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0:56 ─〇───── 4:25
⇄ ◃◃ ⅠⅠ ▹▹ ↻

GREETINGS AND SALUTATIONS!!!!!1!!!!11
I'm Jasper Rose but I go by Jay
You might know me from my old users "Honeybea" "vanilla 'BEA' frappuccino" or just "Bea" in 2022-2023
Here's a bit about me since it' been awhile.

Jasper Rose

He/Him
Demiromantic, Pansexual, Transgender.
atheist but I respect religion
TAKENN!!!!!
15
favorite colors are yellow and purple
i'm a huge object show fan
(im literally x and airy guys)
i play roblox sometimes i guess
i like regretevator and pressure.
(im literally mark guys)

real ones:

A.A (the mallow man)
Marcus
Strawberry jam
Cleo
Jayden

Im currently making an object show
and I'm hopefully gonna be voice acting in another one

The one I'm making is Battle for Animemaker(Bfam)

and I didnt get permission to talk abt the other one so I'ma not

i dont post anyways so heres a wall of copy pastas you can use

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣟⣾⡭⢹⣯⠌⣿⡭⢹⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣟⣾⣼⣿⣏⣾⣿⣴⡿⣞⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣿⣼⣿⣯⢿⣿⢿⡾⠽⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣾⠿⡿⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⣠⣴⢟⡫⢕⣪⡓⡵⢪⡕⡻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣤⡾⣛⡭⢳⡭⡝⣻⣆⠀⣠⡾⣛⠴⣃⡾⠉⢀⡟⡴⢃⡞⡱⢎⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣣⠟⠉⠙⠉⡵⢹⡔⣿⣴⢯⣑⡎⠶⡏⠀⢀⠎⠑⠓⢯⡴⡙⢦⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢟⣸⠋⠀⢀⡜⠊⠀⠈⣾⣿⢏⡶⠁⠀⢸⡀⡠⢪⠀⢈⠆⠀⢱⡹⣼⡟⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⣟⡞⠻⣀⡠⠊⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠁⠀⠀⠠⠊⠀⠀⢨⢵⣿⣒⠏⠂⠁⠈⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠟⣮⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⢀⠀⠀⠀⠸⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣞⣹⠃⠀⠀⠀⣀⣤⣴⠶⠾⠿⠟⠛⠛⠛⠛⠛⠛⠛⠙⠛⡛⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡧⠇⠀⠀⣠⡾⠋⠁⠰⢶⣤⣤⣤⣤⣤⡴⠶⠶⠶⠾⠛⠛⠛⠀⣠⣤⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡗⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡧⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣿⣿⢳⢿⡇⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⢰⣿⡄⠀⢸⣿⠿⣜⣯⣿⡇⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡇⠀⠀⠀⠘⢿⣣⠀⠀⠹⣿⣾⡿⣿⡇⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢀⣠⣴⣶⣿⣿⡇⠀⠀⣽⡿⣽⣿⡇⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⡅⠈⣿⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⡿⣟⣯⣷⠿⣿⡇⠀⠀⣿⣿⣿⣿⡃⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣷⠀⣿⡀⠀⠀⠀⠀⠀⠀⠉⠀⢹⣿⣹⣿⠉⡆⢇⣿⠁⠀⠀⢿⣿⣿⣿⠇⠆⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠸⣇⠐⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣝⣌⣾⡟⠀⠀⠀⠀⠙⢻⡿⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠹⣆⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠀⠐⠀⣠⡾⠁⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠙⢷⣄⡀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠞⠋⡀⠀⠀⠀⣰⣼⣷⣦⣄⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀
⢀⣴⠾⠛⠛⠛⠶⢶⣄⡀⠙⢧⣀⠈⠙⢛⠷⠶⠶⠶⠞⠛⠛⠛⠛⠛⠉⠉⠀⠀⢀⣠⢀⣀⣴⣾⣿⣿⣿⣿⣿⠀⢠⣴⠞⠛⠉⠉⠉⠉⠙⠛⣶
⠸⣧⠐⠄⠀⠀⠀⠀⣨⡷⠀⠀⠉⠚⢤⣌⣦⣤⣤⡤⢤⠤⣤⢤⣤⣒⣲⣶⠬⣟⣛⣭⡽⣿⣿⣿⣿⣿⣿⣿⣿⠆⢿⣅⠀⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠈⠻⠶⠶⠶⠾⣿⠉⠀⠀⠀⠀⣴⠿⣿⠀⣼⣿⣿⣿⣍⠉⠉⣹⣿⣿⣿⣿⣯⣟⠾⣵⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⣹⡟⠛⠛⠛⠛⠛⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢼⡁⠀⠀⣰⡾⠉⠀⣸⠏⣹⠿⣿⡞⣿⢿⡾⣿⣿⣽⢹⢿⣿⣿⣿⣣⢷⣻⣿⣿⣿⣿⣿⠃⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣇⣤⡾⠋⠀⠀⢠⠏⠀⡟⠀⣿⡽⣞⣭⣿⣿⣿⡇⣿⠈⣿⣿⣿⣟⡮⢷⣿⣿⣿⡟⠁⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⡟⣠⣾⣷⣶⣾⣿⣿⣼⣿⣿⣿⣇⣯⣀⣸⣿⣿⣿⣹⣏⣿⡏⠉⠻⢶⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡟⣿⡻⣽⡹⣏⡿⣽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣞⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⠄⠀⠀⠀⠀⢀⣀⣸⣿⣇⣻⡽⢶⡻⣝⡾⡵⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣤⠴⠶⠞⠛⠛⠉⠉⠈⠙⠻⢿⣯⣽⣳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠁⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣀⣀⣀⣀⡀⠀⢤⣀⣠⣄⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⣄⣀⣀⣀⣀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⣀⢀⣀⣀⣀⣀⣀
⠀⣿⣿⣧⠹⣿⣦⠈⢻⢿⣿⡇⢸⣿⣿⣄⠈⣻⣿⣿⠶⠿⠛⢻⣿⣿⣿⠛⠿⡇⣴⣿⣿⡿⢛⣷⠈⢻⡿⠇⠀⠈⣷⣶⣶⡳⠀⠀⠀⠀⠸⡟⢻⣿⣿⣿⡝⠿⠿⠀⠀⣼⣷⡀⠀⠀⠀⠀⢀⣴⣿⡿⠋⢳⣤⠄⣰⣾⣿⡏⠻⣿⣦⣠⠀⠀⠀⠀⠸⠿⠛⣿⣿⣿⡟⠻⢿⠀⠀⣼⣿⡀⠀⠀⠀⠀⢸⣿⣷⡌⣿⣷⡄⢹⣿⣿⡟⠁⠀⠀⠀⠈⣿⣿⣿⠉⠫⣿
⠀⣿⣿⡟⢠⢟⡿⠀⢸⢸⢻⠁⢠⡿⢟⡿⠀⡏⡟⣿⠀⠀⠀⢸⢸⡇⣿⠀⠀⠀⣿⣿⣿⢄⡙⠃⠀⢸⡇⠀⠀⠀⡏⡟⢸⡇⠀⠀⠀⠀⠀⠀⢸⡏⡿⣸⡇⠀⠀⠀⣼⢿⣿⣇⠀⠀⠀⢀⣿⢿⡷⠁⠀⢠⡧⣼⢿⣿⠏⠀⠀⢹⡿⡟⡄⠀⠀⠀⠀⠀⠀⡇⢿⢹⡇⠀⠀⠀⣸⣻⣿⣧⠀⠀⠀⠀⣼⣿⡟⢃⡜⣻⠃⢸⢻⢻⡇⠀⠀⠀⠀⠀⣟⡏⣟⣀⣴⢦
⠀⡏⢹⡏⢻⣿⣄⠀⢸⣘⢸⣡⣞⣿⡾⠃⠀⣇⡁⣿⠀⠀⠀⢸⣘⢸⡟⠀⠀⠀⠈⠳⢭⡲⠹⣆⠀⣸⣤⣤⣤⣴⣇⡁⣼⡇⠀⠀⠀⠀⠀⠀⢸⡇⡁⣿⠄⠀⠀⣸⡏⠻⡿⠟⣆⠀⠀⢸⡷⢸⡇⠀⠀⠀⠀⢧⠨⣿⠀⠀⠀⢸⢳⣿⠁⠀⠀⠀⠀⠀⠀⡇⡁⣜⡇⠀⠀⣰⡟⠙⣿⠟⣧⠀⠀⠀⣼⠁⣏⠻⣿⣥⠀⢸⠘⢸⡇⠀⠀⠀⠀⠀⣿⠃⣯⢰⠏⠀
⢰⡏⢹⡇⢨⢏⡿⡄⢸⠈⢹⠹⣏⠉⠀⠀⢀⡇⢁⡿⠀⠀⠀⣾⠈⢸⡇⠀⠀⢀⣶⡀⢀⡹⢂⣿⠀⣺⢇⠀⠀⢸⡏⠁⣿⠃⠀⠀⠀⠀⠀⠀⢸⠇⠁⣿⠀⠀⣰⡟⠒⠒⢻⡞⠹⣆⠀⠈⢧⣸⡴⠀⠀⣀⡦⠘⣆⣹⡣⠀⣠⣯⣮⠃⠀⠀⠀⠀⠀⠀⢰⡇⠁⡿⡇⠀⢰⣗⠒⠒⠺⡞⠛⣆⠀⠀⡞⠁⣿⢀⡟⣹⡇⢸⠈⢸⠇⠀⢀⣴⡇⠀⣯⢹⡇⠈⣀⣤
⠘⠳⠾⠷⠿⠟⠊⠰⠿⠶⠾⠆⠘⢦⣀⡀⠸⠿⠾⠷⠆⠀⠠⣧⡤⢼⢷⠀⠀⠘⠛⠽⠿⠶⠟⠁⠘⠿⣛⠆⠀⠚⢷⣲⣛⡖⠀⠀⠀⠀⠀⠀⢼⣤⠤⠿⡌⠉⠫⠿⠇⠀⠘⠻⠶⠿⠷⠆⠀⠉⠛⠖⠾⠟⠁⠀⠀⠉⠟⣛⡩⠝⠁⠀⠀⠀⠀⠀⠀⠀⢼⣧⠤⢿⡆⠉⠫⠿⠗⠀⠘⠻⠶⠿⠷⠖⠳⠶⠷⠿⠿⠓⠁⠻⠭⠿⠧⠟⠿⠟⠁⠺⠿⠾⠷⠾⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⡶⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⢟⢫⣭⡽⠿⠛⠶⠶⠶⠦⠿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠞⣉⡴⣧⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣆⡀⢀⣀⣠⣶⣾⣿⡿⠶⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠶⢦⣍⣉⠉⡴⢣⡾⣡⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡴⣾⠟⣫⣭⣽⠿⠿⠷⠶⠶⠶⠾⠬⣷⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡹⣷⣿⢳⡏⠀⠀⠀⢀⡀⠒⢦⣤⢄⠀⢰⣞⣋⣠⠞⢉⣰⣇⣾⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣦⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠳⣿⣿⡏⠀⠀⠀⠀⠈⢷⡀⠈⠋⠀⠀⠀⢸⡿⢡⡾⢋⣥⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠁⢀⣀⣀⡤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢰⢯⡾⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⢠⣞⣵⡟⣴⡟⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⣤⠶⠛⠀⠀⠀⠀⠀⠸⣇⠋⠉⢁⣠⣶⣾⣿⣿⡷⢶⣶⢦⣄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢸⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢲⡟⣾⡿⣧⡟⠀⠀⠀⠀⠀⣦⠀⠌⢹⡿⠒⠀⠀⠛⣶⡶⠖⠂⠀⠀⢀⣠⣴⡿⠿⢛⣛⣻⣿⣾⣯⣥⣤⣦⣌⣑⣎⣻⣆⣀⣀⣀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠤⠤⠤⢀⣇⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣿⣷⡿⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠁⠀⠀⠀⠀⠙⠀⠀⢀⣠⠾⠋⣽⠋⡔⣩⡿⠟⠋⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠛⠻⠿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠒⢦⣄⡀⠀⠀⠀⠀⠈⠛⠶⠧⢤⣤⣰⣆⣀⣀⣀⣤⣿⣶⡤⢼⠇⣼⠏⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⣰⠟⢁⣠⡶⢿⣼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣉⣻⣿⣿⣿⡿⠷⡟⠀⢸⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⢶⡾⢃⣴⠟⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣄⡀⠀⠀⠀⠀⢻⡍⠉⠉⠀⢨⣿⣶⡇⠀⠈⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣡⣾⢇⢸⡾⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⡄⢸⣿⣇⢈⣙⣿⣷⣦⣴⡿⠿⠿⠦⠀⠀⠀⠀⠈⠳⢦⣤⣟⣀⡀⠀⣠⠀⠀⠀⠀⢀⣰⣶⣤⣀⣀⣀⣠⡟⣼⣿⣿⣸⡟⠁⠀⠀⠀⠀⠀⣄⠀⠈⠙⢳⣶⠦⠄⠀⠈⢯⣉⣁⣀⣀⡄⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⣿⣿⣿⣿⠟⠻⢯⣽⡇⠉⠛⠿⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠿⠿⢿⣽⠖⠒⠶⣿⣿⣿⣿⣏⢉⣿⡿⢹⣿⣧⣿⡝⠁⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠘⠟⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⢿⢿⡿⣦⡀⠀⠙⣿⠶⣤⡀⠀⠀⠉⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠦⣤⡴⠟⠛⠋⠉⠉⠉⣽⠃⢨⡿⢯⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠿⠿⠁⠀⠀⣿⠀⠈⠙⠳⢦⣄⡀⠀⠙⠻⢷⣦⣤⡔⠶⠚⠉⢉⣀⣿⣦⠀⠀⠀⠠⣀⠀⠀⢠⡟⠀⣼⠃⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠟⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣆⠀⠀⠀⠀⠉⠛⠶⣤⡀⠀⠉⠻⣿⣷⣦⣐⠛⠛⠛⠛⠓⠀⠀⠀⠀⠉⠀⣼⠃⠀⣿⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⠶⠶⠶⠶⠶⠞⠂⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣄⡀⠉⢿⢻⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⠷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣬⣿⣿⡏⠙⠿⣷⣦⣄⡀⠀⠀⠸⣧⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠉⠛⢿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣛⠋⠉⠀⡀⠀⠀⠀⠈⠑⠒⠦⠤⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⣄⠀⠈⢙⡿⣿⣶⣤⣀⠈⠙⠻⢾⣧⣤⣤⣄⣀⣿⣀⣀⣀⠀⠀⣠⣴⣿⣿⣷⣤⡤⣤⣤⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⣿⠉⠙⠻⠿⣶⣤⣄⡀⢀⣀⣤⣶⡾⠟⠋⠛⠻⢿⣿⣿⣿⣿⣶⣤⣅⣀⠆⢀⡀⠀⠀⠀⠀⠈⠁⠀⣠⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⣿⡟⠿⣦⣞⣰⡿⠉⠉⠙⢳⣦⣄⠀⠀⠀⠀⠈⠉⢽⣭⠟⠉⠛⠻⣿⣿⣿⣿⣿⣧⣀⣸⣿⣿⣿⣷⣤⣄⣀⣀⣀⠀⠀⣴⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀⢀⣀⣭⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣶⣦⣌⣂⢀⣠⣴⠾⠛⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⣼⣿⣿⣶⣶⣶⠿⠛⠛⠻⣿⣶⣤⡀⠀⠀⠀⣿⢶⣤⣤⣴⡿⠛⠛⠋⠉⠈⠉⠉⠙⠿⣿⣿⣿⣿⠉⠉⠉⠙⢛⡟⠚⠲⠶⠾⠃⠀⠀⠀⠀⠀⠀⣿⣿⣤⣶⣾⠿⠟⠛⠉⠀⠀⠀⢙⣿⡿⠶⣦⣄⣀⠀⠀⠀⠀⠀⢸⣿⣿⠙⠛⠟⠀⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠛⠉⠁⠉⠻⢷⣦⣀⠀⠀⠉⠻⢿⣷⣦⣄⢻⣧⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⠈⢹⡟⢷⣦⣀⣀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠉⠛⠻⠶⣦⣄⡀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⠟⠻⠗⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⠀⠀⣨⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣄⡀⠀⠈⠉⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣾⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⣿⠀⠀⠀⠀⠀⣀⣤⣶⣾⠟⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣤⣀⠀⠀⠈⠙⠻⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠂⠀⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢸⣿⠀⣀⣤⣶⡿⠟⠛⠁⠀⠀⠀⠙⢿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣀⠀⠀⠀⠉⠻⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⡀⠀⠀⠀⠐⣿⡿⢷⣦⡀⠀⠀⠀⣰⡟⢁⣠⣾⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣶⣤⣀⣀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⣄⡀⠀⠀⠈⣿⡿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠸⣿⡇⠀⠙⢿⣦⣀⣴⣿⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⢿⣿⡏⠛⠿⢿⣿⣿⣴⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣄⡀⣿⡇⠀⠉⠻⢿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⡃⣀⣤⣶⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⣿⠗⠀⠀⠀⢸⣟⣿⡅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣧⣀⠀⠀⠀⠈⠙⢿⣿⣷⣦⣄⡀⠀⠀⢀⣀⣠⡶⠾⣛⣩⣼⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣿⣽⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⠻⢿⣦⣄⡀⠀⢸⣿⣿⡿⠟⠛⠶⠶⢛⣋⣥⣶⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⠀⠀⠉⠛⢿⣶⣼⣿⣿⣇⣀⣤⣶⣾⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆⠀⠀⠀⠀⠈⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡳⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢿⣾⣟⡶⣌⡙⣲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣿⣿⢿⣿⣿⢿⣟⣳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣼⣿⣿⠆⠈⠙⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠸⡟⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡰⣮⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⡿⠃⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠉⠙⠛⠒⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡰⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠓⠒⠦⢤⣄⣼⠐⠁⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣤⠶⠒⠒⠒⢦⣄⠀⠀⠀⠀⠀⠀⢸⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠈⢣⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠈⢏⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢣⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠘⡆⠀⠀⠀⠸⣆⠀⠀⠀⣷⡄⠀⢻⢆⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⡧⠀⠀⠀⠀⢿⠀⠀⠀⠽⡇⠀⢸⠏⢦⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢻⠀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢸⠀⠈⣆⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠸⣇⢧⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣠⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⡏⠀⠀⣽⠀⣞⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⢦⡀⢿⡌⣆⠀⠀⠀⢣⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠁⡇⢰⠇⢸⣏⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣖⡀⠙⢧⣷⣘⣠⣀⣀⠀⣣⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⢸⠄⠀⠀⢀⡇⢸⠀⣼⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣱⡀⠀⠹⣏⠉⠙⣏⢷⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⠀⠀⠀⣸⢡⠏⠀⠸⡓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⢿⣣⠀⠀⠘⢧⡀⢸⣾⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⠀⠀⠀⡇⠋⠀⠀⠀⠘⢦⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢬⣷⣧⠀⠀⠈⢷⣸⣟⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠁⢲⡄⣯⠀⠀⠀⠀⠀⠀⢳⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⡿⠀⠘⠧⣿⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⡀⠀⠀⢀⣼⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠟⢉⣿⣿⣿⣿⣿⣿⣿⡇⣸⡇⠀⠀⠀⣌⣓⣤⢄⢀⣤⣼⠿⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢳⣭⣉⣩⡴⠟⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⡟⡿⠛⢁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⠁⠀⠀⠀⠉⠉⠾⠟⣋⣿⣶⣿⣛⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠸⣇⠈⠁⠀⣰⣿⠇⠄⣸⣿⣿⣿⡿⢠⠒⡤⢃⠭⣹⣿⣿⣄⣼⣿⣿⣿⣇⣤⣶⣿⣿⣿⠿⢻⠿⠿⠿⣿⣿⡟⢰⡿⠀⠀⠀⠀⠀⠀⠀⣼⣯⣿⠿⠛⠙⣏⢿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠹⢷⣶⣾⡿⠋⠀⠀⢽⣿⣿⣿⣇⠣⣑⠢⢍⠢⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡌⢲⠨⢅⢫⣿⣿⠇⣼⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢘⣾⣿⣿⠟⢻⣿⠹⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣇⣦⣉⣆⣣⣿⣿⣿⣿⣿⡏⠿⣋⣿⣿⣿⣿⣿⡇⡹⢄⢋⡔⣿⣿⡟⢰⠏⠀⠀⠀⠀⠀⠀⢠⣾⣷⣤⣠⣤⣤⣶⣿⡿⠟⠁⢀⣾⠏⠀⠹⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣷⣾⣶⣾⣿⣿⠁⡾⠀⠀⠀⠀⠀⠀⠀⣿⠻⠿⠿⠿⠿⠛⠋⠉⠀⢀⣴⡿⠋⡌⠀⠘⢿⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣖⣒⠒⡎⡱⢙⠿⢿⠿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⣼⠃⠀⠀⠀⠀⠀⠀⢀⣿⣄⣀⣀⣀⣀⣠⣤⣶⠾⠛⠉⢀⡞⠀⠀⢸⡘⣷⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡾⠿⣷⣶⣷⣾⣸⣆⣱⣸⢰⠰⡆⠶⢰⡈⢆⡉⢉⡉⡉⠏⠿⠿⠿⠿⢿⡿⣿⣿⣿⣿⣿⡏⣾⠇⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⡎⠀⠀⠀⡏⢰⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠣⢄⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠓⠻⠶⢮⣕⡬⠙⣌⢃⢎⢡⠋⡴⣐⡢⠔⡢⢌⣯⡿⠷⣤⣀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⢀⣷⣾⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⣀⣠⡤⠶⢬⣍⣉⡉⠉⠒⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣶⣾⣶⣾⡾⠛⠉⠉⠛⠻⠿⣭⣀⣀⠀⠈⠻⢶⡄⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⣠⣶⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⠋⡇⠀⠀⠀⠀⠈⠉⠛⠲⠾⠿⠀⠀⠀⠀⠀⣀⣴⡿⢶⣄⠀⠀⠘⢳⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢸⢠⡇⠀⠀⠀⠀⠘⣧⣀⣀⣀⣀⣀⣀⣠⣧⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⢹⡇⠀⠁⢿⠳⣄⠀⠀⢹⡇⠀⢀⣠⣶⣛⡻⢷⣄⠀⠀⣴⣮⡵⢿⡓⠛⠛⠛⠋⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠥⡙⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣏⠹⢷⣄⡈⠑⠢⣤⠤⠤⠖⠒⠉⠉⠉⠒⢤⣀⡀⢸⡇⠀⠀⣼⠁⡝⠂⠀⣾⠐⢲⠛⢹⡇⠀⠀⢸⠛⢦⠸⠋⠁⠀⢀⡿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢫⠑⣪⠑⣼⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠈⠲⢌⣙⠿⣶⡶⠶⠟⠛⡛⠛⠿⠶⣦⣄⡀⠀⠀⣼⠁⠀⠀⣿⠀⡇⠀⢰⡇⠀⠈⢆⢸⡇⠀⠀⣾⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢿⡛⠛⠛⠛⠛⠉⠉⠁⠀⠀⢠⢇⡓⢤⣻⠏⠀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠉⠁⠉⠀⠀⠀⠀⠉⠑⢦⡠⠭⣛⢷⣯⣿⠀⠀⢀⣿⣠⣼⡾⠻⢧⣦⢄⣈⣼⠀⠀⠀⣇⢐⣒⣦⠞⠋⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⡀⠀⠀⠀⠀⠀⣀⠴⢋⢴⣼⡟⠁⠀⠀
⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠁⠀⠀⠙⠚⣿⠀⠀⢸⡟⠋⢩⡇⠀⢸⠿⢿⣾⣿⠀⠀⠀⡿⠟⢉⡤⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⡶⢤⣤⣮⣥⣿⣾⡿⠋⠀⠀⠀⠀
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠀⠀⠀⠀⠀⢰⡇⠀⠀⢸⠃⠀⢸⠧⢤⣿⠀⠤⢈⣿⠀⠀⠀⡗⠒⠁⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢀⣀⡽⠿⠓⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠦⣤⡀⠀⠀⠀⠀⣼⠃⡾⠀⠀⠀⠀⠀⡿⠀⠀⠀⣾⠀⠀⡾⠀⢀⡟⠀⠀⠀⡇⠀⠀⠀⣷⠀⠀⣸⠁⠒⠤⠤⡤⢤⣤⣒⣲⣾⡽⠽⠶⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⡟⠀⠀⠀⢀⣤⡴⠞⠉⠀⠀⠀⠀⠀⠉⠳⢦⣀⣼⠃⢀⣃⡀⠀⠀⠀⣼⠁⠀⠀⠀⢹⡀⢠⡇⠀⢸⠃⠀⠀⢀⡇⠀⠀⠀⢿⠀⠀⡟⠒⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡟⠀⣀⡴⣾⠟⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣯⠉⠻⢦⣀⡼⠃⠀⠀⠀⠀⢸⡇⢸⡇⠀⣿⠀⠀⠀⣸⠃⠀⠀⠀⢸⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⣧⠞⣡⠟⠁⠀⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⣾⣿⣿⣷⡀⢀⡽⠁⠀⣀⠀⠀⠀⠈⡇⢸⠋⠉⣿⠐⡄⢀⡟⠀⠀⠀⠀⠀⣧⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢡⡾⠁⠀⠀⠀⠱⡀⠀⠀⠀⣠⣾⣿⣿⣷⣤⣾⣿⣿⣿⡿⠻⣷⣾⣶⣿⣿⣿⣿⣦⣄⠀⣿⣼⠀⠀⢿⣦⣬⣾⠃⠀⠀⠀⠀⠀⠸⡾⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢙⡿⡙⣄⠀⠀⠀⠀⠘⠦⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⡇⠀⢸⡇⠀⡟⠀⢀⣠⣤⣄⣀⠀⣧⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣷⣑⠚⣦⡀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣿⡃⠙⢿⣿⣿⣿⣿⠿⣫⠊⢸⡛⠛⠛⣧⠸⣧⣾⣿⣿⣿⣿⣿⣿⣿⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⢿⣲⢄⡹⢢⣀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⠀⡔⠒⠒⠦⠤⠴⠋⠁⠀⢸⡇⠀⠀⣷⠀⠹⢿⣿⣿⣿⣿⣿⣿⠏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⢿⣴⢡⠊⢗⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣰⣿⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢿⡹⠀⣀⣉⡙⣋⣉⡧⠋⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠛⢯⣶⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠋⠀⣠⡾⣟⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣠⡤⠤⣼⡧⢠⠃⠀⠈⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣛⠰⣉⣿⣿⣧⣤⣶⠿⣋⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣸⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠻⢿⠿⠟⠛⠉⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢀⡿⠂⢹⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣔⡲⢄⠀⠀⠙⢤⣀⣀⠀⠀⣀⣀⣀⣀⣠⣤⡾⠁⢠⡷⢤⣤⣤⣼⠛⠁⠈⠲⠤⣀⣀⣀⡀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢦⣄⣀⡀⢈⠉⢉⣁⣠⣽⠶⠟⠋⠁⣀⣼⣁⣀⣀⣸⣧⣄⣀⣀⢀⣀⣀⣤⠾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠙⠛⠳⠿⠶⠟⠋⠁⠀⠉⠉⠁⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⡞⠀⢀⠞⠉⠁⠀⠀⠈⠈⠀⢠⠏⠀⠀⠀⠀⠀⢀⠴⠊⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⠎⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀
⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢠⠎⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡰⠃⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⢶⡶⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠞⠁⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⠤⣄⣀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⡉⠙⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣄⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠢⠤⠤⢄⣰⠇⠀⠀⠀⠀⠀⢻⣧⠀⠀⠙⢦⣀⠈⠙⠻⠯⣟⣦⣄⡀⠀⠀⠀⠀⠸⣿⣷⣦⡀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠈⠳⣄⠀⠀⠀⠉⠓⢯⣓⠦⣄⠀⠀⢻⣿⣿⣿⣦⣄⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⡄⣄⡈⠳⣤⡀⠀⠀⠀⠈⠛⢮⣟⢶⣌⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠙⢦⠉⠲⢄⡙⢦⡀⠀⠀⠀⠀⠈⠙⢮⡻⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⡠⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠶⠶⠶⠒⠒⠛⠛⠓⠚⠶⠶⠦⢤⣤⣀⣀⠀⠀⠀⠀⢿⡆⠀⠀⠈⢳⡀⠀⠙⠺⣷⣄⠀⠀⠀⠀⠀⠀⠙⢦⣝⠿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⡔⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠈⠉⠛⢿⣷⣶⣤⣜⣿⡀⠀⠀⠀⠹⣄⠀⠀⠈⠙⢷⡀⠀⠀⠀⠀⠀⠀⠉⠳⣬⣻⣿⣿⣿⣿⣦⠀⠀⠀⠱⡀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⠀⠀⠀⠀⠀⠸⡟⢷⣄⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣇⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠋⠀⠙⢧⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⡀⠀⠀⠀⠀⠹⡄⠙⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠈⣧⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡄⠀⠀⠀⠀⢻⡄⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢸⡆⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⢷⡀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢷⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⠀⣴⠟⠁⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⠤⣄⣀⣹⣿⣿⣿⠁⠀⣠⣶⣷⣦⡄⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣿⡄⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠈⠉⠛⠃⠀⢰⣿⣿⣿⣿⢿⣆⠀⠘⣿⡀⠀⠀⠀⢰⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡏⣷⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⠀⠀⢸⣿⣹⣿⣿⡏⣿⡆⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡟⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠘⣿⡟⣿⣿⣧⣿⡇⠀⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣷⡀⠀⠻⣿⣶⣶⣿⡿⠀⠀⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠛⠛⠉⠀⠀⣴⡟⠀⠀⣾⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⡤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⡿⠛⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣷⣝⢿⣿⣿⣿⣿⢿⣯⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣯⣽⡿⠋⢡⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣬⡉⠒⠦⣄⡀⠀⠀⢻⡙⠂
⠀⠀⠀⠀⠀⠀⠀⣿⠙⠲⠤⠤⠤⠤⠤⠴⠒⠚⠉⠉⠉⠉⢩⡉⠓⠪⣝⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⡤⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡓⠤⣀⠉⠓⢦⣀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢿⡀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣃⣀⣀⣤⣿⠦⠾⠟⠛⠛⠛⠋⠉⠉⠙⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣽⣿⣿⣿⢏⠉⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠵⢤⠈⠑⠢⢄⡈⠓⢿
⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠙⠦⣄⠀⠀⠀⠀⣀⣠⡤⠤⠾⠿⠿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⠃⠀⣠⠏⠀⠀⣀⣠⠤⠴⢒⣉⣉⡤⠤⠤⠤⡞⣀⣀⣀⣀⣉⣑⡂
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠈⠉⣠⡴⠚⠉⠁⠀⠀⠀⠀⣀⣸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢯⣄⡀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠻⠿⣿⣿⡁⠀⣰⡿⠶⠮⣉⣭⣐⠒⣋⠉⠉⠀⢀⣤⠶⠛⠋⣉⣉⡉⠉⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡴⠛⠁⠀⠀⠀⠀⠀⠀⠐⠛⠉⠉⢹⣿⠛⠛⠻⠶⠶⣶⣦⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠩⣷⣮⣅⠁⠒⠤⣄⠀⠀⠀⠀⢀⣠⣽⣿⣿⣿⣦⣄⠀⠀⢈⡟⣹⠁⠀⣰⠏⢠⣶⣿⣿⣿⣿⣟⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢋⠀⠀⠀⠀⠀⠀⢀⣀⢀⣤⣤⠤⢤⣽⣿⣦⣤⣤⣤⣬⣋⣁⡀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡟⠁⣼⣿⣿⣿⣿⣿⣿⣦⠎⡴⠁⠀⣼⠃⣰⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣿
⠀⠀⠀⠀⠀⣀⡠⠖⠉⠀⢀⡞⠀⠀⠀⠀⣀⠔⠉⣠⣿⣿⡟⠀⠀⠀⠀⠈⢧⠀⠀⠈⠉⠉⢻⣄⠀⠀⣠⡿⣿⡆⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⠁⠀⠈⠳⣄⣼⣿⣿⣿⣿⣿⣿⡿⠃⡼⠁⠀⣸⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣾⣿
⠀⠀⠀⠀⢾⣯⣀⠀⠀⠀⠈⢀⣀⡤⠔⠊⠁⢀⣼⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢻⣧⣰⣿⣇⠘⣿⣄⠀⠀⠀⠀⠘⢿⣅⠀⠀⠀⠀⠀⣠⠿⢿⣿⣿⣿⣿⣿⠟⠀⣼⣁⣀⠀⣿⠀⢸⣿⣿⣿⣿⡿⠟⠋⣀⣴⡌⠹⣿
⠀⠀⠀⠀⠀⠈⠛⠿⣶⣦⣤⣀⣀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢰⣿⣿⣿⣷⣄⢀⣴⣿⣿⣻⢛⣧⠼⢿⣿⣦⣀⠀⠀⠀⠉⠛⠃⠀⣀⣼⣿⡄⠘⣿⣿⣿⣿⠋⢀⣼⡽⢭⣉⠛⡏⠀⠀⠀⠉⠉⠉⠀⢰⣿⣭⡀⢷⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⢿⣿⣿⣟⣿⡿⠋⠀⠹⣷⣟⡿⣆⠈⢿⣿⣿⣷⣄⠀⠀⢀⣠⣾⣿⣿⣿⣿⡤⢿⣿⣿⣧⣾⣿⣿⠃⣿⣿⣿⣧⠀⢀⣠⣤⣾⡿⢷⠿⢧⣈⣧⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⣷⣾⣿⣿⣿⣷⠀⠀⠀⢹⣯⠘⠙⣷⠚⢻⣿⣿⣿⣿⣿⣿⡿⠿⠛⢋⣉⡁⠙⣾⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣀⣿⠟⠛⠁⠀⠘⣶⣿⠯⠴⠞⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠘⣿⣿⣛⣻⣿⣿⠀⠀⠀⠀⢻⣇⠀⠘⡆⠀⢹⣿⡿⠟⠋⢁⣠⣴⣾⣿⣿⣿⣦⡘⣿⣿⣿⣿⣿⠁⣾⣿⣿⡿⠟⠋⠀⠀⠀⢀⣠⣾⣿⣿⣿⠂⢠⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠻⠿⠿⠿⠛⣆⠀⠀⠀⣼⠋⠀⢀⣽⠖⠋⣁⣤⣶⣿⢻⣿⣿⣿⣿⣯⣾⣿⣷⠸⣿⣿⣿⣧⡴⠿⠋⠁⠀⠠⣠⠔⣲⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠒⠚⠉⢉⣁⣀⠤⠼⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢰⠏⢀⡴⠋⣠⣴⣾⣿⣿⣿⣟⣿⣯⠿⣿⣿⣿⣯⢿⣿⡇⢻⠟⠛⠁⠀⣀⠀⠀⣀⣴⣵⣾⣯⡛⠿⣿⣿⣿⡿⠁⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠉⠉⠉⢉⣁⣀⡀⠤⠤⠠⡄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⡇⢠⣟⡴⠋⠀⢿⣯⣺⡿⣿⣿⣷⣛⣿⣿⣶⡔⣿⣿⣿⣿⣿⠇⢸⡶⣾⢻⠁⣰⢊⣡⢶⣿⣿⣿⣿⣿⣷⣦⣬⣍⣁⣀⣀⣀⣠⣤
⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠨⢡⣿⠿⣿⣶⣄⠀⠻⣿⣿⣻⣿⣿⣿⣽⣿⣿⣿⣽⡿⠟⠋⠁⣠⣾⣷⣷⣏⣠⡿⠋⠸⡌⣿⣿⣿⣮⡛⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣠⣿⣏⠀⠈⠻⣿⣦⠀⠹⣿⣯⢽⣿⣿⣷⡾⠟⠛⢉⡤⢖⣥⣾⣟⣿⣯⣿⣿⣿⣷⠀⠀⢱⢻⣿⠇⠀⠙⠦⣉⠻⣿⣿⣿⡗⠢⢭⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣧⣠⡿⠃⠈⢳⡄⠀⢹⣿⣧⠀⢻⣿⣿⠿⠋⠁⢀⡤⣞⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠈⡏⡿⠀⠀⠀⠀⠈⠳⣄⠙⢿⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⠁⠀⠀⠀⢷⠀⠀⢻⣿⣆⠈⠉⣀⡤⢔⣺⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠈⠙⠢⣽⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣞⡞⠀⣿⣿⣿⠀⠀⠀⠀⣸⠀⠀⢸⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣞⠀⠀⢹⣿⣿⠀⠀⠀⣠⠏⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣤⡴⠞⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡖⠢⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⢹⣏⡤⢖⣿⣿⣿⣿⣿⣿⣿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢳⠀⠀⠑⢦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⣠⣴⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢠⣞⣛⣛⣛⣛⣿⣿⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠈⠢⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠊⠁⢀⣠⣾⣿⣿⣿⣿⣿⣿⣏⠁⣀⣬⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠧⣤⣴⣿⣭⣭⡭⠉⠀⣿⣿⣿⡇⠀⠀⠙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠉⠁⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⣿⣤⡬⠿⠷⠆⠀⠀⢸⣿⣿⣿⡀⠀⠀⠙⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⣀⠤⠔⠒⠒⠊⠉⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣏⣤⠞⠋⢻⣯⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠈⢿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡶⠋⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⠖⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⡴⣫⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⢠⡏⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣠⠤⢤⣄⣀⣀⣀⡀⠀⡄⠀⡿⢀⡾⢠⡞⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⠶⢶⡄⠀⢀⣴⣿⣶⣶⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢁⡴⠋⠙⠋⠀⠀⠀⠁⠉⠉⠀⠈⠛⠆⢰⠇⠸⢡⠟⠀⠇⣰⠏⠀⠀⠀⠀⠀⣠⡞⠃⠀⠀⢀⣴⣿⡿⠛⠉⠉⠉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⣤⠾⠋⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣷⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣤⣤⣹⣤⡶⠾⠿⣿⣶⡤⢄⣀⣀⣀⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠟⣧⣴⣿⣯⠟⠋⢛⠋⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠉⣍⢻⣿⣇⣥⣿⠿⣿⣷⣬⣉⣭⣭⣍⣷⠶⠍⠡⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡋⠉⠉⠉⠛⠳⢦⣤⣤⣴⣾⠿⠟⠈⠹⣿⣿⡇⠀⠀⠏⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣇⠀⠀⠀⢀⣠⠼⠋⠉⣉⣀⣠⣤⣤⠖⠋⠁⢀⣀⣴⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠒⠛⠋⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠓⢦⣀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⡿⠟⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⠛⠛⠛⠛⠛⠋⠉⠀⠀⢀⣤⣤⣤⣿⡿⡟⢳⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠘⠻⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⡤⠞⠁⠀⠰⣆⠀⠀⣀⣀⡄⢿⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠿⠶⠾⢻⣿⣷⣶⣟⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢳⣿⣦⣤⣀⠀⠀⠀⠈⠉⠉⠉⢹⡷⠛⠁⠀⠀⠀⠀⠀⠋⢀⣤⣤⣶⣂⣁⣠⣦⣤⣤⣤⣘⣷⣤⣤⣉⠓⣄⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠲⠶⠶⠛⠻⠛⠷⢮⣭⣍⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣷⣾⠂⠀⠉⠉⠛⠶⣶⡶⠶⠛⠀⠋⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⣿⢻⣿⠓⠨⣇⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⢒⣒⣚⣛⣲⣶⣄⣤⡤⠼⣿⣿⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⢀⣠⡾⠟⠛⣁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠲⢄⢹⠿⣦⣙⡃⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠉⣉⣥⠴⢄⠀⠀⠀⠀⠉⠛⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠋⠀⣀⣠⣽⡷⣶⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡸⢦⣀⣄⣄⠀⠀⣄⠀⠀⣰⡇⠀⠀⠀⣀⣿⣷⣿⣭⡳⠦⢀⣐⣦⡀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠘⠛⢷⣄⣀⡀⠀⠀⢴⣛⣦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢻⠛⣽⣿⣛⠟⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣀⣱⣤⣿⣿⣿⣦⡀⠈⠀⢠⣿⡇⠀⠀⢠⣿⣿⣿⣟⣩⣵⡶⠶⠿⠟⠳⠶⠄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢥⣄⣀⣀⣀⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⣾⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⢀⣴⣿⡿⠛⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣿⡇⠁⠀⠘⣿⡇⠀⠀⢸⣿⣿⣿⣿⣯⣿⡟⠀⠀⠀⠀⠀⠀⠠⣄⡀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠶⢤⣴⠾⠏⠑⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⠇⣸⠟⠀⠈⠳⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⢈⡃⣠⠴⢋⣿⣟⣋⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣟⣿⣿⡇⠀⠀⠀⣿⣷⡀⠀⠘⣿⣿⣿⣿⢯⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⡶⠟⠛⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣤⣤⣍⠀⠀⠀⠀⢈⣱⣦⠤⠶⣦⢿⠀⠀⠀⢛⣉⢀⣠⣾⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⡀⠀⠀⣽⣿⣷⣶⣤⣿⣿⡀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠈⠓⠆⠀⠀⠀⠀⢤⣴⣓⣛⣷⣀⣀⣤⡤⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠀⣤⣤⣾⣏⣀⣠⣤⣤⣴⠾⠻⠋⢉⣅⠀⠰⡏⠸⣆⠀⠀⢸⣭⣽⣿⣶⡶⠶⠖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⢿⣿⣆⡀⢻⣿⣿⣿⣿⣿⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠄⠀⠀⠀⠀⠀⠀⢤⣬⣭⣭⣭⣭⣤⣤⣤⣤⠀⠀⠀⠀
⣿⣻⣿⡟⠛⠿⠋⣉⣉⠉⠁⠀⠀⣤⠀⣀⡀⠛⠛⣦⣄⡀⣀⣿⡄⠀⡀⢤⣾⣿⣿⠿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣴⠿⠋⢠⡴⢏⣿⣿⣧⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢤⡀⠢⣄⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣛⠛⠛⠛⠻⠿⠿⠿⣦⠀⠀⠀⠀⠀
⠛⠃⠈⠳⣄⠀⣸⠉⠉⠉⢀⣀⡀⠈⠀⠺⠙⣆⠀⣽⣿⣿⣿⣄⡀⠀⣇⢲⣶⣶⣶⣿⣿⣶⠶⠖⠂⠀⠀⠀⠀⠀⢀⣀⠠⠀⠀⠀⠀⠀⢀⣴⠃⠀⢰⠟⣰⠆⢻⣿⣿⣿⣿⣿⣿⣿⡛⢧⡀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⢙⣿⠿⠿⠿⠿⠷⠦⠤⠤⡄⠀⠀⠀
⣤⣀⣰⡾⠿⠿⠁⢀⣠⣤⣤⣭⣿⣆⣠⣤⢤⣴⣾⣿⣿⣏⠙⠻⠇⠀⠙⡟⢋⣉⣩⣤⡶⠀⠀⠀⠀⠀⠒⠀⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠉⣩⠀⢠⣿⣴⡟⠀⣾⢿⣿⢿⣿⣿⡏⠙⢷⣄⣙⣦⡀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣌⣁⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀⠀⠀
⠀⠀⠉⠀⠀⢰⣿⡟⣻⠿⣿⣿⣟⣻⣏⠀⢾⣿⣹⣿⠿⣿⣿⣀⣓⡤⢶⣿⣿⣿⣿⣿⠦⠀⠀⠠⠴⠖⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⡴⣿⣿⡿⠃⠀⢡⣿⠁⠀⢸⣿⡇⠀⣿⣿⡙⣿⣯⣄⡀⣿⡌⠛⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣌⡉⠙⠒⠒⠲⢦⣤⣀⣤⣬⡁⠀
⠻⣄⢷⣤⣀⣀⣽⣿⣿⣶⣦⣈⠉⢿⣉⡛⠚⠚⣧⣄⣀⣿⣿⣿⡟⡁⡀⠿⠟⣛⣩⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣠⡼⢋⡴⢞⣵⠟⠉⠀⠀⢠⡿⢻⠇⠀⣾⣿⢻⠀⠉⠙⢿⡄⢶⡉⠉⠉⡙⡆⣀⠀⠙⠳⣄⡀⠀⠀⠀⠑⢤⡀⠀⠈⠁⠀⠀⢀⣀⠀⠀⠙⠶⠗⠲⢤⣄⡀⠉⠙⠲⠌⠉
⣀⣸⡿⠀⣸⣿⣿⣏⣻⠿⡏⠙⣧⣄⠈⢻⡄⣶⣿⣧⣠⣿⣿⠀⠀⢀⡴⠞⠋⡉⠤⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⡴⠚⣀⡴⣿⣯⣤⣞⣴⣿⡏⠀⠀⠀⣰⡟⠁⣿⡀⠀⣿⣿⡀⠄⢀⠀⠈⢻⣄⣻⡆⠀⢱⠀⢹⣇⠀⠀⠈⠻⣦⣀⠀⠀⠀⠘⠳⢤⠀⠀⠀⠀⠀⠱⣄⣀⡠⢤⣄⡀⠀⠙⠿⣦⣄⠀⠀
⠉⠁⢰⣿⡿⠃⢘⡟⢿⡶⠷⠼⠷⠿⢿⣾⣿⣈⣻⡿⡉⠉⢸⡄⠀⣀⡤⠶⠈⠀⣀⠀⠀⢀⣠⡶⢶⣾⠿⠿⠟⢋⡴⠞⠉⠠⡿⠋⠀⠀⣼⣿⠁⠀⢀⣼⠋⠀⢰⣿⣿⣦⣿⣿⣿⣦⣿⡄⠀⠀⠘⣿⢷⡀⠈⠀⠸⣿⠀⠀⠀⣄⡀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠉⠛⠲⣌⡙⠛⢶⣤⣄⣉⠁⠀
⠀⢠⣾⣿⠃⡿⢿⡿⣿⣿⣶⣰⣶⣶⣾⠿⢦⡏⠙⡟⠁⠀⣮⡿⠋⠁⠀⠀⠔⠋⣀⡴⠞⠉⠁⠋⠉⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⣰⠏⢈⠀⠀⢸⡇⠀⠀⣼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⡆⢹⡈⡛⡄⠀⠀⠹⣦⡀⠀⠈⢻⡀⡄⠈⠙⠄⠀⠀⠀⠰⢦⣀⠀⠀⠈⠳⣤⣤⣀⣉⠀⠀⠉⠀⠀⠀⠀
⠀⠀⢸⣿⡏⠳⣾⣧⣬⣇⣿⠈⠙⢿⣟⠀⠘⣧⢈⣡⣼⣉⠉⢀⡀⠀⢂⣠⡴⠋⣁⡴⢞⣁⣤⠀⠀⠀⠀⠊⣀⣀⣀⣠⡀⢀⡄⢀⣴⣿⠀⢸⡆⠀⣼⡇⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣇⠈⢦⠀⠀⣽⣷⡀⢲⣄⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣰⣤⣈⠙⠳⢯⣝⣶⢤⣀⣀⠀⠀
⠇⠀⢸⣯⣷⣶⢻⣧⣝⣿⣿⣿⣦⣀⠙⣧⠀⠙⠻⣧⣄⡈⣣⣾⠃⡠⠞⣡⣴⣾⣯⡶⢛⣉⣴⠀⠀⣠⠞⠛⠉⠁⠉⠁⠀⠈⠡⠾⠁⢻⠀⠀⡧⣦⣸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⢱⡆⠹⢿⣿⣾⡌⠳⣄⠹⣄⠀⠀⠀⠀⠀⠀⠈⢷⡄⠉⠓⠾⣷⣤⢤⣌⡉⠛⠦⣍⠀⠀
⠀⣠⣼⣿⣿⣤⣾⣿⠿⣿⣟⢳⣶⡿⢷⡾⠿⣶⢲⣿⡉⠉⠹⠿⠋⡀⢚⣩⡶⠛⢁⣴⡿⠋⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣆⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣷⡼⡇⠹⣿⡄⠘⢧⠘⢦⠀⠀⢰⡀⠀⠀⠀⠙⣦⡀⠱⢄⡘⠷⣍⠙⠢⣄⠀⠀⠀
⠛⣫⣿⣿⣿⣿⡉⢹⣷⣾⣿⣶⣿⢷⣄⠀⢠⡟⣾⣿⣇⠀⢰⣶⡏⠀⠈⠁⣠⡶⢿⣉⣠⡾⢛⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠸⣿⡟⣷⠀⢫⠳⡀⠀⠀⠈⢳⠀⠀⠙⣆⠀⠀⠀⢆⠉⠀⡈⠙⢦⡈⠙⢦⡈⡣⠀⠀
⡿⠿⣿⣿⠟⣹⣿⣿⣿⣿⣿⣿⡻⣶⣿⣿⣿⣼⠏⣿⣽⠇⠈⠉⠁⠀⠀⠸⠋⣠⣾⣿⣿⣾⡿⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢽⣿⣿⡇⢿⣿⣿⣧⣉⣿⡉⠉⠉⠉⢹⡏⠉⠉⠙⠋⠉⠉⢿⣿⣿⣿⣿⣿⣧⡀⢹⣧⠘⡇⠀⢦⠱⡀⠀⢠⠀⠱⡀⠀⠈⢳⡀⠀⠀⠀⠀⠑⢀⡀⠙⣄⠀⠁⠁⠀⠀
⠀⣰⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣇⣄⣹⣿⣿⠟⣴⣿⠃⡤⠀⠀⣠⣧⡀⠀⢸⠋⠀⣿⡿⠛⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⢿⣷⢾⣿⣿⣿⡏⠉⠀⠀⠀⠀⠸⠗⠀⠀⠀⠘⠀⠰⢨⣽⡿⣿⣿⣿⣏⠁⢸⣿⡇⠁⠀⠈⠀⠘⢦⡀⠁⠀⠹⡄⠀⠀⢧⠀⠀⠀⠀⠀⠀⠳⡄⠈⠧⠀⠀⠀⠀
⣶⣿⣿⣿⣿⢙⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣟⣵⣿⡟⢀⣾⣿⣟⡓⠀⠀⠀⠀⠋⠀⢠⡞⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⣏⠀⠹⡏⠉⠀⠀⠀⠀⠀⠀⢰⣆⣀⡀⣀⣀⣠⣶⣀⣹⣧⡿⣯⡘⠿⣄⡀⠉⠁⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠹⠀⡀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣿⣼⣿⣯⣩⣿⣿⣿⣿⣿⠟⣽⣿⣽⣿⠿⢻⣷⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⣿⡝⠉⠉⣿⡏⣿⣯⠙⣧⠘⢧⣀⠈⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣼⣿⣿⣿⣲⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣿⡇⠀⠀⠹⣇⢿⡙⠀⠘⡇⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣾⣿⣿⣯⣀⣹⣿⣿⣿⣹⣿⡿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣿⢸⠀⣷⠀⢤⠀⢿⡌⣧⠀⡄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣸⠀⠸⡇⠸⣆⠈⢳⡸⡆⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⣾⣿⣿⣿⣿⣿⣿⡿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣠⠿⠀⢀⣿⠀⠀⣿⠀⢻⡄⠈⠓⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣈⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡄⢠⡇⠀⣰⣿⣾⠀⠀⣿⠀⠸⣧⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢣⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠘⠿⠟⠀⢸⠀⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣽⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠁⠈⠷⠀⠀⠀⠀⠀⠀⠀

⢠⣾⣷⣄⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠏⠀⠀⣿⠀⢀⡾⠛⠋⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡏⠀⠀⠀⣿⢀⣾⠁⠀⣰⠆⢹⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣧⠀⠀⢠⡟⢸⡇⠀⣰⠟⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣆⢀⣸⣇⣸⠃⢠⡏⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⣶⠾⠟⠛⠉⠉⠉⠈⠉⠉⠛⠁⢾⠁⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⠾⠟⠛⠛⣻⣿⣙⡁⠀⠀⢾⣶⣾⣷⣿⣶⣄⠀⠀⠀⠀⠰⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⣶⣶⠾⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⣿⣻⣟⣻⣿⡦⠀⠘⣿⣿⣛⡿⢶⡇⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠙⣿⣿⡗⠀⠀⠿⠉⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⣿⡿⠁⠀⠀⠘⢦⣿⣿⠇⠟⠁⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠟⠛⠆⠀⠀⠀⠀⠀⢀⢻⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠙⠿⣿⣭⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠶⢶⣶⣦⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣓⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⣟⣯⣽⠟⠋⠀⠉⠳⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢇⠀⠉⠛⠷⣮⣍⣩⡍⢻⡟⠉⣉⢹⡏⠉⣿⣹⣷⣦⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢸⠇⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⢠⣠⡶⠀⠀⠀⠀⠘⣧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠘⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⡀⠀⠀⠀⠀⠀⠀⢹⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣥⢠⣤⠼⠇⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡄⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠾⠷⠄⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠋⠀⠀⠀⠀⠀⠀⢰⣾⡿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣠⣿⣿⣶⣶⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠉⠛⢿⣿⣯⣿⡟⢿⠻⣿⢻⣿⢿⣿⣿⣿⣿⣿⠿⠟⠹⣟⢷⣄⠀⠀⠀⢀⣼⠟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠘⢷⣌⡻⠿⣿⣛⣿⣟⣛⣛⣋⣉⣉⣉⣀⡀⠀⠀⠈⠻⢿⣷⣶⣶⢛⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⠀⠀⠀⠹⢯⣟⣛⢿⣿⣽⣅⣀⡀⠀⣀⡀⠀⠀⠀⠠⢦⣀⠰⡦⠀⢸⠀⣏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⡟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⠷⠀⣸⠀⣿⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠀⠀⢦⡀⡀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈⠳⣝⠦⢄⠀⠀⠀⣟⣷⠀⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⡀⠀⠀⠈⠙⠂⠀⠀⠀⢸⣿⡄⠀⠀⠘⢦⡙⢦⡀⠀⠀⠀⠀⢰⣷⣷⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢧⣤⣀⡀⠀⠀⠀⠀⠀⠀⢿⣷⣄⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⢿⡍⠛⠳⠶⣶⣤⣤⣤⣤⣤⣤⠼⠟⡟⢿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣷⣶⣶⣶⣶⣶⣶⣦⣀⣀⣀⣻⡀⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⢀⣼⣿⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⠀⠀⠈⠻⣿⡆⢹⣯⣽⣿⣿⠟⠋⠙⣿⣶⣿⣿⣿⣿⣾⣿⣿⣿⣟⠋⠉⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⠈⢻⣆⣿⠀⠀⠀⢁⣶⣿⠿⠟⠛⠷⣶⣽⣿⣿⣻⣏⠙⠃⣴⢻⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⠀⠀⠉⠀⠀⠀⠀⠀⢹⣿⠀⣀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠉⠻⣿⣧⣿⢀⣰⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣶⣤⣤⣤⣤⣤⣤⣾⣿⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣅⣾⢿⣵⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⢹⣜⠷⠦⠤⠤⠤⠤⠤⠴⠶⠛⣉⣱⠿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠷⣦⣤⣤⣄⣠⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣾⣄⣿⡄⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠸⣿⣦⠀⠘⢷⡀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⣄⡀⠀⢈⡿⠰⢿⣿⠌⣷⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠛⠛⠛⠓⠶⢤⣀⠀⠀⠀⠀⢐⡟⠀⠀⣿⣬⡷⠂⠀⠹⠆⠀⠀⠒⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠁⠀⠀⠀⠀⠙⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠴⠦⢤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⢸⡇⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣼⠇⠀⠀⣀⣴⣷⣿⣶⣦⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⢻⣿⢿⣦⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠙⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⢸⣿⣿⣿⡿⠲⠶⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠛⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀
⠀⠀⠀⢀⣰⣰⣶⠶⠶⠶⠶⠶⢿⣇⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⠹⠷⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀
⢀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠙⠛⠛⠛⠛⠛⠛⠚⠛⠛⠉⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⢠⣤⠶⠶⠶⠿⠶⠶⢴⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢳⡶⠶⠦⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣰⣿⣦⣤⣤⣴⣶⣾⣏⠡⠀⠀⠀⠀⠉⠓⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⣧⠀⠈⢿⣙⣁⣩⣷⡆⠀⠀⢀⣀⣤⣴⠟⣫⡶⠓⠒⠒⠶⠶⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠈⢿⡿⠛⠛⠗⠚⠋⠉⠙⠛⠻⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣆⠀⠀⠀⢀⣾⠿⠦⣤⣤⡤⠶⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠼⠇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣧⠀⠀⠀⡔⠀⠀⠀⣾⠃⠀⣰⣶⡶⣦⡀⠀⠀⠀⢠⡶⢾⠷⣤⣄⠀⠀⠀⠀⣠⡴⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⣼⢿⡄⠀⣸⠇⠀⣸⣯⣤⣥⣼⣗⠀⠀⠰⣿⠷⠶⠶⢶⣿⡀⠀⠀⢼⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⠇⠈⢷⣠⠏⠀⠀⠘⣯⣠⣥⣳⡾⠀⠀⠀⢻⣆⡀⢀⣠⡾⠇⠀⠀⠘⢿⣐⣸⣇⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠘⠟⠀⠀⠀⠀⠘⠿⠛⠃⠀⠀⠀⠀⠀⠛⠿⠟⠃⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠙⣿⣦⣤⣤⣴⣶⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣇⣤⡾⠟⠛⠻⣯⣤⣀⣀⡀⠈⠉⠛⠻⣶⣄⣀⣀⣠⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣴⣿⠿⠋⠁⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠶⠾⠿⠿⢿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣾⣿⣟⣻⣶⠦⢤⣄⠀⠀⠀⠀⣠⣤⡶⠶⣶⣶⣶⣄⠀⠀⣀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠿⠛⠻⠿⣿⣦⣻⣦⠀⣴⣿⣿⣾⠿⠟⠛⠛⠛⠻⠿⢶⣿⣷⣮⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠹⣿⣿⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⡶⠶⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡷⠾⣷⣶⣶⡶⠶⠶⠶⢶⣾⣶⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣶⣶⣿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣇⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀
⠀⣀⣤⣶⣶⣿⡿⠿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣼⣿⣿⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀
⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠉⠀⠀⣰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢡⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣀⡀⠀⠀⠀⢀⣠⣾⣿⣿⠃⠘⢿⡿⢷⣦⣄⣀⣀⣀⣀⣠⣴⣾⠿⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣶⣾⣿⣿⡿⠟⠋⠁⠀⠀⠈⠛⠂⠉⠛⢻⣿⣿⣿⡿⠿⠀⠀⢰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣧⡀⠀⠀⠀⠀⣠⣤⣶⣶⣾⣷⣾⣿⣿⣧⣄⣠⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣶⣿⣿⣿⣿⣿⣿⡿⠟⠋⠛⠛⠛⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠛⣿⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠿⠿⠷⣶⣴⣶⣤⣤⠿⠏⠀⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠈⠻⢶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠙⢿⡀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠹⣦⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⠿⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠌⠙⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋⠀⠀⠀⠀⠉⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⢀⡀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⣀⣀⣀⣾⡿⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣿⡋⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣭⣭⣭⣵⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⢻⣿⣦⣴⣾⠟⠋⠉⠙⠛⠿⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⢁⣾⠛⠉⣁⣉⣅⣤⣤⣶⠶⠶⠾⠛⠻⣿⣶⣄⡀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀
⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡶⢶⣶⣿⣿⠿⣾⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠁⣀⢀⣀⣀⣴⣧⡀⠙⢿⣷⣤⡀⠀⣿⣆⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀
⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣀⣄⣀⣀⣀⣨⣿⣇⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⠤⠶⠶⠶⠶⠒⠛⠛⠛⠛⠛⠉⠉⠉⠉⠛⠛⠚⠛⠛⠋⠛⠙⣿⡄⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀
⠀⠈⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢹⣇⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀
⣀⣈⣛⣋⣉⣉⣁⣀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣷⣾⣿⣿⣿⢿⡿⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣷⣼⣿⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠁⠀⠀
⠛⠛⠛⠻⠿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠉⢿⣿⡀⠀⠀⠀⠈⣿⢻⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⢿⣷⡀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠻⣷⡄⠀⠀⣿⡇⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠙⠛⠀⠀⣿⠇⢹⣿⠀⠀⠀⠀⠀⠀⢰⣿⡇⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⢾⣿⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⣠⣾⡿⠋⠀⣾⣿⠷⠶⢶⣶⣦⣤⣤⣿⡏⠀⢸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠿⣷⣶⣶⡿⠿⠋⢁⣤⣾⡿⠃⠀⠀⠀⠀⠉⢉⣹⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⣀⣠⣤⣴⣾⡿⠛⠉⠀⠀⢀⣀⣤⣴⣾⠿⠛⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣸⡟⠋⠉⠉⠁⠀⢀⣠⣴⣶⡿⠟⠋⣉⣡⣤⣾⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢀⣿⠃⠀⢀⣠⣴⣾⠿⠛⠋⣁⣤⣾⣿⣿⡿⠟⣿⣿⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⢸⣿⣶⡿⠟⠛⣯⣠⣤⣶⣿⡿⠿⠛⠋⠁⠀⠀⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡗⠀⢸⣿⣤⣤⣶⣿⠿⠛⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡟⢹⡏⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢸⡷⢸⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣏⠀⢸⡿⢸⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⠿⣿⣿⠿⠿⠟⠛⢙⣋⣿⡿⠋⠉⣹⣿⡟⠉⠁⠀⣽⣿⡿⠀⣸⣷⢸⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀
⠲⡿⠷⠒⠒⠻⠶⠶⠶⠶⢶⣶⡶⠶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣾⣿⠏⠀⠀⢸⡏⣿⡇⠀⠀⢸⣿⣿⡇⢠⣿⠃⢸⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢨⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⠀⠀⢀⣿⣿⣷⡶⠶⠿⢿⣿⣧⣤⣶⣴⣿⣿⣷⡿⠃⠀⢸⡿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣤⠀⠀⠀⠀⠀
⠀⠀⠀⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣧⠀⠀⠀⠀
⠀⠀⠀⣸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀
⠀⠀⢠⣿⡏⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⠀⣼⣿⠃⠀⠈⠙⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣹⣿⣿⣷⠀⠀
⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⠀⣀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣻⣾⣿⣿⠟⠙⣿⣧⣿⣿⣿⣶⠀
⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠻⠟⠻⠟⠛⣿⣿⣿⡟⠋⠀⠀⢹⣿⣿⣿⣿⣿⠀
⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠸⣿⣿⣿⣿⣻⣇
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣀⣷⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣶⣦⣶⣶⣶⣶⣦⣤⣤⣄⡀⠀⢸⣿⣿⣿⣿⣿
⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣇⣈⣏⣉⠉⠉⠉⠹⠻⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣄⡀⠀⠀⠀⠀⠈⠻⢿⣿⡇⠀⠀⠀⠀⢀⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣷⣶⣦⣄⣀⡀⣹⣿⣿⣿⣿⣿
⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣶⣤⣄⠀⠀⢸⣿⡇⠀⠀⠀⠀⣼⣿⣇⣴⣿⣿⣿⣿⣿⣏⣽⣿⣿⣭⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣟⠁⠀⠀⠀⠀⠀⠀⣼⣻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⠛⠻⠿⢿⣦⣄⣸⣿⠁⠀⠀⠀⠀⠘⣻⣿⣿⣷⢿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⡆⢸⡟⠉⣿⣿⣿⣿⣿⣿
⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⢾⣿⣿⣿⡟⢿⣿⣷⣸⣿⣿⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⡟⠉⠰⣿⣿⣿⣶⢿⣿⠿⣿⣷⣿⠁⠀⣾⣿⢉⣿⣿⡏
⣸⣟⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠿⣿⣿⣷⣾⣯⣾⡿⣼⠏⠀⠀⣿⣿⣿⣿⣿⠇
⠙⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⠿⠏⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠰⣶⣦⣤⣽⣿⣿⣿⣿⣿⡷⠟⠀⠀⢰⣿⣿⣿⣿⣿⠀
⠀⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⢻⢿⢻⣡⣴⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠉⠀⠘⢿⣿⣍⠉⠙⠿⠆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠇⠀
⠀⠀⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⢟⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠀⠀
⠀⠀⠀⠹⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣾⣿⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠙⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⣀⣰⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢠⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠛⠛⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⢀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⣿⠿⠟⠉⠸⠋⣴⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠉⠛⠻⢿⣿⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣄⣤⣤⣶⣾⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣽⣿⣿⣿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⢤⣶⣾⣷⣾⣷⣶⣾⣿⠀⠀⠀⠀⢠⣶⣶⡆⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⣿⣿⡇⠈⠉⠉⠉⣿⡆⠀⠀⠀⢸⣿⣿⣧⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⢸⣿⣄⠀⢀⣿⣿⠛⣿⣦⣠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠻⣿⣷⣿⡿⠃⠀⠘⠿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠹⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣶⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠚⠋⠉⠉⣭⠉⠉⠛⠓⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠙⠻⢶⣭⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠛⠲⠭⣕⡢⣄⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⣸⠁⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢸⡇⢀⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢿⣆⠀⠀⢰⡏⠀⠀⠀⠀⠀⢀⣎⡏⠀⠀⢀⡿⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⣷⢸⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡟⠀⢀⡟⠀⠀⠀⠀⠀⢠⣾⡞⠁⠀⠀⣼⠃⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⣿⠈⠛⠁⠈⠙⠷⣦⣤⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣸⠓⠒⠒⠒⠒⢲⡿⠋⠐⠶⠦⢴⠧⠤⠤⠤⠤⢤⡿⠥⠤⠤⠤⠤⠤⣤⣤⢿⣆⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⣻⠏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣀⡴⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠋⣰⠏⠀⠀⠀⠀⣧⡆⠀⠀⣀⣀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⢠⠏⠀⣠⡾⠋⠀⣀⣀⣤⣤⣶⠶⢦
⠀⠀⠀⠀⠀⠀⢀⣇⡼⠃⠀⠀⠀⠀⠀⠹⣜⡄⠀⢹⠉⠉⠉⠉⠉⢩⡯⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣸⠁⣄⣰⡋⢀⣼⠿⠶⠚⠛⠉⠉⠀⠀⠀⢩⣿
⠀⠀⠀⠀⠀⠀⣼⠞⠁⠀⠀⠀⠀⠀⠀⠀⣹⣧⣄⠘⣇⠀⠀⠀⢀⣞⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⣤⡟⠉⠛⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠉⠓⠿⢦⣤⣀⣘⠀⠀⢠⠀⢀⣀⣂⣤⣦⣿⠾⠟⠋⠻⣆⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⢀⡼⡣⠃⠀
⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⠲⠤⢭⣽⣯⣭⠭⠭⢟⣻⠽⠓⢻⡇⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⣿⣀⡴⡫⠊⠀⠀⠀
⠀⠀⠀⢸⣇⠀⠀⠀⢀⣀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⣀⣤⠶⠋⠁⠀⢀⣾⠃⠀⠀⠀⠈⣷⠀⠀⠀⠀⢠⣿⠻⠾⣥⣄⣀⠀⠀
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣤⠞⠋⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⣼⠏⠀⠀⠀⠀⠉⢙⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣠⡶⠋⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⢰⡟⠀⠀⠀⠀⢀⡴⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⠞⠉⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢠⡟⠀⢀⣠⠴⠛⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⡿⠁⠀⠙⠻⢿⡢⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡟⠀⡾⠁⠀⠀⠀⠀⢀⡽⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣾⠁⣸⠇⠀⠀⣀⣰⡾⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣾⠃⠀⣿⣤⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⡘⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⣤⣤⠄⠀⠀⠀⠀⠀⢰⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠴⠶⢶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⡶⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⢶⣄⠀⠀
⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⠀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠾⣿⣿⡅⠀
⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡆
⠀⠀⠀⢸⡟⠷⠦⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⢿⡇
⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠛⠛⠒⠶⠶⠶⠶⠶⠶⠶⠖⠒⠚⠛⠋⠉⠁⠀⣾⡇
⢀⣴⣷⣿⡿⠶⣤⣄⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡄⣀⡀⢀⡀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⡿⠃
⢸⡟⠀⠈⣿⡀⠀⠀⢹⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⣯⣿⡷⣰⡿⠤⠤⣤⣤⣤⣤⣤⣤⠴⢶⢾⡿⢿⣏⠁⠀⠀
⢸⣇⠀⠀⠿⠷⠶⠾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠋⣿⠃⣿⡇⠀⠀⣶⣷⡄⠀⠈⣿⠀⢠⣾⡇⠈⣿⡄⠀⠀
⢸⣿⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢠⣿⠀⢿⡇⠀⠀⠘⠉⠀⠀⢠⣿⠀⠈⠉⠀⠀⢸⣷⠀⠀
⠀⠻⠿⠿⠶⠶⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢐⢸⡏⠀⠈⢿⣦⣀⣀⣀⣠⣷⡿⠃⠀⠀⠀⠀⠀⢸⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⠈⠙⣛⣛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⢸⡇⠀⠀⣤⣶⠟⠛⠛⠻⢷⣦⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀
⠀⣾⠿⠛⠛⠛⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈⣿⡄⢸⡇⠀⣼⡟⠁⠀⠀⠀⠀⠀⢿⣧⠀⠀⢀⠀⠀⣸⡟⠀⠀
⢸⣿⠀⠀⠀⡀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⠀⠈⢿⣾⣿⠀⣿⡇⠀⠠⣾⣷⡄⠀⠀⣿⠀⠀⢻⡇⢠⣿⡇⠀⠀
⢸⣿⠀⠀⣿⡟⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠈⠻⣷⣤⡀⠙⠛⠂⢿⣇⠀⠀⠙⠉⠀⠀⢰⣿⠀⢀⣼⣿⣿⣫⣿⠀⠀
⠸⣿⣄⣠⣿⠁⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠈⠻⣿⣦⣄⡀⠈⠻⣷⣤⣄⣤⣴⣾⢟⣡⣴⣿⣿⠟⠿⣿⣿⠀⠀
⠀⠙⠛⢻⡁⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢿⣆⠀⠀⠘⣿⣛⣿⣷⣦⣤⣍⣉⣉⣁⣠⣼⣿⡿⠛⠁⠀⠀⠀⠙⣷⠀
⠀⠀⠀⣿⠛⠶⠦⠤⣤⣬⣟⠿⠷⠶⠶⢶⣶⠶⢿⣥⣤⣬⣿⡆⠀⠀⠈⢛⣭⣿⣿⠍⠉⠙⠛⠛⠉⠉⠀⠀⠀⠀⢀⣀⣤⠾⢿⠀
⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⣿⡄⠀⣤⡈⠻⣿⡞⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠋⠉⠁⠀⣰⣾⠀
⠀⠀⠀⠘⠻⠧⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣾⣿⣾⡿⣷⡀⣿⣿⣶⡿⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣤⡿⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠙⠛⠻⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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