⣿⡿⣟⣾⡿⡯⠍⣿⡏⢿⢿⡿⡼⣻⢹⣴⠿⠿⣿⢿⡗⢋⢿⣿⣿
⣿⡫⢽⡝⣿⡛⡷⠈⢠⠞⡿⢿⠃⡌⡏⡗⡌⣉⢞⠳⠓⡚⣻⢿⣽
⣿⣣⡜⠳⠿⢳⠹⠁⣈⣍⣅⢏⢮⢱⣞⠱⡼⠈⣷⣿⡕⢌⢳⢾⣯
⣟⡿⣄⣘⣜⣿⠠⡀⣻⣿⣄⡜⠼⣼⣿⣄⢻⠇⢿⡇⣧⠛⢛⠘⢣
⡯⡫⣪⠞⠺⣏⢸⡿⢟⣙⢿⣮⣳⣿⣨⣬⣭⡅⡸⢀⢺⢈⠢⢍⠻
⣴⡉⢅⢸⠇⠚⡦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⢃⣸⡄⠘⣍⡎⣿
⡿⡴⣾⢈⢨⠐⠘⢹⣿⣿⣿⢟⠻⣛⢻⣿⣿⡞⣄⡿⡅⣼⣔⣽⣿
⣿⣾⣻⣛⡆⠏⡀⢀⠛⢿⣿⣎⡟⢭⣽⡿⠋⢀⡾⣱⠇⠻⠿⠤⣿
⣿⠯⠕⡿⣇⡃⠀⠀⠀⠀⠈⣩⣿⣟⡧⢀⢠⠾⡵⠋⠄⠀⠐⠄⠈
⣿⡟⠀⢣⠙⡆⠐⢠⠀⣤⢻⣷⣾⣯⡞⠀⠈⡎⠂⠊⡄⢢⠀⠚⠀
⣿⡆⠀⠈⢎⠘⣆⠁⢆⠙⣿⣏⡿⣽⣙⣯⡬⠐⡄⠢⣑⠴⢋⠡⠀
⣿⣷⡀⠈⠔⡂⢌⠳⢮⣠⠘⢿⣿⣿⣿⡿⠀⣱⠼⢊⠥⡉⠂⣀⡴
⣿⣿⡇⣤⣄⣈⠂⠱⡈⢌⠑⠪⡻⣿⡿⠡⠞⠁⡔⠡⡒⡵⣼⣿⣣

⠈⠀⠀⠁⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⢰⠀⠀
⠀⠀⠀⠇⠀⠀⠀⠀⠀⣈⣲⣤⣦⣧⣦⣴⠁⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⢀⠀⠀⠀⢠⣴⣿⡿⠏⠿⠿⠿⢿⢻⣧⣄⠀⠀⠀⡆⠀⠀
⠀⠀⠀⠘⠀⡀⠀⠰⠟⠁⠀⡴⢿⣿⢷⠀⠀⠙⠷⠀⢠⠐⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⡑⠺⠿⢊⣀⣀⠀⠀⠀⠀⡄⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⢀⣮⠙⢻⣿⣿⣾⣿⡟⠋⢷⡄⠀⠀⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠑⢀⣸⣿⣤⣾⣿⣏⣽⣿⣷⣤⣾⣇⣀⠈⠀