⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠿⠊⠀⠀⠀⠈⢁⠉⠀⢠⣾⠷⠓⠖⠀⠀⠀⠀⠀⠀⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⡩⠋⠁⠀⠀⠀⢀⡠⠈⠀⠂⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⣅⣀⠁⠄⠀⠁⡀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠶⠀⠀⠀⠀⡃⠀⠀⡤⢀⡠⢂⡭⠂⠀⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣾⡶⣬⡉⠛⣿⣦⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⡰⠖⠻⢟⣵⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡛⢦⠀⠛⠆⡀⡆⠁⠂⠀⠀⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠡⠊⠀⠌⠀⢀⡼⠛⠁⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢻⣷⡻⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡠⠁⠀⠌⡠⠔⡉⠀⠀⠀⢠⡿⠁⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠀⠀⠹⣷⡆⢡⠀⠀⠽⣦⡀⠀⠈⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠰⠀⠀⡘⠎⢑⢋⡴⠀⠀⡄⣼⣤⠆⠀⢠⡞⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠹⣿⣞⡆⡀⠀⠘⢷⡄⠡⠈⠀
⠀⠀⠀⠀⠀⠀⣠⡼⠁⢰⢋⠀⢠⠁⠀⢦⣾⢷⣜⣈⣠⣿⣿⠀⣼⡿⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠹⣿⣷⠻⠀⠀⡼⠁⠀⢲⡃
⠀⠀⠀⠀⠀⠔⠛⠀⠀⡀⡞⡦⠃⠀⣰⣿⣯⣿⣿⣿⣿⣿⡇⣰⣮⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⢻⣿⠮⢤⠀⠐⡀⢠⠸⣟
⠀⢀⠄⠀⠀⡘⠀⠀⠀⢿⣄⠇⡆⠀⣿⣿⣹⣿⣿⣿⣿⣿⣂⠙⠓⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢻⢆⠎⠀⠀⣹⣿⡆⠈
⠀⠈⡔⠀⠀⠁⠀⠀⠀⢂⡿⠀⣷⢠⣿⣯⣿⣿⣿⣿⣿⣿⣿⠧⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣦⠁⢀⡞⡛⢿⠄
⢠⡸⠀⠀⠀⠀⢀⡃⠀⣿⢠⠀⢀⢫⢿⣏⣿⣿⣿⣿⣿⣿⡏⠀⠀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡢⠀⡁⠋⠘⢨
⢾⠁⠀⠰⢀⠀⠀⡇⠀⣷⠈⣼⠸⠾⢸⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠁⠀⢠⡿
⣮⣄⠀⡄⠀⠀⠀⡇⠛⡁⠜⠋⠀⠀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠠⠁
⠛⠉⠁⠀⠀⡇⠀⢹⣐⡀⠠⡖⡀⡄⣾⣿⣾⣽⡿⣿⣿⣿⡿⡣⠋⠀⠀⠀⣠⠀⠀⢀⠻⠇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⢧⠀⢀⠄⠀⠀⠀⠀⢪⣷⡜⣃⡇⢼⡿⠿⠿⣿⣿⣶⣽⡻⠞⣁⣤⣴⣞⠿⡿⠀⠀⢬⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⢠
⠆⢃⢈⢠⠀⢀⣀⣄⣧⠹⡅⠂⢿⣼⣿⡷⣶⣶⣦⣴⣾⡆⡇⠈⢿⣿⣿⣿⣾⠀⡇⣭⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⢠⣶
⠇⠈⡆⠁⠀⠀⢻⣿⠋⠳⣧⠀⢛⢻⣿⣷⢿⣿⣿⣿⣿⠰⠁⠀⠈⢿⣾⣟⡇⠰⣶⡅⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠿
⠀⠀⢧⠘⠀⠀⠀⠛⡄⠀⢸⣷⡄⢤⢙⣿⣧⡹⣿⣿⡇⠃⠀⢠⣐⠸⣿⡿⠿⠜⠚⠓⠀⠀⠀⣰⡆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠐⠀⠂⠀
⠀⡀⠈⡙⡀⠀⠀⠀⢹⡀⢹⣷⠘⡿⢃⣈⡙⠿⣷⡹⠁⠀⣰⣿⣿⣷⣿⣽⣗⠶⠀⠀⠀⠀⠰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀
⠀⠠⠀⠁⣿⣇⠀⠀⠀⣿⣿⣿⠦⠤⠬⠬⠉⠒⠌⠃⠀⢠⣿⣿⡿⣿⣿⣿⣿⣧⢂⠀⠀⡄⠲⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⢇⠀⡄⠃⠘⠈⡱⠀⠹⣿⡿⠁⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠀⠀⠀⢀⣰⠁⠀⠀⠀⡄⠀⠀⠁⢀⠀⠀⠀⠀⠄⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠘⠆⡀⠀⠀⡰⣇⠘⣷⡿⠁⠀⠀⠀⣴⣿⠃⠀⣀⣀⣀⣀⣀⢀⡀⣀⢀⡀⣀⢀⣀⣀⡀⠀⢶⠿⠋⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠐⣤⠀⠐⢽⣱⠀⠁⠀⠀⠀⣬⣭⡅⣰⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⢨⡄⠀⠁⠀⠂⠀⠸⢙⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠉⠁⡀⠒⠈⠀⠀⠀⠀⢠⣿⣟⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⣿⡀⠀⠐⠀⡀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣴⠈⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⡟⠀⠀⠀⠀⢀⠼⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠁⡀⢠⠀⠰⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡄⠀⠀⠀⠂⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠃⠀⠀⠀⠀⠀⠰⠟⠉⠀⠀⠀⠀⠄⠀⠀⠀
⠀⠀⠆⠀⢸⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀
⠀⠁⠀⠀⡈⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⡈⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠃⠀⠀⠀⠐⠀⠄⠈⠀⢠⠄⠀⠀⡄⠀⠀⠀