02
⣧⡀⠀⠈⠲⣵⡄⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠸⡆⠀
⣿⣿⣄⠀⠀⣈⠻⣄⡎⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠒⠒⠤⢬⡃⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⡇⠀
⣿⣿⣿⣿⣿⢛⠿⠻⢤⣀⣀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡄⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⡇⠀
⣿⣿⣿⣿⣿⡜⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠹⡵⠀⢀⡏⠉⢲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣀⠀⢿⠘
⣿⣿⣿⣿⣿⣷⡶⠀⠀⣼⠀⠀⢀⣠⡤⠔⠒⠒⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠒⠒⠤⡽⣄⣸⠀⠐⠛⠂⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⢸⠀
⣿⣿⣿⣿⣿⣿⠿⢦⣴⡟⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⠃⠀⣶⢦⣄⡀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠁⢸⡠
⠙⣿⣿⣿⣿⣿⣴⣧⠈⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣰⠁⠀⠀⠉⠑⠲⣤⡈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠀⠀⠸⣿
⠀⠘⢿⣿⣿⣿⡗⠘⡆⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠇⠀⠀⠀⠀⠀⠀⠀⠈⢙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⣿
⠀⠀⠀⢻⣿⣿⠃⠀⢹⠟⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⡄⠀⡄⠀⠀⠀⠀⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣷
⠒⠒⠶⠾⠿⢿⡈⢸⠀⠀⠀⠀⡄⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⢳⡀⡇⠀⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠸⡆⠀⠀⢿
⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⠀⢠⠀⠀⠘⣧⡇⠀⠀⠀⠀⠆⠀⡇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣷⠤⢤⣾
⣤⣤⣤⣤⣤⣼⡇⢸⠀⠀⠀⣸⡇⡄⢰⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⠀⢀⠀⠀⠀⡇⣆⠀⠀⢸⠀⠀⠀⠸⡇⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⢻⠀⠀⠀
⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⢰⠟⡇⡇⢸⠀⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⢧⢀⠀⠀⢸⠀⠀⠀⣇⢸⡆⠀⠀⣧⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣷⣷⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⣆⣀⣀
⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡞⠀⡇⡇⢸⠀⡇⠀⢸⠀⠀⠀⢠⠀⠀⠀⢸⣸⡄⠀⠘⡆⢳⠀⢿⢸⠹⡄⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡳⣧⣀⣀⡀⠀⣿⡄⠀⠀⠈⣯⠈⠉
⠀⠀⠀⠀⠀⠀⣇⠸⡆⢾⠟⠓⢷⣷⠾⣤⣷⡀⠘⡄⠀⠀⠸⡆⠀⠀⢸⣏⣇⣠⣤⣷⠼⠷⢾⣾⠶⠾⣦⠬⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠋⠁⣀⣟⢧⠸⣷⠀⠀⠀⠘⡄⠀
⠀⠀⠀⠀⠀⠀⣿⠀⡇⣾⠀⠀⢸⣿⡀⢧⢻⠙⠻⡇⢸⡄⠀⢣⠀⠀⢻⢻⣿⠁⠀⢹⠀⠰⡼⣿⠀⠀⠘⣦⢸⡈⠳⣼⡄⠀⠀⠀⠀⠀⡟⠀⣠⠞⠻⣆⠈⡆⢹⣇⠀⠀⠀⢳⠀
⠀⠀⠀⠀⠀⠀⣿⠀⡇⣿⡀⠀⠘⣟⡇⠘⣾⡀⠀⣿⠀⠇⠀⠸⡄⠀⢸⠀⢻⡀⠀⠸⣆⠀⠑⣿⠀⠀⠀⠈⠳⣳⡄⢹⡆⠀⠀⠀⠀⠀⣷⡼⠙⠒⠂⢹⠀⢧⠀⣿⣆⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⢹⡆⢧⣿⣷⣶⣦⣻⣷⢤⣹⣇⠀⡟⡆⢸⡀⠀⢳⠀⢈⠀⠈⢧⠀⠀⣿⡀⠀⢸⣉⣀⣀⠀⠀⣈⠿⣼⡇⠀⠀⠀⣖⠀⡟⣇⠀⠀⠀⣸⠁⢸⡄⢸⣿⣆⠀⠀⠸
⡶⣄⡀⠀⠀⠀⢸⡇⢸⣿⣿⣿⡻⣯⡙⠻⣷⣾⣽⣟⢻⡀⢣⣳⠀⠳⣸⠀⢴⡾⢗⣒⣿⣯⣿⣿⣷⡶⠶⠶⠿⣷⣿⣿⡇⠀⠀⠀⡷⠀⡇⢸⡆⠀⢀⠟⢀⡿⠶⣶⣿⠿⠶⠶⠶
⣿⢳⣭⢿⣦⣄⡀⣇⠸⣻⣿⣿⣇⠈⠛⢦⣐⣏⡛⢿⠃⠹⣎⣿⣆⣀⣻⣄⠀⠘⠻⠟⢻⣿⡛⠻⢿⡆⠀⣀⣴⡿⠏⢸⡇⠀⡆⠀⡏⠀⣿⣾⠧⠞⠉⣰⠏⣷⣾⠿⠿⠿⣧⠀⢠
⠤⢼⡉⣸⢳⠛⡿⣿⠀⠙⣿⣿⣿⣦⠀⠀⠀⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠛⠛⠛⠚⠛⠋⠉⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⡏⠀⠀⣀⠞⠁⠸⣿⡁⣀⣦⠾⠃⠀⠈
⠀⠀⠉⠋⠤⠤⣟⣻⠀⠀⣿⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⣷⡴⣞⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⡿⠀⢸⢿⣇⠀⠀⠀⠀⠀⣰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡇⠀⡇⠀⡏⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⢀⡇⠀⡇⠀⢸⠘⣿⣄⠀⠀⠀⠈⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠄⠀⡇⠀⠀⠀⠙⢦⣄⣀⣀⠀⠀⠀⣠⡶⣄
⣄⣀⣀⣀⣀⣤⣶⣿⡇⠀⡇⠀⢸⠀⣿⣿⣦⡀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠇⠀⠀⠀⢀⡾⠀⢹⣿⣿⣿⣿⡟⠀⢻
⠀⠙⠛⢿⣿⡿⣿⣿⣿⠀⢹⠀⠐⠀⢿⣿⣿⠻⣦⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠔⣒⣢⠄⠀⠀⠀⠀⠀⠀⢀⣰⣿⡇⢸⠀⢸⠀⢸⠀⠀⠀⢀⡼⠁⠀⣾⣿⡿⣿⡋⢷⡖⣾
⠓⢤⣀⠀⠀⠙⠳⢤⣹⠀⢸⠀⠀⠀⣿⣿⣿⠀⠀⠙⡶⣄⠀⠀⠈⠛⠒⠒⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⢻⠀⠸⠀⢸⠀⢸⠂⠀⢠⡞⠁⠀⠀⣿⣿⡇⣿⡅⣼⡇⢹
⠀⠀⠈⠳⢤⡀⠀⠀⢹⠀⢸⠀⠀⠀⡇⠀⢻⡀⠀⠀⡇⢨⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠃⢸⠀⡇⠀⢸⠀⢸⠀⡠⠋⠀⠀⠀⠀⣿⡿⡇⡷⣋⣿⡇⢸
⠀⠀⠀⠀⠀⠙⠢⢄⡸⡆⢸⠀⠀⠀⡇⠀⠈⣇⠀⠀⡇⢸⣿⣇⠘⠛⠦⣄⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉⠉⠉⠙⣿⣄⣸⠀⡇⠀⠸⠀⣸⠎⠀⠀⠀⠀⢀⡼⣿⡧⡇⣿⣿⣿⡇⢸
⠤⠀⠀⠀⠐⠒⠒⠚⠃⡇⢸⠀⠀⠀⣷⠀⠀⢹⡀⢀⣿⣽⣿⠖⢀⢀⣠⣿⣿⣦⣤⠴⠚⠋⠙⢦⡀⠀⠀⠀⣸⠃⠙⡇⢸⠀⠀⡇⠀⡏⠀⠀⠀⢀⡴⠋⠀⣿⡧⡇⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⡄⠀⠀⢹⠀⠀⠀⢷⣸⣿⣿⣿⠀⣠⣿⣿⣿⣿⢿⡇⡀⠀⢀⠀⠀⠙⠲⣴⣀⣹⣦⣀⡇⠸⠀⠀⣿⠀⣇⠀⣠⠴⠋⠀⠀⠀⣸⣧⣷⣿⣿⣿⣿⠘
⣿⣿⣄⠀⠀⣈⠻⣄⡎⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠒⠒⠤⢬⡃⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⡇⠀
⣿⣿⣿⣿⣿⢛⠿⠻⢤⣀⣀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡄⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⡇⠀
⣿⣿⣿⣿⣿⡜⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠹⡵⠀⢀⡏⠉⢲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣀⠀⢿⠘
⣿⣿⣿⣿⣿⣷⡶⠀⠀⣼⠀⠀⢀⣠⡤⠔⠒⠒⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠒⠒⠤⡽⣄⣸⠀⠐⠛⠂⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⢸⠀
⣿⣿⣿⣿⣿⣿⠿⢦⣴⡟⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⠃⠀⣶⢦⣄⡀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠁⢸⡠
⠙⣿⣿⣿⣿⣿⣴⣧⠈⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣰⠁⠀⠀⠉⠑⠲⣤⡈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠀⠀⠸⣿
⠀⠘⢿⣿⣿⣿⡗⠘⡆⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠇⠀⠀⠀⠀⠀⠀⠀⠈⢙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⣿
⠀⠀⠀⢻⣿⣿⠃⠀⢹⠟⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⡄⠀⡄⠀⠀⠀⠀⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣷
⠒⠒⠶⠾⠿⢿⡈⢸⠀⠀⠀⠀⡄⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⢳⡀⡇⠀⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠸⡆⠀⠀⢿
⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⠀⢠⠀⠀⠘⣧⡇⠀⠀⠀⠀⠆⠀⡇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣷⠤⢤⣾
⣤⣤⣤⣤⣤⣼⡇⢸⠀⠀⠀⣸⡇⡄⢰⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⠀⢀⠀⠀⠀⡇⣆⠀⠀⢸⠀⠀⠀⠸⡇⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⢻⠀⠀⠀
⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⢰⠟⡇⡇⢸⠀⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⢧⢀⠀⠀⢸⠀⠀⠀⣇⢸⡆⠀⠀⣧⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣷⣷⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⣆⣀⣀
⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡞⠀⡇⡇⢸⠀⡇⠀⢸⠀⠀⠀⢠⠀⠀⠀⢸⣸⡄⠀⠘⡆⢳⠀⢿⢸⠹⡄⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡳⣧⣀⣀⡀⠀⣿⡄⠀⠀⠈⣯⠈⠉
⠀⠀⠀⠀⠀⠀⣇⠸⡆⢾⠟⠓⢷⣷⠾⣤⣷⡀⠘⡄⠀⠀⠸⡆⠀⠀⢸⣏⣇⣠⣤⣷⠼⠷⢾⣾⠶⠾⣦⠬⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠋⠁⣀⣟⢧⠸⣷⠀⠀⠀⠘⡄⠀
⠀⠀⠀⠀⠀⠀⣿⠀⡇⣾⠀⠀⢸⣿⡀⢧⢻⠙⠻⡇⢸⡄⠀⢣⠀⠀⢻⢻⣿⠁⠀⢹⠀⠰⡼⣿⠀⠀⠘⣦⢸⡈⠳⣼⡄⠀⠀⠀⠀⠀⡟⠀⣠⠞⠻⣆⠈⡆⢹⣇⠀⠀⠀⢳⠀
⠀⠀⠀⠀⠀⠀⣿⠀⡇⣿⡀⠀⠘⣟⡇⠘⣾⡀⠀⣿⠀⠇⠀⠸⡄⠀⢸⠀⢻⡀⠀⠸⣆⠀⠑⣿⠀⠀⠀⠈⠳⣳⡄⢹⡆⠀⠀⠀⠀⠀⣷⡼⠙⠒⠂⢹⠀⢧⠀⣿⣆⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⢹⡆⢧⣿⣷⣶⣦⣻⣷⢤⣹⣇⠀⡟⡆⢸⡀⠀⢳⠀⢈⠀⠈⢧⠀⠀⣿⡀⠀⢸⣉⣀⣀⠀⠀⣈⠿⣼⡇⠀⠀⠀⣖⠀⡟⣇⠀⠀⠀⣸⠁⢸⡄⢸⣿⣆⠀⠀⠸
⡶⣄⡀⠀⠀⠀⢸⡇⢸⣿⣿⣿⡻⣯⡙⠻⣷⣾⣽⣟⢻⡀⢣⣳⠀⠳⣸⠀⢴⡾⢗⣒⣿⣯⣿⣿⣷⡶⠶⠶⠿⣷⣿⣿⡇⠀⠀⠀⡷⠀⡇⢸⡆⠀⢀⠟⢀⡿⠶⣶⣿⠿⠶⠶⠶
⣿⢳⣭⢿⣦⣄⡀⣇⠸⣻⣿⣿⣇⠈⠛⢦⣐⣏⡛⢿⠃⠹⣎⣿⣆⣀⣻⣄⠀⠘⠻⠟⢻⣿⡛⠻⢿⡆⠀⣀⣴⡿⠏⢸⡇⠀⡆⠀⡏⠀⣿⣾⠧⠞⠉⣰⠏⣷⣾⠿⠿⠿⣧⠀⢠
⠤⢼⡉⣸⢳⠛⡿⣿⠀⠙⣿⣿⣿⣦⠀⠀⠀⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠛⠛⠛⠚⠛⠋⠉⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⡏⠀⠀⣀⠞⠁⠸⣿⡁⣀⣦⠾⠃⠀⠈
⠀⠀⠉⠋⠤⠤⣟⣻⠀⠀⣿⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⣷⡴⣞⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⡿⠀⢸⢿⣇⠀⠀⠀⠀⠀⣰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡇⠀⡇⠀⡏⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⢀⡇⠀⡇⠀⢸⠘⣿⣄⠀⠀⠀⠈⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠄⠀⡇⠀⠀⠀⠙⢦⣄⣀⣀⠀⠀⠀⣠⡶⣄
⣄⣀⣀⣀⣀⣤⣶⣿⡇⠀⡇⠀⢸⠀⣿⣿⣦⡀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠇⠀⠀⠀⢀⡾⠀⢹⣿⣿⣿⣿⡟⠀⢻
⠀⠙⠛⢿⣿⡿⣿⣿⣿⠀⢹⠀⠐⠀⢿⣿⣿⠻⣦⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠔⣒⣢⠄⠀⠀⠀⠀⠀⠀⢀⣰⣿⡇⢸⠀⢸⠀⢸⠀⠀⠀⢀⡼⠁⠀⣾⣿⡿⣿⡋⢷⡖⣾
⠓⢤⣀⠀⠀⠙⠳⢤⣹⠀⢸⠀⠀⠀⣿⣿⣿⠀⠀⠙⡶⣄⠀⠀⠈⠛⠒⠒⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⢻⠀⠸⠀⢸⠀⢸⠂⠀⢠⡞⠁⠀⠀⣿⣿⡇⣿⡅⣼⡇⢹
⠀⠀⠈⠳⢤⡀⠀⠀⢹⠀⢸⠀⠀⠀⡇⠀⢻⡀⠀⠀⡇⢨⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠃⢸⠀⡇⠀⢸⠀⢸⠀⡠⠋⠀⠀⠀⠀⣿⡿⡇⡷⣋⣿⡇⢸
⠀⠀⠀⠀⠀⠙⠢⢄⡸⡆⢸⠀⠀⠀⡇⠀⠈⣇⠀⠀⡇⢸⣿⣇⠘⠛⠦⣄⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉⠉⠉⠙⣿⣄⣸⠀⡇⠀⠸⠀⣸⠎⠀⠀⠀⠀⢀⡼⣿⡧⡇⣿⣿⣿⡇⢸
⠤⠀⠀⠀⠐⠒⠒⠚⠃⡇⢸⠀⠀⠀⣷⠀⠀⢹⡀⢀⣿⣽⣿⠖⢀⢀⣠⣿⣿⣦⣤⠴⠚⠋⠙⢦⡀⠀⠀⠀⣸⠃⠙⡇⢸⠀⠀⡇⠀⡏⠀⠀⠀⢀⡴⠋⠀⣿⡧⡇⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⡄⠀⠀⢹⠀⠀⠀⢷⣸⣿⣿⣿⠀⣠⣿⣿⣿⣿⢿⡇⡀⠀⢀⠀⠀⠙⠲⣴⣀⣹⣦⣀⡇⠸⠀⠀⣿⠀⣇⠀⣠⠴⠋⠀⠀⠀⣸⣧⣷⣿⣿⣿⣿⠘
