Biological Species Concept Emoji Combos

🦠🧬🦖

new evolution evolve darwin charles darwin biology genetics species evolutionary biology speciation macroevolution common descent mutation natural selection

🦣🧬🐘

new evolution evolve darwin charles darwin biology genetics species evolutionary biology speciation macroevolution common descent mutation natural selection

🦎🧬🦖

new evolution evolve darwin charles darwin biology genetics species evolutionary biology speciation macroevolution common descent mutation natural selection

🌳💀🔬

new evolutionary biology phylogeny skeletal anatomy macroevolution anatomical study

🦠➡️🌿➡️🦋➡️🐒

new speciation diversification phylogeny evolutionary history macroevolution common descent

🐒➡️🧍🌳

new evolutionary biology natural selection phylogeny human evolution speciation primatology

🐟➡️🦎➡️🐒➡️🧍

new speciation human evolution evolutionary lineage major transitions vertebrate evolution

🌳🐢🐦💡

new speciation natural selection charles darwin galapagos tortoise darwin's finches

🐒➡️🚶‍♂️🧬

new human evolution speciation phylogenesis evolutionary path genetic origin common ancestor

🧬🐟🦎🐒

new hox gene evolutionary biology evo-devo conserved genes comparative genomics animal development

🌳🐒🦋🐟

new tree of life speciation common ancestry phylogenetic branches species relationships cladogram

🧬➡️🌳💻

new phylogenetics evolutionary biology sequence comparison tree building computational genomics

🧬🔬🌿🐒

new biological species speciation

🐒➡️🧍🔬

new richard dawkins evolutionary biology human evolution

🦕➡️🐦🧬

new origin of species speciation phylogenetic tree evolutionary biology animal lineage

🏃‍♀️🧬🔄

new red queen hypothesis evolutionary biology coevolution leigh van valen

👥⛰️👥

new geographic isolation speciation population separation biogeography reproductive isolation

🦠➡️🐠➡️🦎➡️🧍

new origin of life evolutionary biology life's progression abiogenesis common descent from sea to land

🐒➡️🚶‍♂️⏳

new origin of species speciation natural selection change over time

👑🟥🏃‍♀️↔️

new red queen hypothesis evolutionary biology coevolution running to stay in place evolutionary arms race lewis carroll reference

🦁🦓🦒🦋🐠

new biological species animal kingdom speciation life forms

✨🆕🐾

new BNA brand new animal new species beastmen trigger

🧬🌳💻

new PAML phylogenetics evolutionary biology bioinformatics maximum likelihood molecular evolution

🐺→

new common ancestor divergence new species adaptation mammals canids lineage splitting

🧬📖

new richard dawkins the selfish gene evolutionary biology ethology

🌳📈🌿V

new tree of life common descent speciation descent with modification branching evolution

🧔‍♂️🫂🧍‍♀️➡️🧬

new neanderthal DNA ancient DNA interbreeding human ancestry archaic human admixture human origins

🐦→🏞️→

new allopatric speciation geographic isolation reproductive isolation new species divergence birds

🌳🦴➡️💪🐾鰭

new homologous structures comparative anatomy evolutionary biology common descent vertebrate limb

🧬🤝🧬

new genetic relationship sister taxon evolutionary biology related species phylogenetics common descent

🦖🐒⏳

new natural history origin of species evolutionary biology

🧬➡️📈✨

new genetic evolution positive selection evolutionary biology

🧬⏳🦋

new evolution metamorphosis adaptation speciation genetic change natural development biological transformation

🌳🧬🔬

new phylogenetics taxonomy tree of life evolutionary biology classification biodiversity molecular systematics morphology

🌳🪵🦋🦎

new tree of life phylogeny biodiversity speciation common descent life's diversity

🧬🕰️📈📉

new life history evolution natural selection fitness optimization evolutionary biology adaptive strategies selection pressures

🧬🌳➡️🐒

new phylogenetic tree DNA tree common ancestor speciation

🐒➡️🚶‍♀️🧬

new human evolution biological anthropology human origins evolutionary biology human development primatology

🧬➡️✨

new genetic evolution genetic change natural selection speciation biological progress

🐟➡️🦎➡️🦖

new vertebrate evolution origin of species fossil record speciation

🔬🧬🌳

new species study biodiversity research xenobiology evolutionary biology species classification phylogeneticist

🧬👩🌍

new mitochondrial eve first modern human woman human origins evolutionary biology paleoanthropology scientific first woman african eve

🐾4️⃣🌳

new tetrapods four limbs vertebrate evolution evolutionary biology biology 4

🌳➡️🌿+🌱

new phylogenetic tree divergence branching evolution adaptation new species cladogenesis macroevolution

🧬🔄🔗

new hybridization gene flow DNA mixing population genetics interbreeding mixed ancestry

🧬🦎🐍

new squamata reptile classification herpetology taxonomy evolutionary biology lizards snakes

🧬🌳🏝️

new bio-expedition genetic discovery remote exploration island adventure new species field biology eco-adventure

🐺↔️🐕

new coywolf coyote wolf hybrid hybridization coyote wolf mix interbreeding

🧬🐒🧍

new primate genetics human lineage common descent anthropology evolutionary biology

🕰️🦴➡️🦈

new shark evolution ancient fish fossil record phylogeny evolutionary biology

🌳↖↗️🌱

new evolution branching phylogenetic tree common ancestor speciation lineage split cladogenesis

🌳🐾

new animal phylogeny tree of life animal kingdom zoology evolutionary biology

🌋🐦🧬

new hawaii evolution adaptive radiation endemic species finch evolution speciation island evolution unique birds

👑⬏️[🐒+🦋]

new crown group vs stem group cladogram MRCA living descendants evolutionary biology systematics

🦖➡️🐟

new colodus prehistoric fish triassic fauna ancient fish evolutionary biology

🧬⏳➡️🧬'

new genetic drift mutation natural selection genetic divergence molecular evolution new species gradualism

🌳{🐒🦍}

new phylogeny evolutionary tree common ancestor descendants taxonomy speciation hominidae

🌳[🐒🦍]

new monophyletic group cladistics taxonomy classification systematics evolutionary biology tree thinking

🐟➡️🐒➡️🚶‍♂️

new natural selection darwin ancestry human evolution paleontology speciation

🌱🧬➡️🌳⏳

new plant evolution paleobotany tree origins deep time plant genetics speciation

🦖🔗🐦🦴

new archaeopteryx linking fossil transitional fossil dinosaur to bird link bird evolution evidence urvogel missing link evolutionary biology

† ᡣ𐭩 ˚☽˚.⋆

new interbreeding cross

new interbreeding heart

alt
ִ ࣪𖤐ִ ࣪𖤐ִ ࣪𖤐

new cross interbreeding

🌿🎀❄️

new holly genus speciation berry ave family

☦︎🕷👁️⃤🪽☠︎︎༒︎

new cross crosswise interbreeding

👨 ➡ 🐒 human to monkey, evolution reversed

new evolution evolutionary biology genetics evolutionary genetic

      ♱
     ♀

new cross spoil scotch bridge genetic science interbreeding

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

⢻⣿⣿⣿⣿⣿⠀⣾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠛⠻⠿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣈⠁⢹⣿⣿⣿⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀
⣿⡄⠀⢻⣿⣿⣿⣦⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⣀⣠⡀⠀⠀⠀⠀⣸⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⡿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡆⠀
⣯⠀⠀⠀⠙⢻⣿⣿⣿⣷⣤⣀⣀⣀⣤⣤⠀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⠿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⠁⠀
⣿⠟⠀⠀⠀⠀⠀⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣧⣸⣿⣿⣿⣿⣿⡄⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣤⣤⣤⣄⢀⣀⣀⡀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣿⡀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⢻⣿⣿⣿⣿⣿⣿⠿⠟⠉⣉⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⡏⠻⢿⡿⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⠃⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣾⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣿⣿⣿⡿⠟⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣶⣾⣿⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣶⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⢠⣤⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣯⡉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡆⠀⠀⠀⢻⣿⣿⣿⣶⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⣴⣿⣿⣟⣾⣿⣿⡏⢈⣉⠉⠉⠉⠀⠀⠀⠀⣾⣿⣿⡟⠋⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣤⠛⢿⣿⣿⣿⣿⡍⠛⠛⢸⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⢸⡇⣠⣾⣿⣿⣭⣿⣿⣿⣿⠇⠈⠏⠀⠀⠀⠀⠀⠀⠀⠻⢿⡿⠁⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠉⠀⠈⠻⣿⣿⣿⣷⣤⣤⣼⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⡟⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢰⣶⠀⢀⣽⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⢛⣛⣛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣶⡆⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠿⠿⠟⢻⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣤⣤⣤⣤⣄⣀⣠⣤⣄⣀⡀⠘⠃⠀⠘⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣴⣦⣶⣦⣤⣤⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣾⣿⣿⣿⣿⣿⣿⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⢾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⡿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠋⠁⠀⠀⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⡛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣀⣀⣀⠀⣰⣿⣿⠀⠀⠀⢰⣿⣿⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⣿⣿⣿⣿⠿
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣶
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠈⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⡿⠿⠻⠟⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿
⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⣶⣶⡶⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⠀⠀⢠⣄⣠⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⠛⠋⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠋⠀⠀⠀⠀⠀⠰⠿⠿⠛⠀⠀⠸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠿⣿⣿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣷⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣤⣤⣤⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣋⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠺⠂⠙⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⢿⡙⣯⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣤⣤⣿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⢰⣶⠐⠿⠇⠀⠾⠿⠿⣶⡄⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠿⠿⠿⠿⠿⣶⣾⣷⠸⠿⠶⠆⠸⠿⠀⠀⠀⠰⠆⠀⠀⠀⠀⠶⠶⠶⠆⠸⠷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠀⢰⣦⠀⠀⠀⣶⡆⣶⡆⢀⣀⠀⠀⠀⢻⣿⢀⡀⢀⣤⡀⠀⠀⠀⠀⢩⣥⢀⣠⣶⢰⣶⠀⢀⣄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀
⢠⣤⡄⣠⣤⣤⣴⣆⣤⣤⣤⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣾⣎⠁⣀⠀⢠⣿⠁⣿⡇⠘⣛⡀⢀⡀⠛⠛⠛⣃⠀⢉⣀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠈⣿⡀⠻⢿⠀⠘⠛⠀⣀⣀⠀⣀⣀⠀⠀⠀⠘⠛⠃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠈⠉⠀⠸⠿⠀
⠸⠿⢻⣿⣿⠿⠿⢿⣿⣿⡿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⣷⠸⠿⠿⢿⡇⣤⣤⠐⠛⣿⣿⣿⣿⡿⠿⠇⠀⢰⣿⣅⠀⠀⠛⠿⢷⡘⠛⠀⠀⠿⠿⢿⣿⣿⠿⣿⣿⣿⣿⣿⡟⠿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣷⣤

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