⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡂⠁⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢀⠌⣦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠱⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢀⢀⣿⣿⢹⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢰⣿⣿⣿⠀⢻⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⣼⣿⣿⣿⠀⠸⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠈⡉⠣⡿⣿⠀⠀⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣔⣒⣒⡒⣛⣿⣿⣾⣿⣇⠀⢹⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠯⠒⠒⠲⠯⣽⣿⣿⣿⢹⠀⢺⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠉⠀⠀⠛⣻⡛⠿⣿⡤⠹⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢡⣂⣠⣤⣤⣀⣀⡀⠀⠠⠽⣅⠈⢻⣮⢿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣔⣵⣾⣿⣿⣿⡏⠙⣿⡏⠈⣿⣷⣦⣇⡂⠀⠉⣟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠛⠛⠛⠋⠉⠹⣿⣷⣶⣿⣷⣴⣿⣿⣿⣿⣿⡿⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⡻⣿⣿⣿⡿⢟⡵⣿⣻⣿⣷⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢰⡁⣿⣿⣿⡡⡎⠵⢿⣿⡿⣿⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⣾⢛⣯⣹⣷⣠⠶⢿⣿⡿⠉⠛⡅⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠀⠠⠊⠠⣹⠅⠈⢁⣺⣿⠀⠉⠁⠀⣼⣿⣷⠀⠀⠺⢄⢀⠀⠀⠀
⠀⠀⡞⠳⢦⡢⠀⠈⢲⠟⠀⠀⣼⣿⣿⡆⠀⠀⠀⠘⣯⣿⣓⠵⠛⠋⢹⡆⣼⣦
⠀⢰⠁⠀⠀⠈⠣⣲⡏⠀⠀⣼⣿⣿⣄⣑⠀⠀⠀⠀⣳⠟⠁⠀⠀⠀⣸⣷⣻⡿
⢠⠇⠀⠀⠀⠀⠀⡸⠁⠀⣵⣿⣙⣛⣋⣽⡄⠀⠀⠀⠸⡀⠀⠀⠀⠀⠹⣿⣿⡇
⠸⣶⣄⣤⣀⢀⣸⠆⠀⣰⣿⠠⠁⠉⠁⠠⢳⡀⠀⢘⣤⡇⣀⣀⣀⣀⣀⡀⣽⣧
⠀⣾⣿⣿⢿⣿⣯⢀⣰⣾⣧⠁⠀⠀⠀⠀⠀⠫⢄⡀⢞⣿⣿⣿⣿⣻⣿⣿⣿⠟
⠀⠸⣿⣷⣹⠫⢿⣿⣿⣯⡤⢀⠀⠀⢀⢠⡦⠬⢿⢾⠛⠿⢿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠈⠛⠛⠀⠈⢼⣿⣿⢋⣵⣾⣿⣾⣷⣞⣆⡀⢉⡀⠀⢨⣿⣿⣿⣿⠟⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣻⣼⣿⡿⣿⣿⡿⣿⣿⣷⣮⢇⣀⣸⣿⣿⠟⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣏⡿⣿⣿⡿⣽⣷⣷⣀⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠉⠑⠻⣿⣿⣿⣿⣿⡿⠋⠭⠭⢬⣽⣿⣿⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣾⣶⣿⣿⣿⣿⣿⣥⣤⡴⣴⣞⣿⣿⣿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠐⠋⠛⠛⠋⠀⠀⠹⠿⢿⣟⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀