⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢿⣿⣿⣛⢫⡽⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠙⠻⢿⡙⠀⣹⠿⢾⡧⡼⠑⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠺⣭⡉⠁⠲⠤⠼⡇⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣹⠆⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⡀⠀⠈⡟⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢸⡆⠀⠠⡤⠀⢛⡷⠀⠀⠇⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡀⠀⠀⠀⠀⠀⠛⠒⠚⠛⠒⠋⠀⠀⠀⣧⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣶⡟⠛⠛⢆⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⡼⠓⠦⣀⠀⠀⠀⠀
⠀⠀⠀⣠⣖⡽⠋⠁⠀⠀⠀⠀⠑⢄⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⣀⠖⢃⡼⢁⡀⠀⠈⠑⢄⣀⠀
⠀⣠⣾⡿⠿⠤⢤⣀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡈⠙⠓⢦⣄⣠⢾⣁⣠⠏⠀⠈⣇⠀⠀⠀⢈⠎⣧
⣾⢟⣡⣤⠤⠤⣄⡈⠑⣄⠀⢀⡄⠀⠀⠀⠀⠉⠑⠢⠟⠠⡿⡄⠈⠁⠀⠀⠀⠹⡄⠀⢀⡼⠘⣹
⢿⡏⣽⠃⠀⠀⠀⢝⢦⢈⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠹⣶⣫⣠⠾⢻
⠀⣿⡇⠀⠀⠀⠀⠀⢯⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⡦⠤⠀⠀⠀⠀⠘⣏⠀⢀⡞
⠀⠹⣷⠀⠀⠀⠀⠀⠘⡾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠹⡆⣸⠁
⠀⠀⠙⣆⠀⠀⠀⠀⠀⢱⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⠀⠀⠀⠀⠀⠀⢻⣧⠀
⠀⢠⣴⠛⣧⡀⢰⡇⠀⠨⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠰⣸⣿⡄
⠀⠀⠙⢻⡏⡽⠛⡷⢦⡈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⣤⣶⣏⡽⠃
⠀⠀⠀⠈⢿⣿⣤⣧⣨⣾⣅⣀⣦⡀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⣀⣤⣾⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣶⣶⣶⣶⠚⠉⠉⢹⣿⣿⣿⣿⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⢿⣿⡃⠈⠀⠀⠈⠉⠙⢿⠛⠛⠛⠛⠛⠛⠛⠷⠶⠟⢻⣿⣿⣿⡟⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠊⣾⡿⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠋⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢸⡿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⣄⣿⠀⠀⠀⣀⣤⣴⣦⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣤⣴⣾⣿⣿⣿⣷⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠿⠿⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀