⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡧⠖⠚⠉⠉⠀⠀⠀⠀⠀⠘⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡆⠀
⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠻⣗⢄⠀⠀⣀⣠⡤⣤⠔⠛⢩⠟⠀⠀
⠀⢀⣀⡤⠤⠤⣾⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⡀⢤⡒⠥⠒⠉⠘⢯⡽⢿⠉⢀⣴⣁⣤⠴⠧⡄⠀⠀
⠁⠀⠀⠀⠀⠀⡇⠁⠒⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢀⡴⠉⠳⣄⠀⠀⠀⠀⠀⠻⣼⣖⠋⠁⠀⠀⠀⠀⢹⡀⠀
⠀⠀⠀⠀⠀⠀⡇⠐⠒⠂⠤⠤⠤⡿⣄⠤⠤⠀⠀⠀⠀⠀⠀⠀⣽⣾⣋⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠺⠿⣤⠀⠀⠀⣀⡤⡿⠀
⡄⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⢠⣇⠘⢦⠀⠀⠀⠀⠀⠀⠰⠏⣽⡟⠉⠉⠓⣶⣴⣤⡀⣽⠦⠤⠴⡶⠚⠉⠁⣀⣴⠞⠁⡼⠃⠀
⠈⡆⢀⡴⠲⠯⣭⡆⠀⠀⠀⠀⢸⡱⠉⠩⠿⣖⠂⣄⠀⠀⠀⠀⢀⣧⣶⣶⣿⣿⣯⣿⣷⠺⡄⠀⠀⡿⠤⢞⣩⣾⣥⡤⠾⠓⠙⡇
⠀⠙⠯⠤⠤⣤⡴⠻⡄⠀⠀⠀⡞⠁⠀⠀⢀⣈⣳⣼⠛⢦⣀⠀⢲⣿⣿⡿⣿⡇⢹⡟⠛⠀⡧⠀⢠⡇⠀⠘⡆⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠸⣍⠁⠀⠀⡇⠀⠀⣸⡇⣶⠿⣿⣿⣿⣷⡮⠀⠀⠈⠉⠓⠋⠘⢷⡬⠔⠋⡇⠀⠀⢧⠀⡼⠀⠀⠀⠉⠒⢠⡤⠤⣶⠞⠁
⠀⠀⠀⠀⠈⠳⣄⣤⣿⡄⣰⣽⢻⡹⣆⠘⣿⡛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠸⣅⠀⠀⠀⢰⠏⠙⢶⣋⣁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡿⢽⡏⢧⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡼⠒⠚⠳⠀⠀⠈⠓⠦⠤⠼⠛⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢧⠘⡇⠘⣇⠀⠀⠀⠀⠀⠀⠀⣠⠴⣒⡦⢤⡀⠀⠀⢀⣿⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⡄⢸⣦⣀⠀⠀⠀⠀⠀⡟⠉⠀⠀⠀⣳⢀⡴⠋⢸⣄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣛⠋⣳⣰⡇⠈⠛⠲⠤⣄⣀⣙⠦⠤⢤⣲⠵⠋⣀⣤⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠀⠀⠀⠀⠀⠀⣠⣿⣿⣭⡉⣠⣴⠿⡛⢉⣻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣄⣀⣰⣿⢻⣷⣔⣿⣗⢀⣠⣶⣿⣿⣿⣿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠑⡀⣿⣶⣴⣼⣿⣿⣿⢿⣿⣿⢿⣿⡿⠏⣡⠿⠉⠀⢨⣿⡟⡩⠏⠉⠉⠓⠶⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢸⢿⡿⠿⠿⢿⣆⠙⣿⣻⣿⣿⢉⣡⡾⠃⠀⠀⠀⠨⣿⡏⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡞⠀⠏⠂⠢⡀⢹⣿⣿⣽⣿⣿⠾⠯⠀⠄⠤⠀⠔⠚⢸⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠈⠁⣿⡿⣿⠛⡟⣴⠈⠁⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡾⠚⠛⠛⠐⠒⢶⣤⡇⡇⣿⢰⣿⢃⡤⠖⠚⠉⠙⠓⠲⡏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢠⣼⢷⣄⣿⡿⢀⣠⣾⣼⠁⠀⣿⣼⠃⣟⠀⠀⠰⣶⡆⣠⣴⣧⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⢦⣿⡀⠈⣿⠏⠉⢱⡇⢿⣶⣿⣿⡏⠀⡽⠉⠛⠛⣿⠛⡉⣸⠈⢄⡀⠀⠀⠀⠀⢰⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⠒⠒⢳⣾⠀⠉⠂⡏⠀⠀⣾⡇⢸⣿⠻⢿⠁⠀⡇⠀⠀⠀⣿⢠⡇⣿⠶⠒⠛⠉⠉⠉⠙⢚⡆⠀⠀⠀