⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⡿⠿⠟⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⢿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠤⣀⠀⠀⠒⠀⡀⠉⠙⠛⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⡀⠈⠐⢄⠀⠀⠀⠙⡻⣿⣷⣦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠑⡀⠀⠀⠐⠄⠙⠿⣿⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠈⢢⠀⠘⣀⣀⡀⠈⢂⠀⠹⢻⣿⣦⡀⠀
⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠢⡀⠀⢠⣖⣪⠭⢗⣺⠉⠉⡏⢦⠱⣉⢛⡄⠀⣆⡙⣿⣷⡀
⠀⠀⢠⣾⣟⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⣈⠤⢲⣩⡷⠐⢸⠡⢆⡙⢢⠃⠀⣜⣘⣦⣷⣬⣾⣁⡀⢇⠎⡽⣿⣷
⠀⣰⣿⡟⢬⡑⢢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠊⣠⠔⡩⣦⠝⡫⢅⡇⠀⢸⠑⡎⢜⣏⣤⣾⠿⠟⠛⠛⠛⢿⣿⢿⣿⣾⣶⣿⣿
⣰⣿⡟⡜⢢⠹⢆⣣⢚⣩⣒⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡠⢝⠢⡀⡨⢗⠫⡔⣩⢒⡡⠇⠀⡮⢱⣼⣿⡿⠋⠁⠀⣀⠀⠤⠀⣸⡿⠀⠀⠉⠉⠉
⣿⣿⡹⢌⣱⠞⠉⠁⠉⠐⠠⢤⣀⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⠤⡔⣊⢧⡱⢞⠫⢵⠀⢸⠱⡘⢤⠣⢼⠀⢀⣷⣿⠟⠉⢀⠄⠂⡁⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀
⠹⣿⣷⢨⠂⠀⡠⡒⢭⣉⠓⣆⠲⡌⡝⣩⢛⡛⢳⠲⠶⠶⠦⢤⠤⣀⡀⠈⠑⡜⡩⢆⠳⡌⢳⢸⠀⢸⢡⡙⢢⢍⣦⣶⡿⠛⢁⠄⠊⠀⠀⠀⠈⠂⠄⠀⠀⢸⣿⠀⠀
⠀⢘⣿⣷⣤⣰⠱⣉⠦⢌⡓⣌⠲⢱⡘⢤⠣⢜⡡⢣⡙⣌⠣⣍⠲⣡⠚⡆⠀⠸⣑⠪⡱⢌⡃⢞⠀⡜⣢⣱⣿⡿⠟⢉⠠⠂⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣿⡋⠀⠀
⠀⣼⣿⠉⡛⠿⣿⣶⣥⣎⡔⢢⠙⡆⡜⢢⡙⢢⠱⣡⠚⠤⡓⢤⠓⡤⢓⢼⠀⠀⣇⢣⡑⣎⣼⣾⣴⡿⠿⠛⣁⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⣿⡇⠀⠀⠀
⠀⢻⣿⡄⠀⠁⠂⠬⢙⠻⠿⢿⣾⣶⣧⣥⣮⣥⣳⣤⣙⣢⣙⣢⣍⣴⣭⣾⣤⣶⣷⣿⠿⠟⠛⠉⢁⠠⠂⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠚⠈⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀
⠀⣿⡿⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠩⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠠⠄⠒⠈⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⢆⠀⠀⠀⠀⠀⢠⠀⢠⣿⠃⠀⠀⠀⠀⠀
⠀⢿⣿⡀⠀⢀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠠⠂⠀⠀⠀⠈⢆⢀⢰⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⣼⣿⠁⠀⠘⣿⣿⣿⠇⠀⡤⠀⠀⠀⠀⠀⡀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⣰⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠛⠖⠛⠻⣶⣴⠇⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⢿⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠿⢿⣷⣤⣤⣤⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⣿⣿⣷⣶⣤⣤⣶⣤⣀⣠⣄⡀⠀⠀⠀⡀⠀⠀⠀⢀⣤⣶⣶⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠛⠻⠿⠻⠿⣿⣶⣿⠿⢷⣶⣿⡿⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀