⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠔⢛⡇⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⣉⠛⠲⠦⢤⡀⠀⠀⠀⠀⠀⠇⣿⣾⢟⡭⣖⣵⢾⠿⠚⣉⠛⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢘⣖⣿⣟⣷⣮⣔⠽⣱⢶⣚⣏⣉⣀⠿⠁⠏⣎⡭⢢⣤⣾⣶⢢⣶⢼⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⢹⣏⣻⣾⣿⣿⣿⣾⡙⣿⣿⣿⣿⣶⣄⣨⡶⠶⣶⣌⡉⢿⠿⣽⠾⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣸⡟⣭⣾⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⢿⣶⣍⠻⢿⣶⣜⢻⣴⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⡧⠉⠀⣹⣿⠿⠁⠉⠉⠉⠉⠁⠉⠉⠉⠉⠀⠉⢉⣁⣤⣙⠿⣌⣾⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀ ⣰⠃⠀⠀⠸⠻⢷⠶⣤⣄⣀⣀⢀⣀⣀⣀⣤⣴⡤⣿⣿⡿⠿⠘⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀ ⢠⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣱⠈⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⢣⠀
⠀⠀⠀⠀⠀ ⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⣻⣇⡀⠀⢀⣄⠀⠰⣓⣀⡀⠀⠀⠀⠀⠨⡄
⠀⠀⠀⠀⠀ ⡼⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⠀⢻⣿⣿⣦⣺⣵⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⢹
⠀⠀⠀⠀⢠⠅⢀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⣼⣿⣿⡿⣧⣻⠀⠀⣿⣿⣿⡟⠁⠀⠀⡀⠐⡆⠀
⠀⠀⠀⠀⠘⠒⢻⡀⠀⠀⠀⠀⠀⠀⢸⣽⣳⣐⣛⣟⣭⣿⣿⣿⣧⢔⣻⣯⣿⠂⠀⠀⠀⡿⠦⡹⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⡅⣀⡄⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣛⣫⣷⣭⣿⣿⣿⠟⠁⠰⣄⠀⢀⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⢳⡠⢦⠀⣆⠀⢀⡄⠈⠙⣻⡛⠛⠟⠛⠋⠁⢰⡀⠀⡼⠉⠳⣤⠁⠀
⠀⠀⠀⠀⢀⠤⠠⢄⠀⠀⠀⠀⠉⠈⠓⡿⣷⣾⣿⣿⣿⣿⣿⣷⣷⢤⡞⠈⠚⠁⠀⠀⠀
⠀⠀⠀⢰⢧⣿⣿⡎⡇⠀⠀⠀⠀⢀⣞⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⢿⡵⡀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣾⣿⣿⣸⠁⠀⠀⠀⡰⣯⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣦⠀⠀⠀
⠀⠀⠀⢸⣹⣿⣿⣻⡀⠀⠀⢸⡙⠿⣿⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣏⣿⡿⢐⣄⡀⠀
⠀⠀⠀⠀⢦⠻⣿⣯⣽⢒⣴⣾⣷⣶⣄⠹⠅⣼⣿⣿⣿⣿⣿⣿⣿⣿⠄⢀⣾⣿⣿⣧⠀
⠀⠀⠀⠀⠀⠑⢬⣻⢿⢸⣿⣿⣿⣿⣿⡆⠀⠙⠛⠿⠿⠿⠿⠟⠛⠉⠀⠸⣿⣿⣿⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠦⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡴⠒⠋⡟⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⡇⠀⡜⠁⠀⠀⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣿⠀⠈⢦⣀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠲⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠴⠚⠀