⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣹⡀⠀⠀⠀⠐⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⠀⢳⠀⢹⣧⠀⠀⠀⠀⠀⠙⣿⡤⠤⠔⠒⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⣧⠈⡇⠸⣿⠀⠀⠀⠀⠰⣄⡈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡖⠀⠸⢿⣿⣿⡀⣿⡆⣿⠀⣿⠀⠙⠂⠀⠀⠈⠻⣾⡆⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣶⣿⣿⡇⢀⡇⢸⡏⢹⣷⣿⣿⣼⠆⣿⠈⠁⠲⣦⣤⡼⣷⣜⣿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣰⡞⠀⠀⠀⢀⣾⣿⣿⡿⣷⣿⣥⢾⡟⠋⠻⡿⢸⣿⡆⣿⣒⣤⡀⢸⣯⢥⣬⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⢠⡂⠀⠀⢠⣿⣹⠀⢠⣞⣾⡟⣼⡿⣱⣿⠋⠁⣸⣷⣾⣿⣿⣾⠿⣷⣿⢻⢿⣿⡾⠐⡦⡘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣿⣇⠀⣰⣿⣟⡇⣦⣾⣿⣿⣡⡿⢡⡿⠃⠀⢰⣿⡟⢻⣿⣿⣷⣤⣟⠋⢸⠈⣿⢇⣸⢦⢱⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣭⣅⠈⠁⠀⠀⠈⠿⠁⣈⣿⡿⠋⠁⣧⡀⢸⠀⣿⠀⠙⣯⢀⢤⣯⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⡿⠀⢸⠰⠇⠀⠀⣧⠃⣼⡼⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏⢻⣿⡏⢻⣿⠟⣿⣿⣿⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠘⢸⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣠⠴⠺⣿⣿⡇⢸⣿⣷⡏⢁⣀⡘⣻⡿⠛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⣿⣿⣿⣤⣤⣤⣤⡀⠀⠀⠀⠀
⡄⠀⠀⢻⣸⠀⠀⢻⣿⣧⣸⣿⠇⠹⡄⠉⠉⠁⠀⠀⢇⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⢸⣿⠿⠬⠿⠛⠛⠛⠃⠀⠀⠉
⠈⠳⢄⡀⠻⡄⠀⠈⢿⠋⣿⣿⠀⠀⠘⣄⠀⠀⠀⠀⠈⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⣧⠀⣿⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀
⠀⠀⠀⠉⡒⠿⠦⠀⢸⡄⣿⡟⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⢀⣀⣠⣄⠀⠀⠀⠀⣿⣷⣿⡶⠁⠀⠀⠀⢻⣿⣽⠭⠅⠶⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠁⠀⠀⠀⠈⡇⣿⡇⡆⠀⡄⠀⠀⡟⠲⣄⡀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⢸⢐⠎⠙⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠃⡇⠀⠁⡇⠀⣧⠀⡠⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⠀⠀⠀⠀⠀⢸⠏⠀⠀⠘⣶⠦⢤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⡇⠀⠀⡇⠀⠈⠋⠀⠀⣧⣸⣟⠲⣤⣄⣀⣀⡤⠚⣿⣿⢸⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠳⣤⡈⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠀⠁⠀⠀⠀⠀⠤⣤⠀⠀⢸⣿⣿⣷⠏⠘⡅⠀⠀⠀⣿⡟⣸⢀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠁⠶⡄⢘⣿⣿⡟⠀⢑⢻⡀⠀⠀⣿⠇⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣄⣀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢇⠀⠀⠀⡄⠀⠀⠀⠀⠀⣼⣥⣹⠃⠀⠀⠻⢧⡀⢠⣿⢰⠧⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠃⠀⣀⠀⠀⢀⡿⢟⡟⠀⠀⠀⢀⣤⣉⣿⣿⣿⣤⣿⣆⠀⠀⠀⠀⠀⠀⡰⢫⠃⠀⢸⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣿⡆⠀⠀⠀⠀⢘⡠⠖⠉⢀⣼⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⢳⡀⠀⠀⢠⠊⢠⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⡠⠖⠋⢀⡖⠀⡞⣿⠀⠀⣠⠟⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣹⣄⣰⠁⢼⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡒⠀⠄⠀⣾⣿⣿⡠⠊⠀⠀⣰⡿⠀⢸⠀⢹⠀⣴⣣⢔⣻⣿⣿⣿⣿⣿⣿⡥⠖⣡⠖⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀