⣄⣙⠉⠁⠀⠀⠀⠠⠞⠋⠉⢻⣭⡛⢹⡇⠀⣀⡼⠟⠛⠉⠉⢉⣉⠛⢷⠟⠛⠂⠺⢀⣴⣾⣛⠁⢈⣭⣿⣿⣯⡍⠉⠁⠀⠀⠀⠐⢀
⠋⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠙⣿⣷⠟⠉⠀⠀⠀⣠⡾⠿⠛⠓⠀⠀⠀⢠⣶⠋⠁⠩⣿⡁⠈⠙⣿⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⢀⡾⠃⡴⠛⢦⣀⠀⠀⢀⡾⠁⠀⣠⣶⣏⣿⠀⠀⣹⣤⣀⢠⣴⢤⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⢠⠎⠀⣰⢚⡷⣄⡾⠛⠉⠀⠀⠀⠃⠀⠉⣹⣁⣴⣿⡿⠟⠁⣹⣶⣾⡿⠋⢹⠈⡇⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡏⠀⢠⠃⡼⠁⣿⣤⣶⣶⣄⢠⣾⣭⣭⣭⣿⣿⠿⠋⢀⣤⣾⣿⡿⠉⢀⣴⣿⠀⠁⠀⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⣾⣤⣤⡏⢰⠁⣸⣿⠏⢩⣋⣉⡍⣥⣿⣿⣿⠙⣿⣶⢶⡿⠿⢯⣄⣧⣾⡿⠋⡏⠀⠀⠐⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣇⣠⡄⠃⢰⣿⢻⢀⣼⣹⣿⣤⣼⠾⠞⠛⠛⠛⣿⡿⠷⣤⡀⠙⠿⢧⣠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡄⣀⡀⢸⠻⣼⣯⣈⠉⠳⣿⡟⠾⠾⣿⡿⠋⢻⡇⠀⠀⠀⠀⢀⣏⣷⡀⢸⠙⠳⢤⣀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡁⠙⠛⠢⢄⡉⠙⠀⣰⠁⣷⣴⣾⣿⣿⣷⡟⠀⠀⠀⣠⠜⡿⠁⠸⡄⣸⠀⠀⠀⣿⠉⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡞⠛⠋⠀⠀⠀⠀⠙⣶⡞⢉⣹⣏⣹⡿⠹⣿⣿⠃⠀⣠⣾⣋⠜⠁⠀⠀⣷⡇⠀⢰⢀⣇⠀⢸⠀⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢿⣶⢄⡀⠀⠀⠀⣰⣿⠏⠉⢀⣼⣿⡀⠀⣬⠟⠒⠋⠙⠛⣽⣿⠷⠞⠛⡿⠀⢀⣿⣸⢯⡙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡼⠁⠀⠉⠓⢦⡼⢻⠙⣦⡀⠈⡟⢿⡋⠛⠉⠀⠀⠀⠀⠀⠉⠙⠛⢶⣾⣥⣶⣫⡿⠃⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠏⠀⠀⠀⠀⣰⠏⠀⣾⠀⠈⠙⢻⡇⢀⣷⡀⠀⢰⡶⢤⣀⠀⠀⠀⢀⣼⠋⣧⠈⣿⠛⠲⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⡼⠁⠀⠀⠀⠀⡴⠃⠀⢀⡇⠀⠀⠀⠸⠷⠋⠀⣿⣶⣤⣉⣐⣋⡠⠤⠒⠋⠁⠀⢸⣼⢿⠀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋
⢀⠞⠀⠀⠀⠀⢀⣾⡧⢤⣠⣾⠳⠶⢤⣤⣤⣤⠤⠤⢿⡙⠛⠛⠻⣄⣀⣀⠀⠀⠀⠀⠈⠁⠸⡄⠛⠉⢉⡗⠀⠀⠀⠀⠀⡰⠋⠀⠀
⡏⠀⠀⠀⠀⠀⢻⢸⠇⠀⠀⢹⠉⠉⠁⠀⠙⢯⣷⣄⡀⠙⠢⣄⠀⠀⠒⠬⠟⣷⠐⠀⠀⣄⠀⢧⠀⠀⣏⡤⣖⠀⠀⣠⡞⠀⠀⠀⠀
⠙⣦⣀⠀⠀⠀⡼⣸⠀⠀⠀⣼⠲⠦⠤⣄⡀⠸⣿⡿⣿⡢⣄⡈⠓⢆⡀⠀⠀⢹⡆⢀⣀⣸⣄⠸⡄⠀⠀⠀⢸⠀⡼⠁⢧⡀⠀⠀⠀
⠀⠀⠈⠉⠉⡿⠷⠧⠤⣄⣼⣇⣀⠈⠁⠀⠀⠀⣿⣿⠿⠿⢷⣿⡷⠀⠙⢦⣤⣿⣷⣏⠁⠀⣹⣿⣧⠀⠀⠀⢸⠈⠀⠀⠀⠉⠓⠂⠤
⠀⠀⠀⠀⠀⡁⠀⠀⠀⠻⣤⣈⣓⣺⠏⠀⠀⣸⡟⣧⣀⣠⣤⣿⣼⣷⣶⣤⣬⣿⣿⣿⣿⣿⣏⣿⣿⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠁⠈⠉⠉⠉⠉⠙⢿⢻⣿⣿⣷⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⣇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣃⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣿⣙⣿⣿⣼⣿⣿⣿⣿⣷⣿⣿⣿⡿⠻⣅⠀⠹⣆⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠉⠛⡆⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡟⢧⣀⠔⣻⣷⠞⠛⢦⠀⢹⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢃⠀⠀⡇⣸⠀⣀⣀⣀⣀⣀⣀⣀⠀⣸⣿⣿⣼⣷⣿⣿⣿⣷⣿⣿⣾⣿⣇⣀⣙⡿⠛⠁⠀⠀⠈⣇⢸⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡘⠀⠸⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡽⠋⠀⠀⠀⠀⠀⣠⠏⠈⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡇⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⢹⠖⠲⢶⣶⠄⢠⠤⣲⡶⠖⠚⢻⡉⠳⡄⠀⣀⡤⠞⢻⠀⠀⣷⠀⠀⠀⠀⠀⠀