⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠳⢶⣶⡄⢀⣴⠟⠀⠐⠟⠉⢹⣆⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡽⠗⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣭⣁⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣽⠉⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠃⠀⠀⠀⠀⢀⣠⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⣤⣤⡴⠟⠻⠗⠈⠹⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠼⠋⠉⠦⣄⡰⣦⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠶⠛⠋⠉⠁⠀⠰⣶⣿⡀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠻⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡶⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡤⠀⠚⠾⠁⠀⠀⠀⠀⠀⠀⠈⠉⠿⠶⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣦⡀⣿⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⣉⠉⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣠⣤⣶⣦⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⣠⡟⠋⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡾⢋⠙⠛⠿⠿⠿⠿⠿⠟⠻⠾⢿⣀⠀⠀⠀⢶⡀⠐⢳⣤⢻⡆⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⡌⣿⣸⡏⠀⣶⠞⠉⠀⣀⣤⣴⣶⣿⣡⣧⣴⣤⣤⣤⡠⢄⣠⣤⣤⣶⡠⣍⡷⣶⣶⣾⣿⣤⣼⣿⣾⣇⠂⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⠿⠁⠀⠀⠀⠀⠀⠀⣰⡙⠷⣧⠀⠿⠾⢿⡛⢩⢐⢲⡌⠀⠀⠀⢸⣟⣀⣈⣉⣉⣉⣁⣀⣀⣉⣉⣁⣀⣀⣺⣆⢀⣀⣀⠉⢹⡃⠆⠀⠀⠀⠀⠀⠿⣄⠀⠀⠀⠀⠀
⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠰⣿⣴⣴⣤⣄⠀⠀⣸⡇⠀⠨⣼⢇⣠⡶⠶⣾⣿⣿⣿⣿⡛⣿⠛⢛⣋⣉⣩⣉⣉⣛⣿⡛⠋⢿⡉⠛⢫⣷⡜⡀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀
⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢀⣼⠇⠹⣧⣸⠏⠤⠀⣸⡏⢾⣧⠶⠿⢿⣬⣭⣽⣯⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⡷⢿⣶⣼⣧⡶⠾⠟⢿⡠⠀⠀⠀⠀⠀⠀⠘⠷⣄⠀⠀
⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢾⣧⣤⣴⠟⡡⠊⠀⠀⠛⠛⠋⠐⠒⠂⠒⠀⠉⠉⠑⠢⠒⠐⠈⠒⠐⠂⠒⠐⠂⠒⠁⠒⠂⠉⠛⠛⠳⠮⠑⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡀
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀