⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⣀⡠⠤⠒⠒⠒⠒⠂⠀⠉⠉⠁⠈⠉⠀⠈⠉⠉⠉⠉⠉⠙⠒⠲⠬⠿⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠔⠁⠀⠀⠈⠀⣀⣀⢀⣀⣠⣤⣤⡄⠀⠒⠒⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⢀⣀⠲⠞⠛⠋⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠤⠀⠀⠀⠀⠀⠀⠀⠙⢢⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⠔⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⣄⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠎⠀⣀⣀⠀⠤⠤⠔⠒⠒⠶⠶⠶⠶⠿⠿⣛⣛⡛⠒⠒⠒⠒⠒⠲⠲⠤⠤⠄⣀⣀⡀⠀⠀⠒⠤⢀⡑⣆⠀⠸⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠒⠉⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠶⠲⠶⠭⣿⣿⣿⣿⣿⣶⣴⣖⣢⣤⣤⣀⠀⠀⠀⠈⠀⠀⠠⡀⠀⠉⠺⢧⡀⢣⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠒⠢⢄⣀⠀⠀⠈⢢⠀⠀⠈⠳⡸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⣤⠾⠗⠉⠉⠀⠀⠀⠀⣀⡀⠤⢤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠖⣶⣤⣀⡈⠑⠢⡀⠀⢱⡀⠀⠀⠹⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠉⠁⠀⠀⠀⣀⠤⠖⠊⠹⠁⠀⠀⢾⣿⣿⣿⣿⣿⠿⣟⣿⣿⡿⢿⣦⣌⣳⡀⠀⠀⠀⢹⣿⣿⣷⣦⣌⣢⠀⢿⡀⠀⠀⢹⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣤⡶⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠟⢻⡇⢰⢫⣿⣿⣿⡆⠙⣿⣿⢿⣄⣀⣴⣿⣿⣿⣿⣿⢿⣿⣧⡸⣷⠀⠀⠀⢧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣴⠎⠰⣽⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⡏⠀⠀⠀⠻⡸⣶⡉⢹⡿⠃⢀⣿⠙⢆⣽⣿⣿⣿⣿⣿⡿⠃⣼⣿⣿⣷⣿⡆⠀⠀⣸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⢼⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⠾⣭⣀⣀⠀⠈⢀⣠⣼⣿⣿⣿⣿⡿⣿⣿⣋⣿⣿⣿⣿⣿⠃⣠⠖⠋⠀⠀⠀⠀
⠀⠀⠀⣀⣠⣤⠾⣿⣿⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣷⣿⣿⣿⣿⣿⠜⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⡟⣿⣿⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⠿⠛⠋⠁⢽⠏⢹⠏⠀⡼⢫⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡿⠀⢻⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢸⣤⣤⠴⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢈⠢⢅⡀⠜⢡⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⢀⣴⠞⠉⠉⠉⠉⠉⠙⠺⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⠛⠀⣠⣾⣿⣿⣿⣿⣿⣿⡏⣿⡟⡄⠀⠀⠀⠀⠀⠀
⢤⠤⣄⣀⣀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠳⣀⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⠀⣣⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠐⠚⠛⣹⣿⣿⣿⣿⣿⡿⠁⣿⡇⠘⣄⠀⠀⠀⠀⠀
⣾⣿⠶⣿⣽⣿⣿⣶⣶⣤⣀⢻⣷⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠻⢍⠀⠈⢹⠟⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠃⢸⣿⡇⠀⠈⢳⡀⠀⠀⠀
⠀⠉⠙⠺⣿⣿⣿⣿⣶⣮⣍⡛⠻⣷⣦⣤⡄⠀⠀⠀⠀⠀⡀⡀⣠⣤⣄⣿⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⠟⠁⠀⢸⣿⠀⠀⠀⠀⠉⠢⡄⠀
⠀⠀⠀⠀⠀⠁⠉⠻⣻⢿⢿⣿⣶⣌⡛⠿⣿⣦⣲⣗⣶⣶⣽⣪⢾⡿⠿⣜⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠫⡻⣝⢷⡄⠀⠈⠓⢿⡳⠿⠭⠖⠁⠀⠀⠘⢿⣄⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⢿⡄⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠻⡝⠲⠶⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⡿⠛⠟⢁⣿⣿⢯⣧⢻⣿⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⣸⠃⠀⠈⠁⠀⠀⠞⠉⠁⠀⠱⢏⢾⣷⡅⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠈⠢⡀⠀⢀⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣝⢾⣢⣮⣂⠀⠀⠀⢄⣀⣀⡢⠄⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠈⠢⣈⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠽⣿⣧⡢⡘⢷⣽⣽⣺⠖⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠙⠛⠓⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠛⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀