⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣤⣤⣀⣀⠀⠀
⣶⣶⣶⣶⣾⠟⣩⠟⠁⠀⠀⢀⠎⠀⠀⡰⠋⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠙⠿⣷
⣿⣿⣿⠏⢉⡾⠃⠀⠀⠀⢀⠆⠀⠀⠰⠁⠀⠀⠀⠀⡜⠁⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⢸
⣿⣿⠉⣰⡟⠁⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡰⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀
⣿⠉⢰⡟⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⢠⢇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⡿⢠⣿⠁⠀⠀⠀⠀⡼⠀⠀⡆⠀⠀⠀⠀⠀⡼⡣⡇⠀⠀⠘⢸⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠈⢿
⡇⡞⠙⠀⠀⠀⠀⣸⠁⠀⢸⠀⠀⠀⠀⠀⣼⡟⠁⡇⠀⠀⠀⡇⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠈
⣿⠁⠀⠀⠀⠀⠀⡇⠀⠀⣸⠀⠀⠀⠀⢀⣻⠀⠀⢸⡀⠀⠀⢳⡀⠀⠀⠀⣞⢸⣆⠀⠀⠀⢸⡀⠀⢰⠀⠀⠀⢳⠀⠀⠀⠀⠁⠀⠀⠀
⠇⠀⠀⠀⠀⠀⢸⠀⡀⠀⡟⣆⠀⠀⠀⢸⠧⠴⠆⠀⠳⡀⠀⠀⠳⡀⠀⢸⢻⠲⠼⢆⠀⠀⠀⣇⠀⢸⣆⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⣴⡿⣔⣇⠉⠓⠦⣄⣸⠀⠀⠀⠀⠀⠻⠶⣄⣀⠙⠦⣸⡆⠀⠀⠀⠓⢤⡀⠸⡷⣄⢻⢦⡀⠀⢷⠀⠀⠀⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠛⠀⠈⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠨⠍⠉⠉⠛⠀⠀⠀⠀⠀⠉⠙⠚⠬⠟⠃⠻⡦⣼⠀⠀⣆⡇⠀⠀⠀
⠀⡀⢰⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⢀⢿⠁⠀⠀⠀
⠀⠸⡄⣧⠀⢸⣃⣤⣖⣻⣿⣿⠿⣿⣿⣟⣓⣲⣭⣑⠀⠀⠀⠀⠀⠀⠀⠀⢈⡥⣶⣺⣿⣿⣿⣿⣷⠲⠦⣄⡀⠀⠀⡇⢸⡼⠀⠀⠀⠀
⠀⠀⢱⡘⡆⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠓⠛⠓⠲⣧⡇⠃⠀⠀⠀⠀
⠀⠀⠀⢳⡸⡄⡇⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢳⡹⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠱⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡜⠀⠀⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠁⠀⠀⢀⠎⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⠍⣑⣒⣒⣒⣒⣒⣒⣒⠲⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣠⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢲⠇⠀⢀⡞⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣌⡒⠤⢄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⣉⣵⠟⠀⡠⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠉⢹⠖⠲⣤⢭⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣁⣠⠼⠶⡶⠛⢉⡟⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡸⠀⣰⡟⢠⣷⣷⠻⣿⣿⠭⠭⠽⣿⡏⠿⣫⡽⢿⣟⣧⢸⠀⢰⠃⣀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠃⣰⠟⣠⣿⡿⣻⠀⠀⠙⠛⠛⠶⠒⠛⠋⠉⠀⢸⡝⢿⣮⡆⢸⢈⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⡾⣫⣾⠟⠁⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠉⠻⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠱⣲⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠤⢄⣈⠈⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⣢⠐⡄⠀⠉⠑⠒⠒⠒⣄
⠀⠀⠀⣀⠴⠋⠀⠀⠀⡎⢀⣘⠿⠀⠀⢠⣀⢄⡦⠀⣛⣐⢸⠀⠀⠀⠀⠀⠀⢘
⡠⠒⠉⠀⠀⠀⠀⠀⡰⢅⠣⠤⠘⠀⠀⠀⠀⠀⠀⢀⣀⣤⡋⠙⠢⢄⣀⣀⡠⠊
⢇⠀⠀⠀⠀⠀⢀⠜⠁⠀⠉⡕⠒⠒⠒⠒⠒⠛⠉⠹⡄⣀⠘⡄⠀⠀⠀⠀⠀⠀
⠀⠑⠂⠤⠔⠒⠁⠀⠀⡎⠱⡃⠀⠀⡄⠀⠄⠀⠀⠠⠟⠉⡷⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠴⣄⡸⠤⣄⠴⠤⠴⠄⠼⠀⠀⠀⠀⠀⠀⠀⠀