⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⠉⠉⠑⠒⠢⠶⣿⣿⣿⣿⣿⣏⣭⣴⣾⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠄⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣇⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠚⠛⣯⡼⡷⠦⣄⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢍⡉⠉⠉⠒⠄⠈⠙⠿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠑⠒⡄
⠀⠀⢀⣾⠀⠘⣆⣤⠝⢠⣞⣿⣀⣷⠞⠃⣀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠄⠀⡸⠀⠀⠀⠈⠻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠴⣋⣼⢷⠋⠙⣦⣠⠌⠉⣩⣼⢿⡖⠋⠉⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠤⠐⠒⠁⠀⠈⠀⠀⠀⠀⠈⠁⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀
⠀⠚⠉⣠⠾⣿⢀⡼⢧⠀⠀⠀⠽⠟⠓⠛⠁⠀⠀⠀⠀⠀⠙⢆⠀⠀⢀⠖⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠲⡀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀
⠀⠀⠰⣇⣀⡿⠀⠀⠈⠀⠀⠀⠀⢀⣀⣤⢹⣌⡓⠂⠀⠀⠀⠀⠀⣠⠃⠀⠀⢀⣴⠁⠀⡇⠀⠀⡆⢀⡠⠼⢲⣆⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢷⠠⣄⠈⢩⣥⢹⣴⣋⡀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⣮⣄⣑⡒⠙⢞⠀⡯⣥⣶⠚⠛⠁⣙⢂⡀⠀⠀⠀⠏⢄⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠰⢖⡚⠘⠧⠺⣧⠄⠀⠀⠋⣨⢿⣟⣿⡆⠀⠀⠀⢠⠁⣠⡎⠙⡾⣤⠾⠛⠁⠀⢀⡉⠀⠀⠉⠙⠛⠛⣀⠀⢸⠆⠀⠀⢀⠈⣣⠀⣀⠜⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⣉⢴⣷⣾⣿⣀⠀⠀⠘⠿⠭⠷⢞⣁⡤⠀⠀⠰⠞⢹⠑⢰⠃⠀⠀⢀⠔⠯⠭⠭⠕⠢⡀⠀⠀⠀⠈⡯⠁⠀⠀⠀⢸⠀⠀⠀⠥⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⣼⠿⢿⣏⡽⢁⡀⠀⡤⠖⠛⠉⠁⠀⠀⠀⠀⢸⢸⠀⢸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢰⠤⠤⠴⠊⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣈⣉⡽⠿⠓⠉⠁⠀⠀⢀⡖⠀⣼⠁⢰⠆⠀⡸⢸⠀⠸⡀⠀⠀⠰⣄⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⡇⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠇⠀⡞⠀⠀⡇⠘⠀⠀⠳⡀⠀⠀⠀⠉⠑⠂⠋⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠃⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠴⠀⢠⠀⠀⠀⡇⠀⡆⠀⠀⠈⠑⡢⣤⣀⠀⢀⣤⣴⣶⣶⣶⣶⡎⠀⠀⠀⠠⠏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⢠⠓⢠⣠⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⢀⣠⠀⣠⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠈⣻⣿⣿⣿⡿⠿⠿⠛⢛⣿⣿⣷⣯⣜⡚⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣠⣴⣾⣿⣿⣿⣿⠟⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢈⢿⣯⣿⣿⣿⡿⠋⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠳⡀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⣌⣉⣛⣿⣁⣀⣀⣀⣀⣀⣀⣀⣻⣿⣿⣿⣿⣟⣫⠅⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀