⠀⡀⠁⠘⣿⡝⣮⢹⣿⣇⡳⢭⠶⣙⢮⡝⣿⣎⢧⡝⣣⣷⣿⣿⣿⡿⡟⣽⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⢰⡟⢐⡈⠆⡌⠐⣿⡷⠀⡅⢢⢈⠁⢆⣾⣷⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣿⠿⠋⡐⠨⢐⠠⣡⣿⣿⣿⠖⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠁⠀⠄⠀⢀⠠⠀⠀⠠⠀⢀⠀⠄⠀⣾⠁⣀⣀⠀⣿⠃⠀⠀⠀⠀⠘⣿⠀⠀⠂⠀⠠⠀⠁⡀⠠⠀⢀⠀⠄⠀⢿⣟⠶⣩⣿⢶⡩⢏⡞⡭⢶⡹⣿⣏⢶⡹⢥⣛⢿⣛⣿⣳⣽⣾⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣸⣇⠢⠄⣃⠰⢁⢺⣿⣔⡠⢁⣢⣼⠟⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡆⠀⠻⣧⣤⣡⣄⣥⣦⡿⠟⣉⣷⣎⡐⣼⠇⣀⡴⠞⠛⠋⠛⣛⣳⣦⠴⠶⠶⠦⣿⡉⠛⢦⣤⠴⠶⠶⠶⢶⡴⠞⠉⠁⠀⠈⠙⠳⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢻⡆⠈⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⣿⠛⠉⠁⠀⡆⠀⠀⠀⠀⠀⣀⣿⡆⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡭⡓⣿⣧⢋⡝⣼⠙⣶⣽⣿⣯⣶⣿⠷⠿⠿⠛⠛⠋⠉⠄⠐⠈⠉⠛⠿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣇⠢⡁⠆⠂⡁⠆⠉⠻⠿⠿⠻⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⡶⠟⠉⠉⠉⠉⠁⠐⢰⣾⠃⠉⠛⠿⠶⠿⠴⠶⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠲⠛⠛⠛⠛⠲⠦⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⡆⠀⠀⠀⢸⡏⠀⢀⠈⠀⡀⠂⠁⢀⠈⠀⡀⠁⠀⡀⣿⠀⠀⠀⠀⠛⢛⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠄⠀⠀⠀⡀⠈⠀⢀⢘⣿⠷⡿⢿⠿⠾⠿⠟⠿⠛⠛⢋⡉⡉⢉⠄⠢⠄⠒⡄⢊⠡⣈⠁⠣⠌⡄⠄⡉⠛⣷⣄⠀⠀⠀⠀⠀⠀⠸⣿⣀⠣⢌⠠⢃⠰⡀⠆⠠⢀⠢⠘⠿⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠾⠛⡡⢀⠤⢈⠢⢘⠀⠆⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠈⠀⢀⠠⠐⠀⠀⠄⠀⡀⠄⠂⢀⣾⠿⠋⠁⠀⠀⠀⠀⠀⣀⣴⣄⠀⠀⠀⠈⠀⠀⠀⢸⡇⠀⢀⠐⠀⣼⣇⣴⠟⠁⢰⣿⠀⠢⡁⢢⠡⢘⣶⣖⡈⠱⣈⢂⢩⣰⣿⠋⡔⢨⠘⡠⠘⡄⠡⢒⠠⡑⣈⠢⡑⠌⣂⠱⡈⢸⣿⠀⠀⠀⠀⠀⠉⢙⣊⣡⣴⠾⠋⣁⠀⠆⢂⠂⠔⠠⢈⠐⡀⠢⠐⡀⠆⡀⢀⠀⡀⠠⢐⠠⠐⠠⢁⠂⠌⠠⠐⡈⠄⠡⢈⠈⢻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠙⣛⣻⣿⣿⣿⣿⣿⣛⠛⠋⠁⠈⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⡈⠀⢀⠠⠐⢨⡿⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⣠⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⠂⢀⣠⣾⢰⣿⠉⠀⢀⠠⠈⢿⣮⣁⢒⣀⣶⡿⠋⠹⣷⡥⠐⡌⣷⡿⡁⠎⡰⢁⠆⡡⠑⡌⢡⢂⠱⡐⢠⠃⡜⠰⡀⢆⠡⣘⣿⠀⠀⠀⠀⣠⡶⠟⡉⠙⠻⢷⣤⠀⢌⠂⡂⠌⠠⢁⠂⠰⠠⠑⡈⠔⡂⠄⡃⠢⠐⠡⢂⠘⡈⠔⠂⠌⠠⠑⠠⠐⡈⠄⢂⠌⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣦⡀⠀⣴⣿⣿⣿⡆⠉⠉⠙⡻⣿⣦⠀⢀⣿⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⡐⠀⢀⠀⠻⢷⠾⠿⠛⠻⣦⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⢾⣿⣿⡷⠟⠁⠀⡀⠂⠀⠠⠀⠉⠛⠛⠛⠉⠀⠠⠀⠹⣿⢀⣿⡟⠰⢄⠣⡐⢡⠊⡔⠡⡜⢠⠊⡔⡈⢆⠱⣈⠱⡈⢆⠡⢼⡏⠀⠀⠀⣴⡟⣀⠒⣈⠐⠡⠙⢿⣿⡀⠒⡄⢊⡐⠤⢈⠅⠢⡑⢌⠰⢁⠢⢁⠡⢉⠂⡅⢊⠐⡌⢨⠐⡡⠌⡁⢂⠐⡈⠄⠌⡀⢿⡆⠀⢠⡦⠀⠀⠀⣀⣤⣿⣤⣤⣾⣟⣈⣬⣿⡇⢸⣿⣿⣿⡿⠥⢤⣤⣤⡤⣿⣿⣷⡾⠃⠀⠀⠀⠀⣸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠄⠐⠀⠠⠀⡀⠠⠀⠠⠀⠌⣻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣍⣀⡀⠠⠄⠂⢀⠀⠁⠠⠀⠁⠄⠠⠀⠐⠀⠁⡀⢲⡿⣸⣿⠁⢇⠊⡔⠡⢆⠣⢌⠱⡈⢆⡱⠠⢍⠢⡑⡄⢣⡘⢄⢊⣿⠃⠀⠀⣰⡟⡀⠆⡱⢠⠘⡠⢡⢈⠹⣧⡜⠠⢂⠔⣂⠡⢊⡁⠒⡌⢢⠁⠎⡄⠣⢌⠒⡄⢃⠒⡈⢆⠱⠐⡌⡐⡁⠢⠐⡌⡐⡈⠜⣿⡀⠈⠛⠳⣾⢻⡟⠉⠻⠿⠛⠉⠀⠀⠀⠀⢰⣄⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⢈⣿⡶⣤⠴⣦⣀⣠⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠌⢀⠈⡀⠐⠠⠁⢂⠁⢤⣼⣟⣡⣌⣝⣛⣻⣷⠶⠶⠶⠶⢶⣶⢛⣛⣯⡿⠟⢫⡉⣍⠩⡙⢿⣦⠀⠁⠠⠀⢈⠀⠄⠁⠠⠀⠂⠁⡈⢀⣤⣿⣿⣿⠃⣍⠢⠱⢌⡱⢈⠖⡨⠆⣍⠢⠔⣉⠦⡑⠤⢃⠥⡘⢤⣺⡏⠀⠀⢀⣿⠡⠜⡠⡁⠆⣁⠂⠆⡌⡐⢻⣧⡑⢌⠢⢄⠃⠆⡌⠱⡈⢆⣉⠒⡌⡑⢢⠘⡄⢣⠘⡰⢈⠆⡱⠠⣡⢐⣥⢁⣿⠰⢐⡈⢽⣇⠀⠀⠀⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠈⠉⠁⢰⡆ ⠀⠀⠀⠀⠀⠀⣠⣀⠀⣠⣾⠃⠄⡈⠄⠐⡀⢂⠡⠈⢄⣾⡿⢳⣿⠛⡩⢍⠫⡙⢛⢻⣶⠟⢛⠛⠛⣿⡏⡱⢢⡙⠤⡑⢄⢣⣘⣰⣿⠃⢈⠀⡐⠀⠠⠀⠌⡀⠐⡀⢁⠀⠿⠟⣻⣿⢃⠇⡆⡍⡱⢂⡱⢊⠜⡰⢡⠆⡱⢩⡐⢆⡑⢎⡡⢚⡐⣲⡟⠀⠀⠀⣼⡇⣂⠣⡑⢌⠒⠤⣉⠒⠤⡑⠌⣻⣧⠌⡒⢌⡘⠒⡌⠱⣈⠆⠤⢃⠴⡁⢆⠣⡘⡄⢣⠑⡌⢢⢁⢒⣿⢼⡗⣸⡿⠘⣄⣆⣿⠏⠀⠀⠀⢿⡇⢻⣧⣄⠀⠀⠀⣀⣠⠔⠋⠀⠀⠈⠑⠦⣄⣀⣀⣀⣀⣠⣾⠟⠁⠀⠀⠀⠀⠀⣠⡟⠀ ⠀⠀⠀⠀⠀⣸⡏⠛⠛⡉⢄⠘⡄⡐⢈⡐⠄⠂⣄⣳⡿⣋⠔⡣⢿⣧⡱⣈⣶⣵⡮⢸⣿⢀⢣⠘⡄⣿⡧⢑⠣⣌⠣⣘⡘⠿⢟⢻⣷⣀⡌⠐⡐⢌⠠⠁⠄⠠⠁⡐⢂⠈⢄⣶⡿⢡⠎⡜⡰⢡⢃⢇⠲⣉⠬⡑⠦⣙⠰⣃⠜⡢⠜⡢⢅⢣⢺⣿⠀⠀⠀⢀⣿⠰⡁⠖⡉⢆⠩⠒⠤⡉⢆⠱⢌⡐⢿⣇⠜⢢⢘⡡⢌⡱⠄⡎⠱⢌⢢⠱⡈⠖⡡⠜⠢⠍⡴⢁⠎⡘⢿⣿⡿⢺⡧⢩⡿⠿⠋⠀⠀⠀⠀⠈⣿⡄⠀⠉⠹⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠈⠀⠀⠀⠀⣀⡶⠟⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⠄⣁⠒⡈⠄⢒⠠⡐⢡⠐⢨⣴⡾⢏⠲⡡⢎⣱⣮⣿⠟⣫⠔⡢⠜⣹⣿⡀⢆⠡⣂⣿⣧⢉⠖⡰⢃⠖⡌⡓⣌⢲⣿⠙⠻⢷⣦⣄⣂⡑⢈⠂⣁⠂⠤⣨⣾⢟⡰⢃⠞⡰⢡⡃⢎⡌⠳⣌⠲⣉⠖⣡⠓⣌⠲⣡⢣⡑⢎⣱⣿⢿⡇⠀⠀⣸⣏⠆⣍⢒⡉⢆⡩⢉⠆⣍⢢⢉⢆⡘⠜⣿⡜⢢⡘⠔⡢⢆⠩⡌⢓⢌⠢⠥⢩⠜⡡⠎⠥⢋⡔⢡⢊⠱⣨⣿⠡⣿⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣷⣆⠀⠀⠐⠾⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⡐⢰⡈⠜⡠⢃⠜⣀⣾⡿⢫⠜⣬⣳⣽⠿⠛⢹⣷⣾⣤⣷⣷⡿⣿⡛⠛⠻⠛⠛⠉⠛⠻⣿⣶⣿⣶⣷⣷⡾⠿⢉⠐⠢⢄⠨⢉⠛⠿⢷⣶⣤⣅⣲⣿⠏⢦⠱⣉⢎⡱⢣⠜⣡⠎⡵⣈⠳⣌⢚⠤⣋⡔⢣⢆⠣⡜⣬⣿⠏⣾⡇⠀⠀⣿⣷⣮⣔⣌⣘⣰⣈⣑⣊⣔⣢⣍⣦⣼⡾⢿⣷⠡⢎⠸⣁⢎⡱⢌⠣⣌⠣⣙⢂⢎⡱⢌⡃⠧⡘⢆⠥⢓⡘⡋⢖⣿⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁⣀⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⢿⡇⡘⢄⠣⡘⣾⡟⢬⣷⡿⢛⠩⡐⠂⡍⠠⢄⡈⣁⠢⠄⡰⢈⠻⣦⣄⠀⣀⣤⡶⠟⡋⠤⠠⢄⠠⠄⡰⢀⠎⢨⠐⡌⡐⠢⠌⣴⡾⠛⠉⠉⣿⢇⡻⢌⠳⡌⡖⣡⠓⣎⡱⢚⠴⣡⠳⡌⢎⡵⢒⡬⢃⡎⠵⣌⣿⡏⢞⡸⣿⠀⢀⡿⠀⠀⠉⠉⠉⠋⠛⠙⠋⠉⠉⠉⠁⠀⠀⠀⣿⡎⣌⠓⣌⠲⡰⣉⠖⡤⢓⠬⣘⠢⢆⠣⣌⠱⣑⠪⠜⣢⠱⣉⢼⣏⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣄⣀⣀⣀⢀⢀⣀⣀⣀⣀⣠⣤⡶⠞⠛⣹⣿⡿⠛⠉⠉⠉⠙⢳⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣃⠱⡈⠇⢼⣿⡩⣾⣿⠠⡉⢆⠡⢃⠌⡡⢂⠔⡠⢂⠱⣀⠣⡐⢌⣿⣿⣯⠡⡐⢢⠑⡌⢡⠊⡔⢨⠐⡂⢌⠂⠥⡐⢡⠑⣾⠏⠀⠀⠀⢰⣟⠮⡱⢎⣣⠳⣘⢥⢫⢔⢣⣋⠶⣡⠳⡜⢣⡜⢥⡚⢥⡚⡱⢬⣿⣏⠶⡱⣻⡇⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⣌⠳⣨⠱⡑⢦⡉⢖⡩⢒⡡⡙⢆⡓⠬⡱⢌⢣⡙⢤⠓⣌⢺⣧⣤⣀⣀⣙⣷⣤⣤⣦⣴⠶⠟⠛⠷⣶⣦⣤⣤⣤⣬⢽⡏⠉⠛⠋⠉⠉⠉⠉⠁⢀⣀⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠒⡩⠜⣼⣿⣱⣿⡏⡔⢡⠊⡔⢡⠊⡔⢡⠊⡄⢃⠆⠥⢣⠘⣾⢿⣿⡿⢠⠑⢢⠑⡌⢢⠑⡌⢢⠑⡌⢢⠉⢆⡱⢂⣽⠏⠀⠀⠀⢀⣿⢫⡜⣱⢫⡔⣫⠜⣦⢫⣌⠳⣌⠶⣡⢳⢩⡓⣜⢣⢞⡡⢞⡡⢧⣿⣏⡞⣱⢹⣷⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⡗⣌⠳⡄⢧⡙⢦⡙⢢⡑⢣⠒⡍⢦⡙⢦⡑⢎⠦⣉⠦⡙⢤⢻⣿⣭⣭⣯⣽⣭⣿⡄⣿⠁⠀⠀⠀⠀⠀⠉⠻⠶⣦⣤⣸⣇⣀⣀⣀⣤⣤⣴⠶⠿⠛⠉⠀⠀⠀⢀⣠⣴⠷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠱⣉⣾⣷⡟⣸⡗⣈⠆⡱⣈⠦⡙⢤⢃⠜⡠⢃⡌⣓⠢⣹⣿⠂⣍⠰⡁⢎⠢⡑⡌⢆⡱⡘⢆⠣⠜⡠⢍⠲⣄⢣⡿⠀⠀⠀⢀⣾⣏⠳⡜⣥⠳⡜⣥⢛⡤⢳⣌⠳⣬⠳⣥⢋⠶⡹⣌⠳⣎⠵⣋⠼⣡⢿⣷⡸⢥⣫⡿⣿⣿⣻⣟⠷⡶⢶⡶⢶⠶⡶⢶⠾⡟⣟⣻⣫⣽⣿⡧⢌⡳⡘⢦⡙⢦⡙⢦⡙⡌⢧⡙⢦⡑⢦⡙⡌⡖⣡⠞⡱⣊⢽⣏⠉⠉⠈⠁⠀⠸⣇⠻⣧⠀⠀⠀⠀⢠⣶⢶⣤⣄⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⢉⣀⣠⡤⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣮⣿⡿⠀⣿⡃⢦⠩⢔⠢⡜⠱⡌⡜⢢⠱⡡⢎⠴⢱⣿⠇⣜⠰⡃⣍⠢⢣⠱⡘⠦⡱⡑⢎⡑⢎⠱⡌⡓⢤⣻⠇⠀⢀⣴⡿⢯⡜⣹⡜⢶⡹⡜⢦⢫⡜⢧⢎⡝⢦⡛⡴⣋⠷⡱⢎⡳⣬⠳⣍⠞⡥⣿⣷⣙⢾⣿⣧⢿⡁⠉⠙⠛⠛⠳⠾⠷⠿⠾⠛⠛⠛⠛⠉⠉⠁⣿⢧⢹⡰⡙⢦⡙⢦⡙⢦⡱⡙⢦⡙⢦⡙⢦⡱⢱⣊⢕⡪⠵⣘⠺⣿⣤⣤⣤⡶⢶⠿⣿⡿⢋⡀⠀⠀⠀⠈⠛⠗⠈⠉⠛⠷⢶⣤⣤⣤⣤⡴⠀⠀⠀⠀⣾⣿⡵⠶⠟⠛⠉⠁⠀⠀⠀⢀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃⢠⣿⠑⣎⠱⣊⠵⣈⠷⡘⣌⢣⠓⡴⣉⠖⣿⡟⡸⢄⣣⠑⢦⡙⢆⡣⢝⠢⣕⠩⢆⡍⢆⠳⣌⠱⢢⣿⣠⣴⡿⢯⡹⡖⣭⠳⣜⢧⠳⣍⠯⣖⡹⣎⢞⡼⢣⡝⢶⣙⠮⣝⣹⠲⣕⣫⢜⣫⣜⣿⣗⢮⢭⢳⣿⣿⣦⣀⣀⡀⡀⢀⠀⡀⢀⠀⣀⣀⣀⣀⣠⣤⣴⣿⡇⢧⢣⡝⢦⡙⢦⡙⢦⣓⠹⣆⡝⢦⡙⢦⢓⡣⡜⢎⡜⣣⢍⡳⣹⣿⡔⣣⠞⣥⠳⣽⣧⡘⢷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠃⠀⢸⣟⡸⢤⠓⣌⠖⣱⢪⠱⡌⢦⡙⡴⢡⢾⣿⢡⠳⡌⢦⡙⢦⡙⢦⠱⣉⠳⡌⡝⢢⠜⣪⠱⣌⣣⣿⡿⣏⢷⣩⢗⡳⣝⠮⣝⡞⣎⢿⡸⣝⡲⡽⡜⣞⡼⢣⣏⠷⣪⣛⣬⠳⣝⢮⣜⡳⣜⣾⡿⣹⢎⡯⢞⣿⣿⡭⣛⡛⣟⠻⡟⢿⠻⡟⢿⣛⢻⡙⢯⡝⣭⢒⢿⣿⡎⢧⡚⣥⢛⢦⡙⡦⣍⠳⡜⣜⢣⡝⣪⢕⡣⡝⢮⡜⡥⢎⡵⣩⢿⣷⣡⢛⣴⡿⠏⠙⠻⣦⣍⡙⠋⠁⠀⠠⠀⢀⠠⠈⠀⣀⣤⣤⣴⠶⢶⡶⠆⠀⠀⠠⠀⠀⢀⣠⣴⡿⠛⠉⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣽⠇⠀⠀⣿⡇⢮⢅⠏⣆⡛⡴⢃⡳⢜⢢⢳⡘⢣⣿⢇⠧⡣⢝⡢⢝⡢⢝⣢⢛⣌⠳⣍⡜⢣⡚⢥⢋⣼⣿⢳⡝⡾⣬⢳⣎⠷⣭⢻⡜⣞⡭⢶⡹⢮⡵⡳⣝⢮⢞⡳⣎⡟⣥⢳⣎⠿⣜⢧⡞⣵⣿⢻⡜⣧⢻⣜⣿⡟⣿⠶⣍⡳⣬⢳⣙⢎⣳⡙⣦⣙⢦⡛⢦⡝⢦⣋⠞⣿⣟⢦⣙⢦⢫⢖⡹⢲⣍⢳⡹⣌⡳⣜⡱⢎⡵⣙⠶⣸⢱⣋⠶⡱⢎⣿⣧⣿⠟⠁⠀⠀⠀⠀⠉⠛⠻⠶⢶⣤⣤⣀⣄⣀⣀⡙⣋⢉⣀⣀⣀⣀⣄⣤⣤⣶⠶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⣛⣾⠏⠀⠀⢰⣿⡙⢦⣋⠞⡴⡹⢜⣣⢓⡎⡳⣌⠳⣽⡟⡜⢮⢱⣋⡜⣣⠞⡱⢎⠧⣎⠳⣜⡸⢣⡙⢮⡱⣿⣯⢳⡝⣧⢏⡷⢎⡿⣜⢧⡻⣼⡹⢧⣛⢧⡳⣝⢮⣏⢾⡱⢯⡜⣧⢻⡬⣟⡼⣣⢿⣿⣭⣷⣿⣾⡿⣿⣿⡇⣿⣏⠶⣣⢧⢳⢎⡝⡦⣝⠦⡝⣦⢫⢳⡜⢧⡺⣙⡞⣿⡞⣜⣎⢳⢮⣙⠧⣎⢧⢳⡜⡵⢪⡵⣋⠶⣍⠾⣡⠗⣎⡳⢭⡓⢾⣿⠏⠀⠠⠐⠀⠠⠀⢀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠋⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠ ⣤⣀⣄⣀⣀⣀⣠⣿⣷⣿⣏⣲⣖⣤⣾⡷⣽⢶⣭⣾⣵⣽⢾⣴⣯⣶⣷⣼⣳⣿⡽⣮⣧⣷⣼⣼⣵⣮⣽⣬⣷⣬⣽⣬⣵⣧⣽⣦⣽⣿⣧⣯⣾⣥⣿⣼⣯⣼⣭⣾⣵⣧⢿⡽⣮⣽⣵⢯⣾⣬⣷⡽⣧⣿⣼⣧⣽⣮⣵⣯⣿⣯⣿⣭⣿⣼⣽⣶⣿⣬⣿⣬⣷⣭⣮⣽⣮⣽⣵⣮⣽⡽⣦⣯⡷⣼⢧⡽⣵⣮⣿⣿⣬⣮⡽⣦⣭⡷⣭⣮⢷⡼⣭⣧⢷⣭⣽⣬⢯⣵⣯⡼⣵⣯⣼⣽⣏⣤⣤⣤⣤⣤⣤⣤⣤⣤⣌⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣠⣄⣤⣤⣤⣀⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠤⠆⠦⠪⠃⠛⠙⠋⢋⠫⣩⡹⢍⣖⡂⠢⡄⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡦⡚⡉⠅⠄⠄⠄⠤⠧⡀⠢⡀⠡⠲⢕⣁⠄⣀⣂⣔⡀⣄⣀⡀⣀⠢⠒⡠⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠓⣄⡤⣲⣢⣤⡶⠶⠽⠛⢛⠋⡛⡛⢍⢉⢫⣛⣓⣛⣵⣒⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⡀⣀⡦⠞⡋⠹⡯⠃⠁⠁⠁⠁⠀⠀⠀⠀⠀⠳⡄⠀⠀⠈⠋⠐⠐⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⢀⡀⢀⡴⠚⠁⡀⠂⠀⠠⡇⠀⠀⠀⣢⣤⡄⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡟⢀⡀⠂⠀⠀⠀⡁⡇⠀⠀⠀⢿⣛⡁⠀⠀⠀⠀⠀⠀⣗⠀⠀⣀⢤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠇⢸⢠⠃⠀⠀⠀⠀⠀⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣠⢅⡥⢓⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠊⢆⡄⠄⠀⠀⠀⠀⠀⠀⢀⢐⣀⣏⡟⡇⠖⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡛⣖⡲⣦⡆⣶⣾⡯⣣⡻⠑⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠋⠗⠶⠕⠤⠦⠵⢩⠃⡉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⣿⣿⣿⡿⡛⠁⣠⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⠀⠹⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⡫⠋⢀⠊⣰⠇⢀⣔⣡⠃⠀⠀⠀⢀⡄⠀⠀⡇⠀⢳⠇⢠⣽⢸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢫⣾⠁⡴⠃⢔⡽⠀⢸⢷⠞⠌⠀⣰⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠛⡇⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣧⢝⣠⣾⣇⠇⢠⣏⣦⢀⠠⠀⡇⡇⠿⢰⠀⠀⠀⠀⠀⠀⠀⠀⢇⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣷⣿⣿⢫⢁⣟⣽⣧⣍⢇⢳⡀⢘⢃⡜⢰⠀⠀⠀⠀⡆⠀⠀⠈⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⡯⡛⠛⢰⣾⢿⣿⣿⠟⣾⣸⣁⣜⡂⡇⡄⠀⠀⠀⣴⠀⠀⠀⠀⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡎⠽⡏⠀⠀⠈⠙⠏⣽⣿⣼⣥⡿⣿⣏⠃⢠⠁⠀⠀⣠⠇⡄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢸⡃⠀⠀⠀⠀⠀⠀⠀⠈⣝⠞⣣⠿⢸⠏⠀⠀⣸⢋⢜⡺⠀⠀⠀⢡⢹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣴⣹⣷⣄⠀⠀⠀⡠⢰⢊⠋⢐⣟⠇⡌⠀⠀⣰⣷⡟⣼⡇⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡁⡯⣿⡉⠉⠀⠠⠊⠀⢧⠇⢀⡞⡟⡀⠁⠀⣼⠟⣵⣾⣿⡇⠀⠀⡀⠀⡿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⣿⣯⣙⣦⣴⣄⣶⡿⡎⣦⢱⢀⠁⣠⡞⠑⣱⣽⣿⡿⠃⠀⠀⢿⢰⡧⠃⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣷⣿⣿⣝⣛⡏⢁⣷⣿⢿⠘⢀⣴⢋⢄⡬⢞⠋⢿⠅⡼⠀⡀⡎⣼⡇⢀⠙⢹⢝⣺⡻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣾⣾⡐⣿⡸⠤⠿⠓⠛⡛⠈⠁⠀⠸⣤⣃⡆⢇⣧⢠⢱⡸⣦⠸⣾⣾⣧⠘⣷⣯⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡍⠀⠀⠀⠀⠀⠈⢦⡀⠀⣐⠸⡿⡴⠈⡇⢪⠀⡇⡽⡀⢱⣥⢽⣗⡜⡝⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠹⣰⢻⡿⡧⢱⠸⠆⣿⣧⠳⡀⢻⣷⣿⡤⠙⣌⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣷⡄⠀⠀⠀⠀⠀⠀⢀⢠⠒⡿⣾⢗⢛⢧⢣⢻⣏⠻⣆⡑⡀⠱⡮⣳⠀⠈⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⢿⠷⣄⠀⢠⠴⢆⠑⢋⡣⠩⣟⠚⢙⡅⣣⣣⢌⠲⡈⠺⡚⡦⣈⣹⠀⠀⠀⡟⡽⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⣿⣗⢁⠀⡈⢥⣪⠪⡀⠈⠦⡐⠨⠙⣮⣷⡣⣫⠢⡈⢪⠺⠸⠀⠀⠀⡇⣟⣿⢛⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡃⣿⣤⢦⡅⠠⣑⠉⢳⠀⠀⢀⣑⢢⠀⢁⡾⠷⣓⢌⢇⠱⡇⠀⠀⢠⡽⣼⢹⣗⡼⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡴⡸⡾⣾⡇⠀⡟⠀⠸⣔⡉⢀⠘⡌⢀⠜⢏⠀⣻⡤⢯⠢⢳⠀⠀⡾⣿⣿⢋⡹⡽⣜⡿⣿⣿⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢷⢨⡟⡿⣧⡰⣀⣀⠀⠁⠱⠀⠀⠀⠀⠀⠈⢏⠀⣧⠀⢀⠆⡄⣼⣿⢹⠘⠀⠑⣟⣽⣷⠷⠶⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣷⢫⣧⠃⠇⠘⣫⣖⠾⠉⠉⠁⠀⠀⠀⠀⠀⢠⠀⢢⠿⢐⠀⢰⣿⣇⠛⢸⢸⠀⣀⠜⡿⣿⡆⡠⠄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣘⣼⣷⣽⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠑⡄⠱⡀⣼⡩⠈⢿⠀⢸⣟⠀⢻⠀⠐⣽⣹⣿⣿ ⣿⣿⠟⢻⣿⣿⣿⣿⣿⢹⡿⠿⣛⡛⢇⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠁⣿⢶⡀⠠⡓⢼⣯⠑⡈⣷⢄⠈⢻⣿⣿ ⣿⣿⣆⣿⣿⣿⣿⡟⡟⡗⠊⢉⣮⠰⠸⢰⠀⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢯⣞⢷⢄⣹⣆⡉⠦⣈⢺⣦⡑⠢⢤⠭
⠀⠙⠀⠀⠀⠀⠀⠘⣷⡀⠀⠈⢳⡘⡄⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⡇⡇⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⡞⢷⢹⠘⣶⡄⠀⠀⠀⢀⣀⣠⠴⠞⣿⡇⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣄⠀⠀⠳⣽⡄⠀⠀⣀⠹⡄⠀⠀⠐⣆⠀⠀⠀⠈⢧⡇⣷⠀⠀⡀⠀⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⢻⣾⣼⢀⣟⠉⠛⠋⠉⠉⠉⢹⠀⠀⢻⡿⣆⠀⢧⠀⠀⢣⡀⠀⠀⠀⠀⢻⡜⢦⠀⠀⠹⣷⡀⠀⠘⢆⢻⡄⠀⠀⠘⣆⠀⠀⠀⠈⣧⣿⣰⠀⠹⣆⠀⢹⡉⣓⡦⢄⡀ ⠀⢀⡼⠁⠀⠻⡅⣾⡿⠀⠀⠀⠀⠀⠀⠈⣧⠀⠘⢷⠙⢦⠈⢧⠀⠀⠱⡄⠀⢳⡀⠘⡝⢮⣳⡀⠀⠹⡷⡄⠀⠈⣾⡟⣆⠀⠀⠸⡆⠀⠀⠀⠸⣿⢻⡄⠀⠹⣆⠀⢷⠋⢀⡴⠋ ⠒⣈⡴⠀⠀⡀⣷⣿⡇⠀⠀⠀⢠⠀⠀⠀⡾⢧⠀⠸⡄⠀⠙⢮⣷⡄⠀⠘⣶⣄⠙⢤⢳⠀⠙⠻⢦⣀⢹⡌⠳⣄⠸⡇⠈⢣⡀⠀⢻⠀⠀⠀⠀⢻⡀⢳⡀⠀⠹⡄⠈⢷⠀⠀⠀ ⠀⣸⠁⢀⡞⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⣳⣄⣷⢴⠀⠀⠈⠙⠣⣄⠘⢯⠓⠦⣤⣧⠀⠀⠀⠀⠉⠃⠀⠈⠳⡇⠀⠀⠙⢄⠘⡇⠀⠀⠀⠈⡟⣦⢳⠀⠀⠀⠀⠈⢣⡀⠀ ⠀⠃⢀⡞⠀⠀⢸⡇⠀⠀⠀⠀⢿⣧⠀⠀⡟⠉⠀⠀⠉⠃⠀⠀⠀⠀⠀⠈⠓⠦⣷⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡄⠀⠀⠛⣧⠀⠀⠀⠀⢹⠈⣿⣆⠀⠀⠀⡀⠀⠀⠀ ⠀⢀⡟⠀⠀⢀⣾⠀⠀⠀⠀⠀⠸⣿⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢁⣼⣶⣾⣿⣿⣷⣦⣄⠀⢸⠀⠀⠀⠀⢸⣷⣸⣿⡀⠀⠀⠹⣦⣄⣀ ⠀⡜⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⢹⣷⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣴⡿⠛⣁⣤⣤⣤⡀⠉⠻⣷⣸⡇⠀⠀⢰⠀⡇⢳⣏⡇⠀⢱⠀⠹⣧⠈ ⠈⠀⠀⠀⣸⢹⠁⠀⠀⠀⠀⠀⠀⢸⡿⣧⢸⠀⠀⠀⣄⠀⠒⠲⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢀⣼⠟⢳⣄⡉⠙⢷⡀⠈⢻⡇⠀⠀⢸⣀⡇⠀⢳⣧⠀⢸⡇⠀⠘⡇ ⠁⠀⠀⢠⠇⢸⠀⠀⢀⠀⠀⠀⠀⠀⡇⠈⣿⣧⣾⡿⠿⠿⠿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠀⣞⣿⣿⡆⠀⣧⠀⢸⡇⠀⠀⢸⣿⠁⠀⠈⣿⠀⠈⡇⠀⠀⢷ ⠀⠀⠀⣼⠀⣿⠀⠀⢸⡄⠀⠀⢠⠀⣇⢀⣾⡟⠁⣠⣶⠾⠿⠶⣤⡈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠻⠿⠿⠃⠀⣿⠀⢸⠁⠀⠀⢸⡿⡆⠀⠀⢻⠀⠀⡇⠀⠀⢸ ⠀⠀⢠⣿⠀⣿⠀⠀⠀⢳⡀⠀⠸⡆⢹⣼⡟⠀⣼⡟⠉⣷⣶⣦⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⢀⡴⠋⠀⣾⡇⠀⠀⡾⠁⠃⠀⠀⠘⡆⠀⡇⠀⠀⠈ ⠀⠀⢸⢸⡀⢻⠀⠀⠀⠈⢧⠀⠀⢳⠘⣿⡇⠀⢿⠱⠸⣷⣿⣿⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠀⠀⢰⣿⡇⠀⣼⠁⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀ ⠀⠀⠸⡄⣇⢸⢰⠀⢠⠀⠸⣷⡀⠈⢧⣿⣧⠀⠘⣇⠀⠉⠉⠉⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⠃⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀ ⠘⢶⡀⢣⠘⣾⡏⣇⠘⡄⠀⠹⣷⣄⠘⢿⡝⢧⣀⠈⠳⣤⣤⣤⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣾⣾⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀ ⠀⠀⠉⠲⠷⡿⢻⢹⡀⢳⠀⠀⠈⢿⣷⣌⡳⣄⠈⢉⣐⠀⠀⠀⠀⣀⠴⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⢸⣧⠇⠐⠀⡀⠀⠀⣸⡇⣀⢰⠃⠀⠀ ⠀⠀⠀⠀⣴⠃⢨⣧⢷⡈⢧⠀⠀⠸⣿⠹⣟⠛⠷⢤⠈⠑⠦⡴⠚⠁⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⢠⠇⠀⢀⣿⠃⡇⢸⡄⠀⡀ ⠀⢀⡠⠞⠁⢀⡞⢨⢿⣧⠈⢧⡀⠀⢹⡄⠘⣦⠀⠘⡆⢀⣠⠞⡿⠀⠀⣇⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⣾⠀⠀⡼⣸⣸⢧⣀⢳⡀⠈ ⡚⠉⠀⣀⡴⢛⣄⡞⠀⡟⢧⡀⠳⡄⠈⢧⣦⠈⢷⡄⠱⣯⢟⣾⣡⡾⠇⠈⠳⣄⠀⠀⠀⠀⣿⠖⠛⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⡇⠀⠀⢰⡏⠀⣸⡃⣿⡧⠋⢈⡽⠛⢶ ⠉⠛⠛⠛⠋⣹⡿⠁⠀⡇⠀⠙⢦⠙⢦⡈⢿⣇⠘⣷⣄⠀⠾⠜⢹⣷⡾⠇⠀⠈⠓⣦⠀⠀⣇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⣴⡿⠀⢸⠁⠀⠀⡾⠀⣰⢻⢳⣟⣀⣴⣋⣠⠔⠋ ⠀⠀⠀⠀⣴⣿⠄⠀⠘⢠⡆⠀⠀⢻⡦⣝⡲⣿⣄⠹⣿⣷⠞⣷⡄⢠⠖⠒⠋⠉⠉⠁⠀⠀⠈⠳⠖⠚⠀⠀⠀⠀⠀⢀⣴⣿⠋⣀⠀⣿⠀⠀⡼⠁⢰⡇⡏⢸⠇⠁⠈⠀⠀⠀⠀ ⠤⠴⠒⠋⠉⠀⠀⣠⠴⠋⠀⠀⠀⢨⣷⡠⠉⠉⠻⡗⢿⡟⠼⢹⡟⢾⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢻⡟⣿⡀⢻⣠⡇⠀⡸⠁⣰⠟⡿⣿⠸⡆⠀⠀⠀⠀⠀⠀ ⠙⠒⠦⠤⣤⣴⡿⢥⡶⠋⢀⣠⠔⠃⡇⢹⣄⠀⠀⠙⡞⠀⠀⣼⢿⡭⠒⠚⠻⣿⠷⠶⢤⣤⣤⣀⣀⣀⣤⠞⠋⠁⠀⢸⣿⣿⠻⣤⡿⢀⡼⠁⡴⣿⠀⡇⠈⠳⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣻⠤⠒⠛⠛⠋⠁⠀⠀⢰⣣⠏⢘⣦⣀⠞⠀⠀⢰⠛⢿⣄⣀⠀⣠⡞⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢠⡿⠁⢻⡴⣻⠃⠀⢠⣾⡁⢣⡀⢳⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠐⠒⠛⠓⠚⠋⣰⠋⠀⠀⢠⠿⣧⣾⣿⡿⠉⠙⢷⣏⠉⠉⠙⠢⠤⣄⡀⠀⠀⣠⡶⠋⠀⠀⠀⣻⠃⢀⡴⡿⠟⢉⡟⠷⢬⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣰⡏⠀⠈⠳⣾⡇⠀⠀⠀⠈⠛⠦⣄⣀⠀⢀⣨⡽⠛⠁⠀⠀⠀⠀⡴⠁⣰⠋⢰⣇⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠒⣫⠟⠛⣳⠦⢄⣴⠃⠀⠀⣰⣏⣽⣆⠀⠀⠙⣧⠄⠀⠀⠀⠀⠀⣠⣼⣛⣻⣧⣄⠀⠀⠀⠀⠀⡼⠁⣼⠃⠀⣸⠈⢳⣦⣄⣀⣀⣤⣖⣛⣟⣛⣛⣤⡄⠀ ⠀⠀⠀⠀⠀⡴⠋⢠⣾⠥⠤⢶⠓⢲⠟⠁⠀⢀⣴⠏⢀⡾⠉⢧⠀⠀⠈⢇⠀⠀⠀⠀⡾⣿⡿⠁⣦⣮⣻⣣⡀⠀⠀⣸⠁⣰⠋⠀⠀⡟⠀⠀⢳⡌⠉⠉⠉⣩⠞⠁⠀⠀⠈⠉⠓ ⠀⠀⠀⠀⠸⣠⠞⠉⠀⠀⠀⠀⡱⢋⣀⣀⣠⣿⣟⡤⠿⠤⠴⢾⣧⠀⠀⠈⣧⠀⢀⣼⡇⣿⣿⡶⠾⣿⣿⣿⠷⣄⠀⡏⠀⡟⠀⠀⢂⡇⠀⠀⣠⠿⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢧⠀⠀⠸⣤⠞⠉⢷⡙⢿⣶⣾⡿⣯⠟⠀⠈⢻⠃⢰⡇⠀⠀⢸⣷⣠⠞⠁⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡞⢀⠆⠀⠀⠰⠤⠤⠤⠤⠖⠒⠋⠉⠹⡏⣇⢰⠀⣧⠀⠀⠈⠉⠒⠶⠶⠚⠁⠀⠀⠀⠀
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