⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⡁⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢁⠀⠀⠀⠀⠀⣸⠟⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣿⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⡷⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⡄⠀⠀⠀⢴⠟⠛⠻⡗⠒⠒⠠⠄⣀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠇
⠀⠀⠀⠀⠀⠠⠔⠊⢡⢮⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢡⠀⠀⣠⡿⢀⠖⢄⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⢥⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣣⣟⠛⢘⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃⠈⠆⠀⣿⠡⠃⠀⠈⠢⣙⣆⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⠀
⠀⠀⠀⠀⠀⠀⢀⣿⠟⠁⡤⠋⠘⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠘⣼⣧⠁⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠈⢏⠢⢄⡀⠀⢸⠀
⠀⠀⠀⠀⠀⢀⣾⠃⡠⠊⠀⠀⠀⠨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⣨⡻⠃⠀⣀⣀⣀⣀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠈⢆⠀⠈⠒⢼⠀
⠀⠀⠀⠀⢀⢿⢃⢔⣡⣴⣶⣤⣄⡐⠾⢧⡀⠀⠀⠀⢀⠀⠀⠀⠘⣇⣼⠁⢠⠾⠒⣉⣩⣤⣴⣶⣶⣶⣶⣮⣷⣆⣀⠀⠀⠣⣀⡀⣸⠀
⠀⠀⠀⢠⢾⣤⣷⣿⣿⡿⠿⠿⣿⣿⣷⣦⣷⡄⠀⠀⠀⠢⠀⠀⠀⢹⠃⠀⠐⢶⣿⣿⡿⣿⣿⣿⣿⣿⠻⠿⣿⣿⣿⣷⢄⡀⠈⠻⣝⡓
⠀⠀⡰⠃⠸⣿⣿⠟⠁⠀⣇⢀⣼⣿⣿⣿⣿⡝⢷⡀⠸⡀⣱⡄⠀⠈⡇⠀⠤⠛⢹⣄⢀⣼⣿⣿⣿⣿⡗⠀⠈⢻⣿⠟⠀⠈⠑⠢⢽⡇
⠀⡰⠁⠀⠀⡟⢿⡆⠀⢺⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣆⢳⡏⢿⣄⠀⠸⡀⠀⠂⣼⣟⡉⣿⣿⣿⣟⢿⡗⠀⠰⠟⡯⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠹⡀⠙⠀⠀⣿⢿⣿⣿⣿⡿⣿⠀⠀⠀⠈⠻⣷⡀⠈⠛⢦⡱⡄⢠⢹⡿⣧⣿⣿⣿⡿⣿⡇⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⡄⠀⠀⠀⢳⡀⢡⢄⠑⡎⠻⠿⠟⢡⠃⠀⠀⠀⣀⣀⡈⠀⠀⠀⠀⠈⠛⠀⢆⢫⢌⠛⠒⢫⢠⠟⣴⠒⣮⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠹⣦⣀⠀⠀⣫⡀⠉⠑⠚⠶⠶⢶⡇⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⠳⡶⠾⣟⠀⣀⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡞⢡⡟⢳⢤⡀⢿⣀⠎⡠⡣⠊⡔⠙⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢁⢊⢔⠜⡡⢊⣮⠋⠀⢀⣤⠊⠀⠀⠀⠀⠀⠀
⠀⢸⢁⡿⠀⡷⠀⢹⡓⠻⠮⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠁⠔⠀⡼⢣⡤⡖⠉⡎⠀⠀⠀⠀⠀⠀⠀
⠀⡮⠻⡀⢴⡃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠁⢈⣧⣸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢣⠀⢳⠀⢇⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠂⠈⠒⠒⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢀⡏⠀⠀⠀⠀⠀⠀⡀⠀
⠀⠀⢧⡁⢿⠘⠃⠀⠈⠣⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⠀⣸⠇⠀⠀⠀⠀⠀⡔⠁⠀
⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⣇⠀⠀⠀⠀⢀⠎⢠⡶⠁
⠀⠀⠀⠉⠱⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⢎⡴⠏⠀⠀
⠀⠀⠀⠀⠀⡿⠓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢲⣤⣀⡀⠀⢀⣀⣀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⢀⣮⡞⠁⠀⠀⠀
⠄⠀⠀⠀⣸⣧⡀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⢸⡟⢿⡿⠛⣿⣧⠁⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢧⣀⣴⣺⠋⠀⠀⢀⡠⠖
⠘⡄⠀⣰⠟⠷⣍⠶⣄⠀⠀⣘⠉⠀⠀⠀⠀⠀⡟⠀⠈⠁⠀⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠒⣖⣾⣿⣿⣿⠘⡜⠘⠁⢀⣠⡶⣫⠖⠊