Mastroni475
Male
United States
21Followers
321Following

About

Mostly use this in school
Pfp history:
something to something: default
something to 12/15/24: Blue Ryai


MBTI Type: ISFP-T
Favorite youtuber: Blue Ryai


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡹⠟⠛⠒⢤⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⣤⣄⠀⠀⠁⠀⣴⣶⣾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡎⠀⠀⠘⠿⠛⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢠⡀⠀⡄⢀⣠⣄⢀⡀⠀⣄⠀⠀⣤⡀⠀⣤⣀⣀⣤⡀⠀⣄⣀⣀⡀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠐⠂⠒⠒⠲⣄⠀⠀⠿⡾⠁⡞⠉⣨⡿⡇⢀⣿⠀⢰⡇⠙⣦⢸⣯⢸⣯⡼⠯⠁⣇⠀⠙⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠲⢶⡖⠉⠀⠀⠘⠃⠀⠙⠚⠛⠀⠙⠚⠁⠀⠘⠛⠒⠋⠛⠛⠚⠃⠉⠓⠀⠋⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠦⠤⣀⠀⠀⢸⠀⠀⠀⢉⠏⠉⠉⠫⡉⠝⠻⠍⡹⠋⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣯⠤⠤⠤⠤⣍⣲⣼⠀⠀⢀⡎⢀⠴⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣹⠗⡇⠀⢼⢸⣋⡷⢸⣉⡿⠙⣄⡞⠁⠀⣧⠜⠋⢻⠉⢹⠀⠀⡇⠀⢸⣏⣉⣹⡉⣲⠀⠀
⠀⠀⠀⠀⢀⠜⢠⠇⠀⠀⠀⠀⠀⠀⣹⡟⠒⠚⣿⡛⠉⠁⢹⡓⣄⠀⠀⠀⠀⠀⠀⠀⠀⡿⠼⠇⠳⠤⠏⠸⡥⠝⢸⡥⠿⠀⡾⠁⠀⠀⡏⠳⠤⠼⠤⢼⡤⠤⢧⠤⠼⣤⣦⠸⠝⠳⢤⡄
⠀⠀⠀⢠⠋⠀⡾⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡃⠀⠀⠈⣇⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡴⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢻⡇⠀⠀⠀⢸⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⠃⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢸⡇⠀⠀⠀⠘⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⡀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢸⣷⠀⠀⠀⠀⣇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢇⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⢸⣿⠀⠀⠀⠀⢸⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢦⡀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⢘⣿⠀⠀⠀⠀⣸⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⢻⣤⣄⣀⣀⣀⠀⠀⠀⣸⣿⣀⣠⣼⣿⣶⣶⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⠇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⣿⣿⣿⣿⣿⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠹⣿⣿⣿⣿⣿⣇⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡄⣘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠋⠉⡏⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⢻⠉⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠒⢲⠞⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠸⠦⢤⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣀⣀⣘⣳⣲⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⢤⣄⣤⣏⣠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀


⠀


⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⡀⠀⡖⠤⡀⢠⠤⡀⠀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⢄⠑⠾⡀⢌⠑⢵⡑⡌⠲⣷⡝⢆⡇⢣⠀⢀⣀⣀⡀
⣀⠀⠀⠀⠀⠀⠀⠈⣢⣵⠒⠷⣄⠁⢀⣵⠬⢤⣌⠘⠀⠣⣇⢖⢽⡦⡽⠃
⢿⣇⠀⠀⠀⠀⠀⡼⣿⣿⣿⡆⠈⡷⢻⣾⣷⣦⠈⢷⠀⢀⠁⠰⡥⠚⠁⠀
⠀⢋⢿⣁⠒⠒⡒⣇⠻⠿⠿⠃⢠⣇⠸⣿⣿⠟⠀⣼⠀⠈⡄⠀⠘⡀⠀⠀
⠀⠀⠢⡈⠛⠔⣂⠈⠳⠤⠤⠶⠋⠘⠶⣤⣤⡴⠞⠁⠰⡀⠀⠀⠃⢇⠀⠀
⠀⠀⠀⠈⠢⡀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠐⠒⠤⡀⠀⣡⠂⠆⠀⢸⠀⠀
⠀⠀⠀⠀⠀⠀⠑⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡇⣶⢸⠀⡆⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢱⠀⠀⠃⡇⠀
⠰⣾⣷⡄⠀⠀⠀⠀⠀⢸⠠⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⡇⣾⠀⡄⠀⢳⠀
⠀⢱⠹⡀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⢸⡛⢳⠀⠀⠀⠀⡇⢸⠀⡇⢸⢸⠀
⠀⠘⡆⢳⠀⠒⠂⠀⠀⡇⢸⠐⠀⠀⠈⠱⡨⡢⣀⣀⡰⢏⡏⠀⠁⠈⢈⠀
⠀⠀⠘⢄⠣⣀⣀⡀⠜⢠⠇⠀⠀⠀⠀⠀⠈⠪⠤⠒⠥⠊⡆⠀⡄⠀⢈⠀
⠀⠀⠀⠈⠑⠠⠤⠍⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠃⠠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⠀⠀⠀⢸⡄⠀⠀⢀⡀⣴⡿⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢸⣇⠀⢠⣿⡅⣿⡇⣸⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⡀⢸⠻⣦⣈⡿⢿⣿⠃⣏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⠉⠁⣼⡆⣿⣿⠃⢰⣿⣿⡟⠀⣿
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠈⠻⣿⣿⡇⠀⢹⣧⣙⠃⠀⢴⣿⠟⠁⢰⣿
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣀⣰⠟⠋⠀⠚⠋⠁⠀⣠⣼⡇
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢠⣴⣾⣾⣿⣿⣷⣦⣀⣀⣸⣿⠟⠀⠀⠀⢆⢠⣤⣾⠟⠋⠀
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢰⣿⣿⣿⠉⠁⠈⠙⠟⠊⠉⠉⠀⠀⢀⠀⣮⢿⣼⣿⠃⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⢿⣯⣿⣿⡆⠀⠀⠀
⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣖⣺⣷⠀⠀⠀⠀⠀⣆⠀⠀⠀⢹⣿⣿⡿⢿⣿⣧⣀⣀⣀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⡭⢥⠀⠀⡀⢀⣶⣿⣷⡦⣤⣈⣿⠃⠀⠈⠛⠿⠿⠛⠋
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⢿⣿⣿⣷⣥⣤⣴⣳⣼⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠛⡁⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⡞⣝⣲⠇⠀⠀⠀⠈⠉⠒⢤⡠⣚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⡷⣨⢼⠀⠀⠀⠰⡂⡅⠐⠂⡱⣖⡪⢍⡔⣠⡀⠀⣤⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣋⡖⡃⡄⠀⠀⠀⠀⠃⠈⠉⠀⠀⠈⠁⠀⠀⠉⢡⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⠿⡹⣻⠿⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡞⢠⠼⡠⢣⠀⠀⣀⣠⠤⣄⣦⠀⣴⣶⢦⣠⡤⣠⣦⣀⣴⣆⣄⢀⣤⣤⢄⠀⢠⡄⢤⢀⣀⣠⡤⡄⣤⣤⣤⣄⣠⡄⣡⡏⣤⣤⠄⣰⠶⣢⢟⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⢡⣿⠀⡇⡉⡄⠀⢷⣩⡚⡴⡻⠃⠛⡏⡘⢿⠿⢻⣼⡙⡟⢻⢻⡜⢷⢎⡿⠀⡏⡔⡽⢻⣡⢏⣾⠟⢷⣎⠓⠳⡞⠴⣿⡎⡕⡿⠇⠿⢧⢃⠞⡇⠀⠀⠀
⠀⠀⠀⠀⠀⢀⢯⢲⡘⠀⢻⠠⢱⠀⠀⠘⡧⡑⠜⡀⢠⠃⠄⢻⠀⠀⢸⢭⣤⢞⣻⠀⢈⡌⠱⡠⠗⣼⠀⠀⢸⢎⡇⠀⠀⣿⣣⡴⢻⠆⠀⡟⢸⠀⠀⠀⡼⠙⣦⠇⠀⠀⠀
⠀⠀⠀⠀⠀⡜⡀⣶⢃⠀⡘⣆⠢⡆⠀⠀⡇⠿⡜⢃⡞⢡⣮⢺⠀⠀⣸⢆⡾⠓⠁⠀⢀⡂⡡⠒⡎⠼⠀⠀⢸⠎⡇⠀⠀⡟⡔⢻⣇⡆⠀⡏⢹⠀⢀⢀⡏⣇⢹⢸⠀⠀⠀
⠀⠀⠀⠀⢰⠁⡸⢁⢇⠀⣿⢈⡆⢾⢰⡐⠃⢸⢹⡈⠐⡸⡧⠈⠉⡆⡞⠀⣃⠀⠀⣼⠉⠀⡅⠀⡇⢀⠓⣶⠉⠄⠓⡄⡖⠁⠣⠘⠀⣧⠖⠃⡈⢲⡏⠉⢠⠤⢆⠀⠣⣀⠀
⠀⠀⠀⢀⠇⡐⢀⠂⡐⠠⠃⠠⢈⠘⢃⠳⠬⠜⠀⠙⠛⠁⠳⠜⠚⠀⠧⠴⠚⠀⠀⠈⠒⠲⠃⠀⠓⠒⠚⠈⠓⠚⠒⠃⠛⠒⠒⠒⠛⠀⠓⠒⠒⠃⠘⠦⠋⢰⡚⠈⠄⠠⣸
⢠⠦⠤⠊⡀⠐⡔⠋⠉⠉⠉⠓⡆⠈⠌⠢⠔⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠁
⢸⡄⢀⠂⠄⡁⠌⢡⠀⠀⢾⠉⠁⠌⠐⡀⢂⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠒⠒⠒⠒⠤⠋⠀⠀⠈⠳⠬⠒⠓⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀


⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠉⠉⠀⠉⠉⠉⠛⠛⢶⣾⡀⠀⠀⠀⠀⠈⠉⣻⣷⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠙⠻⣦⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⠀⠀⠀⠀⠀⢹⡗⠀⠀⣀⣤⣶⣾⡿⢿⠛⡛⠛⠛⠿⢶⣦⣄⠀⠀⠀⠀⠘⣷⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣤⣀⣀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⣀⣤⣶⣾⠿⠛⠛⠛⠻⢷⣦⣀⠀⢸⣿⣶⣿⣿⣿⡿⢷⡙⢎⠱⡐⢀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⣀⣤⣶⠾⠟⠛⠋⠙⠋⠛⠛⠻⢶⣤⣀⠀⠀⢸⣇⣀⣴⣾⣿⠛⡉⠀⢀⣐⣀⣀⠀⠀⠉⠛⣿⣾⣿⣿⣿⡿⢏⡝⠢⠍⠦⡑⠌⡄⠩⢷⣤⡀⠀⠈⢻⣦⡀⠀⠀⠈⣿
⠀⢀⣴⣿⠟⠉⡀⠄⠐⠠⠁⢂⠐⢀⠀⠀⠀⠈⠛⢷⣤⣸⣿⣿⣿⣏⣶⣷⣶⣿⠿⠟⡛⡁⢀⠀⠀⠀⠈⠿⣿⣯⠷⡙⣌⠰⡩⠘⡤⢑⢸⠠⣁⠂⠹⣷⣄⠀⠀⠹⣷⡀⠀⠀⠀
⢀⣿⡿⢡⠂⡐⠀⠌⡀⠡⠐⢀⠈⠠⢀⠡⠀⠀⠀⣠⠿⣿⣿⣿⣿⡿⡛⠭⣁⢦⡘⣆⠱⡈⢆⠒⡠⠀⠀⢀⡉⢎⠱⢁⢂⠡⡐⡁⢢⢡⢪⣕⡤⣈⠐⠈⢿⣦⠀⠀⢹⣷⠀⠀⠀
⣼⣿⢏⠥⠐⠀⠌⢀⠐⣠⣈⣄⣈⣤⣤⣶⣶⣿⠿⠋⠀⠘⠿⣟⢯⡱⢁⠚⡼⣞⣿⣾⢧⡳⣌⢦⡁⠇⡌⠰⢈⠰⢈⠢⠌⡐⠀⠠⢁⢻⣿⣿⣳⢦⡁⠂⠘⢿⠀⠀⠀⢿⡆⠀⠀
⣿⣿⢮⡑⠀⠁⠂⠀⣶⣿⣿⣿⣿⣿⣿⣿⣳⢤⢂⠄⡀⠠⡐⢌⠲⢡⠀⠀⠻⣿⣿⣿⣿⣿⣿⣶⡻⡔⡈⠰⢁⠢⠌⠐⡐⠠⠁⠀⢠⢏⣿⣿⣷⣣⠝⡠⠁⠀⠀⠀⠀⢸⡇⠀⠀
⣿⣿⢧⣸⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣻⡼⡘⠤⢃⠇⡸⢀⠇⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⢣⠀⠃⠄⠀⠀⢄⠻⣇⡤⢀⢄⣿⡟⢿⣿⡜⡿⣀⠃⠀⠀⠀⠀⢸⡇⠀⠀
⣿⣿⡿⣧⢋⠄⠀⠀⢹⣿⢻⣿⣿⣿⣿⣿⢷⣯⡑⠣⠌⣂⠡⠌⡐⢌⡀⠀⠀⢻⣿⢻⣿⣿⣿⣿⡗⡂⠡⠈⠀⠀⠀⠈⣽⣿⣳⣯⣾⣿⠁⠘⣿⣿⡵⣊⠔⡀⠀⠀⢀⣿⠇⠀⠀
⣿⣿⡿⣝⣏⠀⠀⠀⢸⣿⡀⣿⣿⣿⣿⣿⣻⢦⡙⠤⠑⡠⢒⡄⠢⠄⠡⠀⠀⠘⢿⣿⣿⣿⣿⡟⡡⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⠙⠉⠀⠀⠘⢿⣿⣦⡓⣄⣂⣴⣿⡿⠀⠀⠀
⢿⣿⡿⣽⣎⠆⠀⠀⠸⣿⣷⣿⣿⣿⣿⣏⠗⡢⠐⡈⢥⢳⣿⣾⠅⠂⠀⠀⠀⠀⠀⠉⠁⠋⠍⠀⠁⠀⠀⠀⠀⡄⠀⠀⣿⡇⠈⠙⣿⡄⠀⠀⠀⠀⠙⠿⢿⢿⡿⠟⠛⣧⠀⠀⠀
⠸⣿⣿⣳⢯⢆⠀⠀⠀⠙⠛⢻⠟⣏⠳⠌⠊⠀⠀⢄⢫⣿⣿⣏⠎⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⣿⠂⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⠤⠀
⠀⢽⣿⣯⡟⡎⠄⠀⠀⠀⠀⠀⠩⠀⠂⠀⠀⠀⠀⣨⣿⣿⣿⣌⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⣿⣇⠀⠀⠀⠈⢻⣆⡀⠀⠀⡀⠀⡀⠀⡀⠀⠀⡀⠀⠀
⠀⢺⣿⡷⣝⢎⠘⡀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⡎⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠈⠻⣦⠀⠀⠀⠀⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠻⢶⣤
⠀⢾⣿⡟⡼⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠘⣷⡄⠀⢀⣿⣿⣿⣶⣄⣀⣀⡀⠀⠀⠀⠀⠀⠈
⠀⣿⣿⠽⣑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⢹⣷⣀⣾⣿⣿⠿⠿⠟⠛⠛⠛⠿⣶⣄⠀⠀⠀
⠀⣿⣿⡙⢆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⣾⣆⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⢿⡋⠔⡀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀
⠀⣿⣿⡉⠆⠀⠀⠀⠀⠀⣠⡄⡄⣀⢀⡀⣤⣰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣂⢦⡐⣬⣿⣿⣿⠠⠀⠀⠀⠀⣿⠃⠀⢸⣿⢣⠞⡡⢂⠈⠄⠠⠀⠀⠀⠀⠀⠈⢿⣆⠀
⠠⣿⣧⠉⠄⠀⠀⠀⠀⣼⣿⣿⣿⣦⣷⣿⡿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣇⠧⡀⠄⠀⠃⠀⢀⣿⣯⢻⡜⡄⠢⢌⠠⣁⢂⠡⠀⠀⠀⠀⢸⣿⡀
⢸⣿⡧⢉⠀⠀⠀⠀⠀⣿⠟⠻⣿⣟⡿⠁⠀⣻⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠙⠻⢿⣿⣿⣿⣿⣿⠳⡌⡐⠈⠀⠀⣰⣿⣯⢷⣹⣼⢳⣎⣷⢢⡌⢂⠅⡀⠀⠀⢸⣿⡇
⢸⣿⡑⠂⠀⠀⠀⠀⠀⡿⠀⠀⠈⣿⡇⠀⠀⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣿⢿⣿⣿⣿⡟⡴⠐⠀⠀⠀⢸⣿⣿⣯⣷⣿⣿⣿⣞⣷⡙⢆⠰⠀⠀⠀⢸⣿⡇
⣿⣿⡐⠁⠀⠀⠀⠀⠀⡅⠀⠀⣠⡿⠀⢀⣼⣿⠿⡙⠄⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢿⣆⠀⢀⣿⣿⣿⣿⣿⡻⡔⡉⠀⠀⠀⠈⢿⣯⣽⣿⣿⣿⣿⣟⣮⢝⠢⣁⠂⠀⠀⠀⣿⡇
⣿⣿⠰⣁⠀⠀⠀⠀⠀⣏⠀⢠⣿⣃⣴⣿⡿⣋⠧⠑⠠⠀⠀⠀⠀⠀⠀⠐⢦⠀⠀⠈⠻⢿⣿⣿⢿⡿⢿⡏⡗⠰⣁⠂⠄⠀⠀⠀⠉⠛⡿⢻⡟⣷⢫⠞⡌⠱⢠⠁⠀⠀⠀⣻⡇
⢸⣿⡗⡆⡆⠀⠀⠀⠀⣿⣤⣿⣿⣿⢻⠙⡆⢡⠂⠁⠀⠀⠀⠀⠀⡄⢠⠀⢠⠀⠀⠀⠀⠀⠐⡌⢳⡜⢣⡜⡌⣧⣤⢣⡌⢰⢠⡄⢠⠚⢡⠃⡞⢡⠃⡎⡌⠑⠂⠁⠀⠀⠀⢹⡇
⠀⢻⣿⡵⣊⠄⠀⠀⠀⢿⡿⢟⡿⡍⢆⠣⠌⠐⠈⠀⣄⢢⣼⣤⢃⠄⠂⠌⢠⠚⢠⠀⡄⢠⠠⡑⢢⡑⢦⣱⣻⣼⣿⣮⡜⢤⢂⠱⣋⠔⣈⢒⣤⣃⠘⠠⠌⠁⠀⠀⠀⠀⠀⣸⠃
⠀⢸⣿⡗⣧⢂⠀⠀⠀⠈⠐⠩⠓⡈⠄⠂⢌⡐⣡⢣⣾⣿⣿⣿⣣⢎⠱⡈⠆⡜⢠⢃⠜⡄⢣⠉⡔⢨⣳⣿⣿⣿⣿⣷⣻⣖⣬⣲⣼⣾⣿⣿⠿⠋⠀⡀⠀⠄⢂⠈⠀⠐⢰⠃⠀
⠀⣸⣿⡽⢦⡃⠆⡀⠠⢀⠀⠠⠑⡰⢈⡒⢦⣳⢮⣷⣿⣿⣿⡷⣯⡚⢤⡑⢬⠰⣡⢊⡜⣬⢣⣎⣔⡡⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⠠⢀⠡⢀⡁⠂⠄⠂⠀⠀⠀⡀⠀
⠀⣿⣿⡽⣣⠕⣂⠰⣁⠆⡌⠰⡁⠄⢣⢞⣽⣿⣿⡿⠛⣿⣿⣟⡷⣝⢦⡘⢆⡱⢀⠎⣼⣳⣿⣾⣿⣿⣿⡿⣿⡟⠛⢿⣿⣿⣯⡿⡥⢈⠠⠁⠂⠄⣂⣷⣮⣑⠂⠌⠠⢀⠀⣐⡄
⠀⣿⣿⣽⢣⡓⣄⠲⣭⣞⣽⣳⢼⣘⢦⣿⣿⠿⣧⣤⠀⢹⣿⣿⣽⢯⣷⣻⣽⣦⣵⣾⠿⣿⣿⣿⡿⠿⣿⡇⢸⣟⠀⠀⠀⠉⢿⣿⣕⠂⡀⠂⠁⣾⠿⠛⢿⣾⣭⣆⣁⣠⣶⡿⠂
⢨⣿⣿⣞⡷⣱⢌⡟⣷⣿⣾⣽⣯⣿⣿⣿⡁⠀⢸⡿⠀⠀⠻⣿⣿⣿⣿⣿⣿⡟⠋⠀⡀⣿⡟⠉⠻⣷⣿⣧⣼⠟⠀⠀⠀⠀⠸⣿⣿⡄⠠⠁⣼⡟⠀⠀⠀⠈⠙⠛⠿⠿⠋⠁⠀
⠀⣿⣿⡾⣽⢧⣟⣾⡿⠉⠛⠿⠟⠋⠁⣿⡃⠀⢸⣯⠀⠀⠀⠀⠈⠉⠹⣿⣷⣍⠆⣐⣼⡟⠀⠀⠀⣹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣷⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⣿⣿⣿⣿⣿⢋⡀⠀⠀⠀⠀⠀⠀⣼⠿⠾⠿⠋⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⡛⣇⠀⠀⣰⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀



⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⡿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⣴⣿⣟⣿⣿⣿⣿⣶⣤⣀⣀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣤⣤⣀⣠⣶⣾⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⣿⣿⡇⠋⠉⠉⠻⣿⣿⣷⣄⠀⠀⣸⣿⡿⠋⠁⠈⠉⠉⢻⣿⣿⣿⡯⠽⠯⣿⣿⣷⣦⡀⠀⠀⣠⣾⣿⡿⠿⠶⠾⣿⣿⣿⣿⣾⠉⠉⠙⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣿⣿⡇⠀⠀⠀⠀⠸⣿⣜⢿⡇⢸⣿⣿⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣧⠀⢠⣿⣿⡿⠃⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠹⣿⣧⠀⠀⠀⠀⠀⢹⣿⣾⣿⣿⣿⠃⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⢿⣿⣇⣸⣿⠋⠀⠀⠀⠀⣠⣠⣿⣿⣿⡇⠀⠀⠀⠀⢘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠹⣿⣿⣿⠏⠀⠀⠀⠀⣿⢧⣿⣿⣿⣿⣿⣿⠙⢿⣆⠀⠀⠈⢿⣿⡿⠃⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣏⠿⡦⠀⠀⠀⠀⠹⣿⠏⠀⠀⠀⠀⢀⠃⣼⣿⣿⣿⣿⣿⡿⢀⣬⣿⣇⠀⠀⠚⠟⠁⠀⠀⢀⣰⣿⣿⣿⣿⠟⠹⣿⣿⠁⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⢿⣦⣔⣦⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠌⠀⣿⣿⣿⣿⢿⣿⣿⢾⣿⣿⡟⣂⠀⠀⠀⠀⠀⢠⣾⢛⣾⣿⣿⠏⠀⢸⣿⡇⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⣿⣾⣿⡆⠀⠂⠀⠄⠂⠈⣀⣄⠠⠀⣿⣿⣿⠇⠾⣿⣿⣾⣶⣾⣿⣿⡀⠐⠀⡐⢀⣾⣴⣿⣿⡿⠁⠀⠀⢸⣿⠁⠀⡀⠁⠈⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⢿⣿⢻⡄⢠⡁⠂⣄⣿⣿⣿⢦⠀⣿⣿⣿⠀⠀⣿⣿⣌⣿⠏⠀⡉⠠⠐⠠⢀⠂⠘⢿⣿⡛⠀⠀⠀⠀⣻⡏⠀⠠⠐⡈⠐⡀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⣆⢡⡜⢰⡿⣿⣿⣿⢸⡀⣿⣿⣿⠆⠀⣹⣿⠋⠁⠙⢿⠠⣁⣣⣱⡆⡘⢄⡈⠹⣿⣦⡀⠀⠀⣿⣧⡾⣇⠡⢂⡱⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⡇⢎⡹⢄⡃⣿⣿⣿⡆⠅⣿⣿⣿⡀⣸⣿⡯⠀⢀⡒⣌⢣⣽⣿⣤⣿⡜⢢⠒⡤⠘⢿⣷⡀⠀⢻⣿⡇⢈⡇⢣⢒⣅⣺⣯⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠐⡟⣜⡣⢏⡆⣿⣿⣿⡇⠀⣿⣿⣿⣷⣿⠟⠀⣜⡳⡜⣬⡿⢳⣿⣿⣧⠹⣧⡛⡴⣣⠀⢻⣿⣄⠀⣿⡇⠸⣿⢥⣋⠀⠙⠛⠋⠉⠉⠋⠛⠿⣿⣶⣤⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⣿⡼⣱⢯⡇⢻⣿⣿⣧⣀⣿⣿⣿⡿⠁⣠⡟⣶⡹⣾⡿⣳⣿⣿⡿⢿⣷⣉⢷⣝⢮⡳⡄⠹⣿⣷⣿⡇⠀⣼⢳⣎⠷⣶⢶⣶⡻⣭⣳⣶⣤⠄⡽⣿⣶
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⣷⣯⣟⣧⢹⣿⣿⣿⣿⣿⣿⣿⡁⣾⣵⣻⢶⡿⢟⣿⣿⣿⠟⠀⠀⢻⣿⣎⡛⣯⣷⣿⠆⣼⣿⣿⣯⠐⣼⣷⡾⢿⣞⣷⡾⡽⢓⣯⣼⣧⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡘⠻⣿⣾⣷⢸⣿⣿⡇⠈⠉⠛⣿⣿⣶⣻⣟⣯⣡⣿⣿⣿⠋⠀⠀⠀⠀⠻⣿⣿⡼⣯⣶⣼⣿⣿⣿⣷⡀⣽⣷⣶⣶⣶⣬⣷⣿⣿⣿⣿⠿⠛⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣮⠹⣿⢿⣿⣿⡇⠀⠀⠀⢸⣿⣿⠸⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠙⣿⣷⡹⣿⣿⡿⠟⣿⣿⢇⣻⣿⡿⠿⢿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢷⣯⣾⣿⣿⡇⠀⠀⠀⠀⣿⣯⣔⣺⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣽⣿⠀⠀⢻⣿⣣⠞⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣯⣷⣻⡟⣿⡇⠀⠀⠀⠀⠸⣿⢬⣳⢯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⢸⣿⣥⣋⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⣽⣯⣷⢹⣿⠃⠀⠀⠀⠀⠀⢻⣿⣭⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⢹⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢴⣫⣿⡜⣹⣿⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠾⣥⢻⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣹⣿⠆⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⠻⣃⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣽⡻⢯⢋⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀


⠀⠀⠀⢀⣀⣀⣀⣀⣶⣶⡶⢦⣀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⣿⢟⡭⡿⣛⡵⢞⣕⡫⡫⢋⣳⡀⠀⠀⠀⠀
⠀⠀⢸⣷⣚⠾⡼⡾⢞⣗⠦⡪⣏⣢⣎⠟⣆⠀⠀⠀
⠀⣼⣿⡤⢻⢤⡧⢧⢻⡧⡟⢼⡣⡤⡧⡼⢸⢿⡀⠀
⠀⢹⣿⡝⣿⢻⡹⣵⡫⡗⡪⡵⣻⡯⡻⣹⡯⡟⠀⠀
⠀⣿⣿⢻⣼⡿⣼⠼⡷⢬⢾⣗⡽⡯⣾⡏⣼⣏⠀⠀
⠀⢹⣟⣿⣷⣿⣼⡻⡟⢛⣣⣍⢺⣏⢠⣷⡿⠃⠀⠀
⠀⠀⠈⠙⣯⢿⣾⣿⣿⣿⡿⣿⠛⠺⠿⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠈⠁⠉⣿⣿⣽⡣⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⣀⣀⠀⠀⣿⣿⡷⡆⣷⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⢟⢫⢟⡧⠀⣿⣿⡷⢣⣇⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣷⡘⢢⣿⢦⣀⣿⣿⣹⡇⡧⠀⠀⠀⡀⠀⠀⠀⠀
⠀⢹⡿⠟⠙⠻⢮⣹⡼⣿⡌⡧⠀⣴⣾⡟⢶⡲⡄⠀
⠀⠀⠀⠀⠀⠀⠈⣿⣟⣧⠩⣷⢀⣈⣷⡕⢎⣰⣇⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣎⡇⣛⣫⣷⠛⢿⣶⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡇⣿⠋⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⡿⣧⣗⠺⢿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣠⣿⢻⣿⣷⡳⢨⡳⢦⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠘⡿⠻⣾⠿⠿⢶⣧⠿⢯⠾⠦⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢞⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢞⣩⣶⣿⡟⠀⠀⠀⠀⠀⣀⣤⡴⠖⣻⣛⣛⣭⣭⣽⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣶⣿⣿⣿⣿⠀⠀⣀⡤⢖⣫⣽⣶⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣾⣿⣿⣿⣻⣿⣇⡠⣮⣵⣾⣿⣿⡿⣟⣿⣿⣽⣾⠟⠁⠀⠰⠛⠛⣦⠀⠀⣠⢴⢦⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡟⠻⣽⣿⣿⣟⣿⣿⣽⣿⣿⡿⣿⣻⣽⣿⣿⣿⣽⡿⠃⠀⠀⠀⠐⠀⠀⠹⡆⢠⠁⠀⠸⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣻⣿⡇⠀⠘⢿⣿⣿⣿⣻⣿⣯⣷⣿⣿⡿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢰⠀⠀⠀⣧⡏⠀⠀⢀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣽⣿⣿⣅⣠⣤⣼⣿⣿⡿⣿⣷⣿⣟⣯⣷⣿⣿⣿⣟⣻⣓⣒⣶⡶⠶⣶⡎⠀⠀⠀⠏⠁⠀⠀⡼⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣿⣿⢿⡿⣫⣭⣭⣯⣿⣿⣿⣽⣾⣿⢿⣟⣿⣯⣿⢿⣿⣿⣿⣿⣿⡿⠗⠃⠤⠀⠀⣃⡀⠀⠞⢦⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣎⣿⣿⣻⣟⣾⣿⠛⠍⠝⢻⣿⣽⣿⣯⣿⣿⢿⣟⣿⡿⣿⣿⣾⢿⣷⣿⡇⠀⠀⠀⠀⠀⢀⣹⠏⠀⠀⣧⡀
⠀⠀⠀⠀⢰⡞⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠘⣿⣯⣿⢿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⡇⠀⠨⠒⠲⢲⡿⠋⠀⢀⡼⠀⡇
⠀⠀⠀⠀⠀⠙⢮⣛⣿⣿⣇⣿⣿⣾⣿⣿⡃⠀⠀⢰⣤⡀⠈⣿⡟⠛⢿⣿⣿⣿⣻⣽⠿⠖⠂⡟⡁⠰⡄⠀⠀⠀⠀⠟⡆⠒⠃⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣿⢿⣿⣽⣿⣿⣧⠀⠀⠀⠘⢾⣦⠏⣰⠀⠀⣿⠿⠋⠉⠀⣀⣠⣤⣷⡿⣄⠈⠂⢤⠤⣠⢀⣝⡦⠖⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣿⣿⣿⣽⣾⣿⣇⠀⠀⠀⠀⡜⠀⡘⠀⣼⣿⣤⣶⣾⣷⣷⣿⣿⣣⣤⣼⣳⣶⣭⡵⠚⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢮⡙⢿⠿⣿⣆⠤⠐⠊⠀⠀⢀⣼⣿⣿⣿⣿⣻⣽⣿⣯⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣲⣭⣿⡷⠀⠀⣀⣤⢶⡟⣿⣿⢿⡷⠿⢿⣿⣿⣿⣻⡷⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠷⠞⠋⠋⡁⠀⢏⠓⣔⣸⣧⢿⣿⣷⣿⣷⢿⣟⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣖⠲⡶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⡧⣤⣤⡤⠔⢣⠀⢼⡾⣾⣯⣿⣯⢿⣿⣿⡖⣉⡖⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⢯⣳⢹⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⢇⡀⠀⢀⣀⣴⣿⣿⣿⣿⡿⠛⠉⡳⣿⣿⣿⠟⠀⢹⠄⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⣯⣝⡆⡅⣿⣞⣿⣏⠢⡀⢰⠊⠉⠉⠛⠯⣿⣿⣾⣿⣿⠟⠁⠀⠀⢰⡁⠛⠋⠁⣀⡀⠀⣠⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⣗⣞⣧⢃⢿⣾⣳⣿⠀⠈⢋⠉⠁⠀⠀⣄⡨⠹⡿⠋⠁⠀⠀⠀⠀⠀⠉⢲⠂⠉⠀⣠⡔⠛⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣫⢞⡽⡼⡸⣷⣟⣾⠀⠀⠀⢱⣄⠀⠀⠈⣆⠀⣏⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠈⠉⠀⠀⢠⡚⣤⢻⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢻⣯⣛⠷⡕⣿⡾⠃⠀⠀⠀⢸⣿⣿⣦⠈⢸⡞⠁⠀⠀⠀⠀⠀⠀⢀⣿⡾⣿⢿⡿⣶⡔⠏⣜⢝⣜⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⣟⣻⢻⢮⡢⡄⣀⡀⠔⣹⣿⣿⣿⣷⠚⠁⠀⠀⠀⠀⠀⠀⢠⣿⣯⢿⣽⣯⢿⡽⣿⣄⢊⢎⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠻⣿⣾⣿⣿⣦⣠⣴⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⢾⣻⡷⣯⣿⣻⣽⢞⡥⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢿⣽⣻⢗⡿⠓⡱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣯⣿⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠤⠭⠴⢊⡩⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣩⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣄⣒⣶⣶⣶⣿⣿⣿⢿⣿⣷⣖⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠻⣿⣿⣦⣍⠓⠫⣗⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣷⣄⠀⠙⠢⡑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠶⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣤⡀⠈⠢⠵⣤⣤⣤⣤⣤⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣹⣿⣝⣿⣿⣿⣿⣷⣄⣸⡞⣿⣿⣿⡿⡱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠲⣻⣿⣜⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠗⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣈⢿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣮⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢤⣤⣤⠤⣤⣤⣤⣤⣤⣤⣤⠤⢞⠕⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⡟⡇⠻⣿⣮⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠛⢿⣿⣿⣶⣾⣦⣤⣤⣭⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠷⣄⣸⣿⠃⠀⠈⢿⣷⣿⣿⣿⣿⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠉⠻⢄⣀⣀⣀⡙⣿⣷⣿⣯⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⢋⣾⣿⣿⣿⣿⣿⣿⣧⠀⠟⠁⠲⢄⠀⠀⠀⠀⠀⠈⠀⠈⢻⡿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣽⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠁⠀⠀⠀⠀⢀⣠⣶⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣮⣭⣾⣽⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠒⠶⣞⣻⠟⠁⣾⣾⣿⡖⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢹⣿⣿⣿⣿⣿⣷⣤⣤⣀⠀⠈⠀⢈⣽⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⠿⠟⠉⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣠⣾⣿⣯⡣⣤⣿⣯⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣬⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠾⠿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡝⣋⠭⢭⡳⡶⡝⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⣱⣸⡇⢿⡟⢿⣿⣿⣿⣿⣿⡟⠛⣻⣟⣿⣿⡟⡜⠱⡇⠀⣨⡟⠸⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣉⣉⣉⡙⠻⣷⠈⠁⠸⢃⣹⣿⣿⡿⢹⣿⣡⠬⠟⠓⣺⢗⣻⢟⣻⣿⣅⢣⡀⣠⠏⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡞⠁⣰⠃⠀⢀⡀⠙⢺⣤⣴⣾⣿⣿⣟⣸⣷⣯⠟⠀⢀⡠⠞⣱⣟⣡⢿⠟⠻⣿⣽⣺⡝⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢱⠃⣰⡃⢀⣴⡇⣸⠀⠈⡇⠀⠀⢀⠔⣹⣿⣿⡿⠔⣊⡥⠶⣋⡵⢻⣇⣽⣿⣷⣼⣿⢹⢙⣲⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡽⡞⣏⠹⡧⢪⡞⢈⡁⠤⠔⡇⠀⣠⡟⣼⠟⣉⠥⢖⣋⠭⠶⣏⡁⠙⠾⣯⡙⠿⢛⣻⡿⢸⣉⣧⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠾⠶⠓⠺⠬⠥⠤⠤⠔⠁⣰⡟⣰⢟⣩⠵⠲⣏⡥⠴⢺⣟⡯⣷⢤⡈⠻⢏⡉⣽⣧⣿⢉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⣠⣿⣯⣤⠴⠋⢡⣤⣄⡘⢿⣿⣞⣆⣽⡀⣠⠽⣫⡞⢻⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢘⣆⠛⢿⣷⣄⠘⢿⣿⣷⠀⣩⠟⢁⡴⣻⡵⠋⠉⠛⠳⢮⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⣾⣷⢤⡙⠿⣿⣦⣤⣴⣋⡽⣾⣵⣿⡿⠤⢄⡀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣤⡟⡶⣌⣿⣿⢿⢻⣿⣿⣿⣿⠃⠀⠀⠈⠑⠦⣀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢸⡟⠎⣯⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⣀⣼⢯⠿⡔⠢⢄⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⠾⠋⠁⠈⣷⡽⠦⢤⣈⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⢹⡛⠛⢻⠤⢤⣀⣀⠀⠀⣀⡴⠯⣀⠀⢀⣴⠛⣡⠖⣶⣤⣄⠈⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠂⠛⠦⠼⣆⡀⠀⠀⠀⠁⠀⠀⠀⣠⠿⣏⣴⣾⣵⣿⢽⣿⡟⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⡤⢄⣀⣠⠞⢁⡴⣏⠀⠀⣿⣯⣾⡟⡜⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠭⣛⠷⠮⣷⣶⣶⣿⣋⡟⠀⠀⠀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡀⠀⣾⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠀⡴⠁⣴⠃⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⢠⡞⠀⢰⠇⠀⠀⠀⠀⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⣰⠋⠀⠀⣼⢀⣠⡄⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢀⡴⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣻⠏⠳⣄⠀⠀⠀⣠⣴⠟⠉⠀⠀⠀⢀⡜⠁⠀⠀⢀⡿⠋⢱⡟⢦⣄⠀⠀⠀⠀⠈⠳⣄⠀⡴⠋⢀⠆⠈⡿⢦⡀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⣰⠋⠀⢹⡌⠳⣄⡾⠋⠁⠀⠀⠀⠀⢀⡞⠀⠀⣠⠞⠉⢀⡴⠚⡇⠀⠍⠳⣄⠀⠀⠀⢀⡼⠋⠀⣠⠋⠀⠀⢻⣀⣹⠶⢋⡴⠹⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⡟⢀⣀⣠⣷⣄⣈⠳⣄⠀⢀⣀⣀⣀⣘⣁⡴⠋⠁⠀⢠⠏⠀⠀⣧⣀⣈⣀⣈⣓⢀⡴⠋⣀⣀⢐⣃⢠⠇⠀⠀⠙⠁⢠⠎⠀⠀⣿⢷⡀⠀⠀⠀
⢠⣤⡴⢶⣤⡚⠁⠀⠀⢸⢇⣿⠏⠉⠉⢉⣿⣆⣼⣫⠵⠛⠉⠉⠉⠉⠙⠲⣄⠐⢣⣡⠞⠉⠉⢁⣿⠟⠉⠻⣏⠀⣼⡿⠓⠚⠛⣇⠀⠀⠀⠀⣠⣿⣯⠿⠛⠛⠻⠿⢦⡀⠀
⢸⠋⠀⠸⣿⣿⠀⠀⢠⠏⣸⣟⣀⠀⠀⣼⣿⣿⡏⠁⠀⠀⢀⣤⡀⠀⠀⠀⠈⣇⢸⠇⠀⠀⢠⣾⣅⠀⠀⠀⢸⡅⣿⠀⠀⠀⠀⡿⢧⡀⠀⣰⠃⣿⣿⠀⠀⣤⣤⣄⠀⠙⣆
⠘⣇⣠⣾⠿⣿⡄⠀⡟⣼⣿⣿⣿⠷⢤⣿⣿⡿⠀⠀⠀⠐⣿⡟⡇⠀⠀⢀⡴⣿⢸⠀⠀⠀⠸⣿⠿⣦⠀⠀⢸⡇⢻⣷⠀⠀⠀⣧⠈⠳⣤⠏⠀⣿⣯⣤⣀⣿⢻⣿⣇⠀⢹
⠀⢹⡟⠁⠸⣿⣷⡿⢧⣿⠟⠉⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⣿⡇⡇⠀⠀⢻⡊⣿⢸⠀⠀⠀⠀⠈⠉⠁⠀⠀⣼⡇⣿⠁⠀⠀⠀⢸⠀⠀⠹⣆⢠⣿⡛⠁⠈⣷⢹⣿⣿⣀⣸
⠀⠘⡇⠀⠀⠙⠉⠀⠘⠉⠀⠀⠀⢰⣿⣿⢹⡇⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠙⣿⣾⠀⠀⠀⢀⡀⠀⠀⠀⣻⡟⠀⣿⠀⠀⠀⠀⢸⡀⠀⢀⡼⣼⣿⡇⠀⠀⣿⠀⣿⣧⡟⣿
⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡇⠀⠀⠀⣠⠿⠿⠿⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡄⠀⠀⠈⣹⡀⣿⠀⠀⠀⠀⠈⠉⠿⠭⠞⢻⣿⣇⠀⠀⠿⢷⣿⡿⠁⢿
⠀⠀⠸⡄⠀⠀⢀⣷⣄⠀⠀⠀⢰⣿⣿⣿⣿⣧⡀⢠⠞⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⢸⣿⣿⣤⠖⠋⠉⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠹⣦⣷⣿⡟⠉⠳⢤⣴⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣦⣤⣤⣾⣿⣿⣿⣦⣤⣤⣴⣿⣿⣶⣤⣴⣶⣶⣶⣦⣴⣾⣟⣷⣤⣤⣤⣤⠤⠴⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⠛⠙⢟⠛⠛⠛⢿⣿⡿⠛⠛⠛⠛⠛⢿⣿⠛⠛⢻⣿⣿⠿⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⡻⣿⣿⠟⣹⡿⠀⠰⣿⣿⡧⠀⢸⣿⠃⠰⣡⣤⣄⠀⠘⣿⣦⠀⠀⠘⣃⠀⢀⣼⣿⣿⣿⣿⡟⢋⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢹⣾⣿⣿⣿⡦⠤⣭⠭⡥⠾⣿⣿⠀⠀⣿⣿⣿⠀⠀⣿⣿⣷⢠⣼⡥⣤⣾⣿⣿⣿⣿⣿⡇⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡈⢿⣿⣿⣧⣴⡀⣶⣶⣦⠀⢸⣿⠀⠀⣿⣿⣿⠀⠀⣿⡿⠉⠀⠀⠀⠈⠙⣿⡏⣽⣿⡿⠁⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣌⠻⠟⣿⠁⠀⢿⣿⣿⠀⢸⣿⡇⠀⢉⠙⠛⠀⢠⣿⠁⢠⡀⣰⣆⠀⠜⠹⡿⠿⢋⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡄⠘⢤⣄⣉⣍⣀⣤⣾⣿⣿⣦⣄⣀⣠⣤⣾⣿⣦⣿⣵⣿⣿⣦⣤⣤⠇⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣦⣭⣝⠛⠻⡿⠏⢽⣿⣿⣿⣿⣿⣿⢿⡉⠿⠿⢛⢋⣥⣬⣿⣿⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣷⣷⣦⣤⣄⡀⠛⠿⢇⣽⣧⢈⣥⣤⣶⣿⣾⣿⡿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⣿⣷⣄⠘⢋⣴⣿⣿⡿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣈⠀⠀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⡔⠒⠒⠯⡉⠢⡀⠈⢱⠀⡖⠁⠀⠀⠀⢠⠁⢧⠀⠀⠀⠈⢱⠀⠐⠒⢪⠉⢂⠑⢆⠀⢎⠁⠀⢉⢆⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⡄⢱⠀⢸⠀⡇⠀⠀⠀⢀⢣⢣⠈⡄⠀⠀⠀⠀⠀⠀⠀⢠⠇⡸⠀⠈⢣⠈⢆⢀⢎⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⢸⠀⢸⠀⡇⠀⠀⠀⠎⣏⣀⣆⠘⡀⠀⠀⠘⠀⠠⡏⠡⡞⠁⠀⠀⠀⠱⡈⢫⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡰⠁⡜⠀⢸⠀⡇⠀⠀⡜⡖⠀⠀⠈⡄⠱⠀⠀⠰⠀⠀⠈⢆⠘⢄⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠀⠑⠒⢒⣊⠥⠊⠀⢠⠜⠀⠳⣤⠜⠐⢤⠀⠀⢠⡝⠀⠓⣤⠜⠀⠰⣤⠀⠳⡈⠒⣤⢠⠴⠃⠘⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣫⣿⣿⣿⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣲⣒⣼⢿⣿⠙⢿⣣⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⣿⣛⣿⣧⣾⣿⣿⣷⡇⠀⢀⢔⣯⣭⣶⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⣿⠵⡍⣿⣯⡞⠁⠀⣏⣿⣿⣽⣿⡇⡆⠀⠀⢀⢴⣲⡲⡀⠀⠀⢀⡠⣴⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠤⡤⡀⠀⠀⠀⠀⠀⠀⠀⢰⣪⣭⡔⣦⣔⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢳⣿⡛⠇⠀⠀⠈⠫⠛⠫⠛⠳⠇⠀⠀⢸⢸⣿⡇⡇⠀⣠⣪⣾⣿⣿⣺⡀⠀⠀⠀⠀⠀⡠⡤⣄
⣱⣿⣿⡾⡄⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⣿⣿⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡇⣧⣺⣾⣿⣿⣟⣱⣶⣯⣆⠀⠀⠀⢸⢹⣿⣏
⢣⢻⣿⣿⡼⡄⠀⠀⢀⣀⠀⡏⣿⣿⡇⢮⣯⡼⣤⣤⠤⠤⣀⣀⣀⢀⣰⢹⣿⣷⣿⣿⣷⣝⠔⣯⣽⢆⠀⣠⢄⠤⡀⠀⠸⢸⣿⣷⣾⣿⣿⣿⠞⠹⡿⣿⢟⠟⠀⠀⠀⡄⣿⣿⠙
⠀⢛⢿⣿⣿⣱⣠⢪⣷⣿⣳⡇⣿⣿⢹⢹⣿⣧⢸⣿⣿⣿⣶⣷⣾⣷⣯⡸⣿⣿⢻⢽⣿⣿⡏⣿⣿⣎⣶⣱⣿⡿⡸⠀⢸⢸⣿⣿⣿⣟⡝⠁⠀⡼⣾⣿⢹⡀⣔⣢⣒⣻⣿⣿⠀
⠀⠈⢋⢿⣿⣷⠿⣿⣿⣿⣷⢹⣿⣿⣾⢸⣿⣿⢸⣿⣿⠛⣿⣿⢿⢻⣿⡇⣿⣿⢻⣠⣣⣿⡿⣜⣿⣿⣷⣿⡿⡳⠁⠀⠘⣼⣿⣿⣿⣿⣝⢦⠀⡇⣿⣿⢘⣾⣿⣿⣿⣿⣿⡇⡆
⠀⠀⠈⠾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡞⡏⣿⣿⢸⣿⡏⣧⡿⢿⣼⢸⣿⡇⣿⣿⣿⣾⣿⣿⡵⠙⡝⣿⣿⡿⡳⠁⠀⠀⢀⣿⣿⣷⢾⢿⣿⣷⣷⣷⣿⣿⢸⣿⣇⠿⢧⣿⣿⣿⠀
⠀⠀⠀⠈⢾⣿⣿⣿⡏⡷⢿⣿⣿⣿⡇⠈⠪⠵⣼⣿⡇⡇⠉⠉⢸⢸⣿⣧⢻⣿⡏⡭⠟⠚⢁⢞⣾⣿⡿⡕⠁⠀⠀⠀⡄⣿⣿⣿⠀⠑⣝⣿⣿⣦⢻⠻⢮⢿⣿⣿⣿⣿⣿⠈⠀
⠀⠀⠀⠀⠈⢾⢿⣿⣹⠀⠱⣛⣛⡷⠃⠀⠀⠀⠑⠂⠈⠁⠀⠀⠈⠑⠛⢺⢸⣿⣿⡇⠀⢀⢎⣾⣿⣟⡜⠀⠀⠀⠀⠀⢰⣹⣿⢿⠀⠀⠈⢺⢿⣿⡎⡄⠀⠑⠛⠉⢝⠿⢯⡇⠀
⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⣿⣿⣷⢀⢯⣿⣿⢟⠏⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠉⠑⠚⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀
⠀⠀

⣰⠶⠰⠄⠲⠰⠐⠦⠄⠤⠌⡖⠲⠼⢣⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢖⠻⠴⠰⠤⠸⠥⠏⠥⠳⠌⠭⠵⢲⢆
⢷⢙⡐⠦⠶⠤⠶⠤⠾⠿⠿⠿⠿⢿⣷⡘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⡽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡋⢼
⣿⠠⡘⠇⣸⠚⠂⠛⠒⠙⠋⠛⣯⣆⢻⣷⡨⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⡜⡌⣡⡿⠉⠋⠛⠙⠓⠻⠛⣾⢘⣿⡑⢾
⣿⠠⡑⡇⢼⠀⠀⠀⠀⠀⠀⠀⠈⢫⣦⢻⣷⡩⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠃⠼⡘⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⢿⢨⣿⡑⣺
⣿⢰⠡⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⢻⣧⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⡸⡙⢡⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣘⣿⡱⢼
⣿⢸⣧⡃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⣿⣇⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢠⠧⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣘⣿⡇⢼
⣿⢪⣟⡧⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡘⡿⣎⢛⣆⠀⠀⠀⠀⠀⠀⠀⢠⣿⢠⣷⢋⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣷⡙⣾
⣿⢱⣿⡅⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠘⡜⣂⢻⡆⠀⠀⠀⠀⠀⣰⡟⣢⣿⠏⣾⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢨⢿⡣⢼
⣿⡱⣿⢆⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⡴⡀⢷⡄⠀⠀⠀⢠⡿⣑⣿⢃⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠴⡇⢽
⣿⡜⣿⠆⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠸⠴⡌⢷⡄⠀⢀⡿⢑⣾⡏⡼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢈⠒⡇⣸
⣿⡜⣿⢣⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠩⡜⡈⣿⣤⣾⢍⣾⡟⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠠⡙⡆⣸
⣻⠜⣿⡃⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠱⣷⡸⢿⣃⣾⡟⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠠⢱⡇⣹
⣿⡹⣿⡱⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠄⠀⠀⠀⠀⣻⣆⢿⣧⠃⣼⣟⢰⣿⠂⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢘⣶⠆⣯
⣿⢱⣿⡅⢾⠀⠀⠀⠀⠀⠀⠠⣟⢮⣑⡩⢿⣄⠀⠀⠀⠘⣿⡌⣿⣦⣿⢢⣿⠋⠀⠀⠀⣰⡿⢥⣋⣚⣇⡄⠀⠀⠀⠀⠀⠀⣿⠸⣿⠣⣼
⣿⢊⡿⡄⢻⠀⠀⠀⠀⠀⠀⢀⣿⢚⣿⣿⡌⢿⡀⠀⠀⠀⠙⢷⣜⣛⡭⢾⡇⠀⠀⠀⢠⡿⢠⣿⣟⡧⢾⠇⠀⠀⠀⠀⠀⠀⣿⢩⣿⢣⢸
⣿⠨⠔⡃⢹⠀⠀⠀⠀⠀⠀⢰⣿⠌⣿⠹⣿⡌⣿⡄⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⢀⡾⢀⢗⠎⣿⠡⢿⡆⠀⠀⠀⠀⠀⠀⣿⢒⣿⢣⢸
⣿⢀⢋⡅⢽⠀⠀⠀⠀⠀⠀⠈⣿⢨⣿⠤⠹⣷⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠁⡜⠎⠀⣧⠀⢿⡁⠀⠀⠀⠀⠀⠀⡿⢨⣿⡃⢾
⣿⢀⠎⡆⢸⠀⠀⠀⠀⠀⠀⠀⣿⠰⣿⢸⣇⢻⣧⡙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⡜⠎⣰⠀⣗⠀⣿⠀⠀⠀⠀⠀⠀⠀⣹⢡⣿⡕⣺
⣿⢘⡆⡇⢻⠀⠀⠀⠀⠀⠀⠀⣽⡘⣿⢨⣿⣆⢻⣷⠸⣵⡀⠀⠀⠀⠀⠀⢀⣼⠃⡜⡼⢰⣿⡀⣿⡂⣿⡆⠀⠀⠀⠀⠀⠀⣿⢘⣿⡆⣹
⣿⢸⣷⡅⢾⠀⠀⠀⠀⠀⠀⠀⣷⢩⣿⠰⣿⣿⣆⢻⣷⠹⣷⠀⠀⠀⠀⢀⣿⢇⣾⡝⢠⣿⣿⡐⣿⡅⣿⡁⠀⠀⠀⠀⠀⠀⣿⢨⣿⡓⣼
⣿⡸⣷⣋⢽⠀⠀⠀⠀⠀⠀⠀⣾⢡⣿⢘⣿⠉⣿⡆⢿⣧⠹⣇⠀⠀⢀⣼⠏⣼⡟⣰⣿⠁⣿⡐⣿⠆⣿⠁⠀⠀⠀⠀⠀⠀⣿⢸⡷⡏⢼
⣿⢸⣿⡅⢺⠀⠀⠀⠀⠀⠀⠀⣿⢰⣿⢨⣿⠀⠘⣿⡌⣿⣧⢹⣷⠀⣼⡏⣼⣿⢱⣿⠃⠀⣽⠂⣿⠃⣿⡆⠀⠀⠀⠀⠀⠀⣿⢰⢻⡍⢺
⣿⡸⣿⡱⢼⠀⠀⠀⠀⠀⠀⠀⡿⢐⣿⠈⣿⠀⠀⠹⣷⡘⡿⣆⢻⣷⡟⣴⣿⢃⣾⠆⠀⠀⣻⡌⣿⡃⣿⠃⠀⠀⠀⠀⠀⠀⣟⢈⠲⡇⢾
⣿⡱⣿⡅⡻⠤⠤⠤⠀⠠⠤⠤⣟⠀⡿⠀⣿⠀⠀⠀⠉⣵⠘⡝⡀⠻⣘⣿⢃⣾⠏⠀⠀⠀⣸⠆⣿⡅⣿⠦⠤⠤⠠⠤⠄⠠⢯⠀⡓⡇⢼
⠿⣸⣿⣦⣵⣮⣴⣵⣮⣵⣮⣶⣥⣄⢻⢀⣿⠀⠀⠀⠀⢸⣧⠨⣽⣤⣿⠇⣞⡟⠀⠀⠀⠀⣽⢃⣿⣦⣶⣭⣤⠆⠥⠢⠔⡠⠤⠰⣍⡇⢸
⠰⣧⣩⢭⣩⣍⣭⣩⣍⣭⣭⣬⣭⣍⣭⠒⠿⠀⠀⠀⠀⠀⠹⣧⠹⣿⠏⣼⠏⠀⠀⠀⠀⠀⠛⠮⠭⣭⡭⣭⣭⣩⢍⣩⣌⣡⣉⢤⠌⡼⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣫⣞⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣉⣉⢳⡄⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⣠⣤⣤⣤⡀⠀⠀⠀⠀⢀⣴⣋⣉⣹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣉⣻⡏⢿⣿⣷⣾⣿⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣾⣿⣿⣟⣿⣏⣿⡟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡉⣷⠈⠛⣻⡿⢿⣿⢻⠟⣻⣿⣻⢿⣿⣿⣿⣻⣿⡋⠛⢿⢿⣿⣏⠻⣼⢿⡏⣻⣿⣇⣀⣠⡤⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣶⣾⠿⣿⠏⢀⣀⡴⢾⣿⣴⠛⣿⡎⢰⢻⠟⠉⣼⣇⣿⢿⠙⣿⠀⠀⣸⣟⠀⢻⣶⣟⣼⡷⣿⣹⡿⣿⣿⡟⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢿⣿⣤⣿⣿⣤⣝⡷⠿⠕⢀⡄⠻⠛⣟⠙⣿⠘⣿⠀⠀⠿⣿⣿⣸⠀⢸⠆⢰⡟⢙⣷⠋⡼⣹⡟⣷⢾⣿⣤⣬⣿⣥⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣈⣹⣿⣶⣾⣟⢛⣳⢶⣤⠀⠰⠋⢠⠅⢈⣿⣾⣿⣆⠸⣇⢿⣆⢿⠏⢧⢆⡏⢀⣾⣧⣼⠃⢸⣣⠏⡠⡏⢿⣴⠾⣻⡿⣿⣷⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣤⣶⠛⠋⠙⢧⣔⠲⢭⣙⢮⣧⡹⣷⠏⣴⢋⣴⣿⣧⣿⣿⣿⣷⣽⣎⢿⣘⠀⠀⡾⣷⣿⣿⣿⣷⣤⣼⣿⢰⡗⢣⡿⢡⣿⠟⠛⠻⣟⠳⢬⣉⡛⣿⠟⣷⣤⡀⠀⠀
⠀⠀⢠⣾⣯⡤⠞⣁⠴⢦⡀⢩⣿⣷⣹⣧⣿⣧⣿⣴⣏⣘⡿⠿⠿⠿⢿⣿⣿⣧⣿⣾⣿⣿⣾⣧⣿⣿⣿⣿⡿⣿⣿⣿⣐⣿⣾⣧⣿⣧⠀⣾⡇⢹⡶⢲⢨⡟⠻⣿⡿⠟⣿⡆⠀
⠀⢠⣿⠟⣋⡽⣛⠲⠶⣿⣷⣿⣿⣿⣿⣿⣿⣯⣛⣛⠛⠻⠿⢷⣿⣿⣾⣿⣯⣿⣻⣿⣯⣿⡏⣽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣿⣫⣿⣿⣾⣿⣴⣿⣷⣿⣿⣾⣄⣛⠻⢯⣻⣧⠀
⢀⣿⡷⣫⣵⠞⢡⡶⣋⡉⣡⣼⠛⢁⣤⡿⡏⢻⣿⣿⣿⣿⣷⣶⣮⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣹⣿⣿⣿⣿⣿⣿⣿⠿⠯⢤⣼⡏⠩⡓⣺⠿⣿⣭⡙⢯⣶⣌⣻⣆
⣿⣿⢻⣿⢋⡴⢋⡴⢿⠛⢻⣏⣠⣞⣡⠇⠙⢦⡙⠻⣿⣿⣿⣿⣿⣿⡄⠙⢿⣏⠻⠿⠟⠿⠿⢋⣿⠟⢀⣼⣿⣿⣿⣿⣟⡿⠛⠁⣀⡴⣦⠈⠿⣗⠀⠈⠻⣬⢿⣿⣌⢻⣎⡟⣿
⣿⣿⣿⣇⣿⢡⡏⣰⢏⡾⠋⡼⠁⢸⡙⢓⣶⣤⣹⣷⣿⣿⣿⣿⣿⣿⣿⣄⠸⣿⣿⣦⡀⣠⣾⣿⣿⢒⢻⣿⣿⣿⣿⣿⣿⣷⣴⡾⢋⣼⠃⢦⠳⡜⢧⡘⢦⡹⡾⣇⢻⡟⣿⣧⣹
⣿⣿⣿⣿⣿⡿⣰⣿⠏⢀⡞⢁⡾⠀⢻⣀⣈⢹⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣧⣿⣿⣿⣷⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣻⡇⣸⠃⣆⠸⣦⠙⢦⡙⢮⡙⢿⢹⡼⣿⣾⣿⡿
⠛⢿⣿⣿⣿⣿⣿⢁⣾⠟⠀⣼⣿⠀⣸⠿⣿⡎⣿⣿⣿⣿⣤⣽⠟⣿⢿⣿⣿⡻⣿⣿⣿⣿⣿⢟⣿⣿⡿⣿⣿⣿⣼⣿⣿⣿⡿⠿⢣⡾⢁⡇⢿⣷⡌⢷⡌⢿⣾⢀⣷⣿⣿⡟⠁
⠀⠀⠙⣿⣿⣿⣿⣿⣿⣮⣼⣿⣿⠀⣿⡄⣹⣷⠻⣾⢋⣴⠋⢡⣼⣿⣷⣿⠙⣿⣾⣏⠁⢿⣧⡿⠏⣿⣿⣟⣿⣷⣿⡆⠻⣭⣿⣤⣿⢁⣴⡇⣸⣿⣿⣜⣿⣼⣿⣼⣭⣿⡿⠁⠀
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣷⣿⣿⡇⢁⣾⣿⣷⡿⠿⣷⣿⣿⣤⡈⣻⣙⣧⣾⢁⢶⣠⣿⣿⣿⣿⣿⣿⣿⣀⠹⠏⣽⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣷⣿⡿⠁⠀⠀
⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⣹⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣽⣿⡿⣿⣟⠉⣹⣷⣿⣛⣿⣾⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣋⣽⣿⡉⠉⠛⠛⠛⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⠛⠛⠉⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠈⠙⠛⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢻⣿⣿⡇⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠁⠀⣿⣿⣟⢛⣿⣿⡿⠀⠀⠀⠀⠀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⣬⣭⣽⣿⣿⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣳⡀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠘⣿⣿⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇⠘⠿⣿⣿⣷⣄⠀⢀⣠⣴⣶⢿⣿⣿⣿⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⠀⠿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⡿⠉⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⣾⠇⠿⣷⣿⣦⠀⠀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡀⠀⠉⢻⣿⣿⣿⠟⠻⡿⠛⢋⠀⠀⣼⣿⣿⣦⣄⣀⣀⣠⣤⣶⣿⣿⠀⠀⣿⣿⣿⣧⣿⣿⣷⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠘⠛⠁⠀⠀⠀⢀⠈⠀⠀⢻⣿⠟⠀⠹⣿⣿⣿⣿⣿⣿⠛⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⢿⡔⠆⠀⡀⠀⠀⠸⠿⢃⡀⠀⢀⣿⣿⣿⣿⠿⠏⣤⠖⠀⠈⠹⠏⢉⣿⣿⡿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⠀⠀⠀⠈⠻⣶⣸⡇⠀⠀⣾⣿⡟⠓⠶⠋⠉⠉⢉⣁⣤⠞⠉⠀⠀⠐⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣼⣿⣽⣶⡾⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢋⠀⣠⣾⠋⠈⢿⣆⠀⠀⢠⣞⠋⠀⠀⣠⣶⠀⠀⠀⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤⣴⣿⢿⣿⠈⢻⣶⡿⣿⣗⣦⣾⣿⣧⠄⠀⣄⣹⣷⣦⣄⣿⠿⣶⠞⠉⣿⡀⠀⠀⠀⢙⣿⠀⠀⢠⡄⠀⠀⠀
⠀⠀⠀⢀⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⠀⠀⢸⠀⣿⣿⢹⣿⢻⡏⠀⠀⢹⡿⢹⡏⣿⣿⠀⡇⠀⠀⣿⣷⣦⠀⢰⣾⣿⣀⣀⣾⡇⠀⠀⠀
⠀⠀⠀⣼⣿⣿⣿⠀⠙⣫⣿⣿⣿⣿⠀⢰⣿⠀⣿⡟⢸⣿⢸⣿⠀⠀⣿⡇⢸⡇⠛⣿⠀⣿⡆⠀⣿⣿⣿⣷⣼⣿⣿⠟⣿⡿⠃⠀⠀⠀
⠀⠀⠀⣿⣿⣿⠛⢠⣼⣿⣿⣿⣿⡿⠀⣸⡟⠀⣿⡇⣿⡇⢸⣿⡄⢠⣿⡇⢸⣿⠀⣿⡀⢸⣧⠀⠿⠿⣿⣿⣿⣷⣄⠀⣿⣧⠀⠀⠀⠀
⠀⠀⠈⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠁⢸⣿⠇⢀⣿⣀⣿⣇⣸⣿⣿⣿⣿⣇⣘⣿⣄⣿⡇⠘⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⡇⠀⣿⣿⣿⣽⣿⣿⣿⣟⢻⣿⣿⣿⣏⣿⣿⣿⡀⢸⣿⡀⠹⣷⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⣿⡟⢻⣟⢻⡿⢀⣼⡟⠁⣼⣿⠁⢀⣿⣽⣿⡟⣿⣿⢻⣿⣯⣽⣄⠛⣿⣧⡀⢹⣷⡀⠻⡜⢻⡟⠛⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣴⣿⣿⣿⣼⣦⣾⣿⠀⢸⡇⣹⣿⣿⠹⡇⢹⡇⣿⣿⢸⣿⢻⠏⣿⣿⣿⢸⡇⠀⣿⣿⣄⣧⣼⣿⣿⣤⣿⡇⠀⠀⠀⠀
⠀⠀⠀⢰⣾⡟⠛⠀⠀⠸⠿⣿⣿⠃⠀⢸⣿⡿⠿⠿⣄⣠⡎⢻⡿⢻⡿⢹⣆⣠⡿⠿⠿⣿⡇⠀⠉⣿⣿⠿⠇⠀⠀⠛⢻⣷⡆⠀⠀⠀
⠀⠀⢀⣸⡟⠁⠀⠀⠀⠀⠀⣼⣿⡀⠀⣸⡟⠀⠀⠀⣹⣿⣇⣼⠁⠀⣧⢸⣿⣿⡄⠀⠀⢹⣧⡀⠀⣿⣧⠀⠀⠀⠀⠀⠌⢻⣇⡀⠀⠀
⠀⢠⣼⡿⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣼⡏⠀⠀⠀⠀⣿⣿⣿⣿⡄⢠⣿⣾⣿⣿⠀⠀⠀⠀⠹⣷⣾⣿⣿⣷⣦⠀⠀⠀⠀⠀⢿⣧⡄⠀
⠀⣸⣿⡀⠀⠁⠁⠀⣤⣿⣿⣿⣤⣿⣷⣤⣤⣄⣀⣀⣸⣿⣿⣿⣷⣿⣿⣿⣿⣇⣀⣀⣀⣀⣤⣾⣿⣤⣿⣿⣿⣤⠀⠀⠐⠀⠀⣿⣇⠀
⠀⡿⠋⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⢋⣉⡉⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⢉⣉⠙⣿⣿⣿⣿⣿⣿⣖⣀⠀⠀⠀⠙⢿⠀
⣾⣿⣦⣤⣤⣶⣿⡟⣿⣿⣿⣿⣿⠏⡀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⠀⠉⢀⠹⣿⣿⣿⣿⣿⢻⣿⣶⣤⣤⣴⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢿⡆⣰⡋⣿⣿⣿⣿⡟⣻⣿⣿⣟⢻⣿⣿⣿⣷⢉⡆⢰⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣰⣿⣿⣿⣿⣿⡟⢹⣿⡿⠋⠙⢿⣿⡏⢻⣿⣿⣿⣿⣿⣄⠀⢾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣍⣁⠰⣿⣿⣿⣿⣿⣿⣷⣼⣿⣧⣀⣀⣼⣿⣧⣾⣿⣿⣿⣿⣿⣿⠆⣈⣩⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀
⠀⢸⣿⣿⣿⠁⢻⣿⢸⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣟⢻⡯⠀⠀⢸⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡟⠈⣿⣿⣿⡇⠀
⠀⠈⢻⣿⣿⡀⢸⣿⠘⣾⣿⣿⣿⣿⣏⢻⣿⣿⣿⣿⡋⠁⡀⠀⠀⠀⠀⢀⠀⢙⣿⣿⣿⣿⡟⣹⣿⣿⣿⣿⠇⠀⣿⡇⢀⣿⣿⡟⠁⠀
⠀⠀⠸⢿⣿⣧⠈⣿⡀⠈⢿⣿⣿⣿⣿⣆⢹⣿⢿⣿⣿⣧⣄⣠⣀⣀⣀⣉⣼⣿⣿⡿⣿⣏⣰⣿⣿⣿⣿⠇⠀⢀⣿⠁⣼⣿⡿⠇⠀⠀
⠀⠀⠀⢸⣿⣿⠀⣿⡇⠀⠀⠙⢿⣿⣿⣿⣇⣿⣧⡀⠀⠉⠛⠛⠛⠉⠛⠛⠋⠉⠀⣴⣿⣸⣿⣿⣿⠛⠁⠀⠀⢸⣿⠀⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡄⢹⡇⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢸⡏⢠⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣿⣇⠀⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢸⠀⣸⣿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⣿⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⣣⠀⠀⠀⠀⠀⠀⢘⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀


⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⣜⡳⢟⡜⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠉⠉⠉⠓⠋⠀⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⡘⠷⠏⡔⠒⠒⠒⠒⢲⢾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣠⣄⡠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢸⢹⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡖⠲⣶⣶⣶⣬⣽⡹⡀⣉⠬⠛⠂⢤⣀⣙⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣸⣵⢯⡯⢯⣿⣅⢹⠁⠀⠀⠀⢄⠁⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣆⢘⡻⠗⡇⢣⠄⢻⣟⣻⡂⡀⠀⠀⡄⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢬⠻⡻⣾⣧⣾⢯⣭⣿⠡⠀⠀⠧⠬⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢳⢛⠙⡶⡇⣯⣵⠿⠛⠁⢀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠓⢶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⡟⣧⣡⡿⠟⠁⢀⣤⣤⣴⣥⣶⣤⣤⣤⣶⣤⣤⣵⣢⢄⠈⠻⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⣻⡞⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣕⡄⠀⠉⠳⣯⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠁⢐⣾⣿⣿⣿⣿⡿⠛⠛⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡼⡄⠀⠀⠸⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢯⣼⣡⡦⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣸⣿⡇⢻⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⢿⠘⠯⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢞⣬⡟⠌⢻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠈⣿⡏⠀⣼⣿⠛⠛⢹⣿⣷⡇⠀⠀⠀⣸⡯⣄⣈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡎⠉⠀⣠⠇⢴⣮⣿⠿⢷⠔⢺⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠙⠁⢸⣿⠁⠀⠀⢸⣿⣿⠞⠀⠀⢰⡿⠡⣿⡆⠀⠁⠸⣴⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡛⠐⢊⣅⣼⣜⣿⣵⣾⡗⠀⣼⡿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⣾⣿⣿⡀⡄⠀⣸⡇⠀⢿⠉⡎⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀
⠶⠶⠶⠦⢷⡾⠟⢹⠁⢿⢩⠄⣾⣿⣷⠀⣿⣷⣿⣿⣷⣦⣆⠀⠀⠀⠀⠸⣿⣿⡯⠾⢿⠆⠄⠀⠀⢿⡇⡇⠀⣿⠂⠀⢸⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣴⠚⠉⠀⠸⡾⡄⣿⢸⢸⣿⣿⣿⠀⡏⢟⣯⣬⣿⣿⣿⣷⡄⠀⠀⣾⣿⣿⣶⣷⣶⣤⣄⠀⠀⢸⡧⠆⠀⣿⡀⠀⢸⠀⡇⠀⠀⡇⡄⠀⠀⠀⠀⠀⠀
⠈⠁⠀⠀⠀⠀⠀⠡⠇⣿⣼⢸⢹⣿⣿⠄⣷⣿⣿⣿⣿⣬⣿⣿⠃⠀⠈⠫⣿⣿⣿⣧⣼⠟⠉⠃⠀⠈⡗⢢⠀⣿⡇⠀⣸⠀⡇⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣊⣿⢸⣿⣿⡆⡟⠀⠉⠉⠉⠰⠋⠀⠀⠀⠀⠀⠈⠲⠌⠉⠁⠀⠀⠀⠀⠀⡇⢈⠀⢹⣿⣿⣿⠢⠟⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⢆⠀⠀⠀⠐⢸⡏⣿⢸⣿⣿⡇⣗⠀⠀⠀⠀⢠⠂⠀⡄⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣽⠀⠸⣿⣿⣿⣦⢀⣾⡋⠑⠢⣄⡀⠀⠀⠀⠀
⠀⠀⠀⢠⠀⡇⠀⠀⢀⠘⣿⣏⢸⣿⣿⣧⢸⡀⠀⠀⣤⣥⣶⣤⣬⣭⣶⣦⣼⠧⠀⠀⠀⠀⠀⠀⠀⢠⡗⣷⠀⠀⣿⡿⠿⠿⠞⢹⣧⡀⠀⡀⠉⠲⣶⡤⠤
⠀⠀⠀⢸⠀⡇⠀⣠⡎⡇⢻⣿⣦⣿⣿⣿⡆⣿⠀⠀⠀⣹⣿⣿⢿⣯⣤⡍⣁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣳⠀⠀⠈⡇⠀⠀⠀⠈⡟⠗⣜⠀⠁⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠷⠋⠊⢂⠼⠻⠟⣛⡯⠭⠟⠷⣜⡆⢰⣿⣻⠋⣘⣟⡙⠿⣷⣮⠳⢆⠀⠀⠀⠀⠀⠀⣼⢸⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠈⢆⠀⠀⠀⠀⠀
⠀⠀⠀⢰⢀⣇⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠙⣿⡌⠿⢏⣹⠛⠛⠛⢭⣩⣿⣿⡞⣀⠀⠀⢀⣠⣾⡟⣼⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀
⠀⠀⣀⠘⣝⣽⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠨⣷⣴⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⡏⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀
⠀⠀⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣰⠏⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠁⠀⠀
⠀⠀⢀⠐⠕⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡸⠏⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⠀⠀⡄⠥⣄⢠⢏⡂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⣛⢿⣿⣿⡿⡿⠿⠿⡛⢛⣭⢔⡉⠄⠀⠀⠀⠀⠀⠀⠀⠈⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣗⠀⠈⢣⡉⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠛⠾⠶⣾⠷⠷⠶⠛⠋⠉⠉⠀⣃⡄⠀⠀⠀⠀⠀⠀⠀⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⡄⠀⠀⢳⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠂⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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