⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⢤⣄⣒⣒⣲⣶⣶⣶⣶⣶⣒⣒⣢⣤⠤⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣡⠞⠋⣿⠨⣏⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⢸⡏⠛⢮⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡟⠀⠀⣿⡄⢿⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣾⡇⠀⠈⣧⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⣹⡇⢸⣇⠀⠀⠀⠀⠀⠀⢀⡿⠀⣿⡇⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⣿⣇⠀⢿⡀⠀⠀⠀⠀⠀⣼⡇⢸⣿⠁⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⡇⠀⠀⢹⣿⡀⠸⣧⡀⠀⠀⠀⣰⡟⠀⣼⣿⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⢸⣿⣷⣄⠙⠫⠭⠯⠭⠛⣁⣼⣿⡿⠀⠀⠀⡏⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧⠀⠀⠸⣿⣿⣿⣿⡷⠺⠿⠲⣿⣿⣿⣿⡇⠀⠀⢸⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⡆⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⣼⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⣤⣿⣿⣿⣧⣤⣤⣤⣤⣤⣿⣿⣿⣧⣴⣼⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢻⣿⡟⠃⠛⣿⣿⠟⣠⣾⣿⠟⠻⢿⣷⣄⠛⣿⣿⣿⣄⠛⣿⡟⠛⢻⣿⡿⠿⠿⣷⣦⠀⠘⣻⡿⣿⣷⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡟⠛⠛⣿⣿⠀⣿⣿⣇⠀⠀⢸⣿⣿⠀⣿⡟⢻⣿⣧⣿⡇⠀⢸⣿⡇⠀⢀⣿⣿⠇⣼⣿⣷⣿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠰⠾⠿⠷⠂⠲⠿⠿⠷⠈⠛⠻⠷⠾⠿⠛⠁⠶⠿⠷⠀⠛⠿⠿⠃⠰⠾⠿⠿⠿⠟⠛⠛⠾⠿⠗⠀⠰⠾⠿⠿⠖⠀