⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⣀⡠⠤⠒⠂⠉⠉⠉⠓⠒⠢⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠰⢄⠀⠑⢦⡀⠀⠀⠀⠈⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⡴⣄⠰⣔⣦⡀⠳⣦⡀⠈⢢⡀⠱⣄⠀⠙⢦⡀⠀⠀⠈⢦⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⠋⠀⠀⠀⠀⠀⣼⠃⠈⢧⡘⣿⡷⣄⠹⣷⣄⠀⠙⢆⠈⢧⠀⠀⠹⣦⡀⠀⠀⢧⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣰⠇⠀⠀⣴⠇⠀⣠⠿⡇⠀⠀⠳⡘⣿⣎⠳⡌⢿⡦⡀⠀⠑⡄⠱⡄⠀⠘⢿⣆⠀⠈⢇⢂⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⡟⢰⠀⢸⠻⠀⠀⡿⠀⣷⠀⠀⠀⠹⡜⡝⢦⠘⢦⠻⣝⣆⠀⠈⢦⠘⣆⠀⠈⢿⣆⠀⠘⡌⠄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢁⡏⠀⣇⡀⠀⢸⡇⠀⢹⡀⠀⠀⠀⠘⣾⢌⠳⡀⠳⣟⣦⣷⣄⠀⠱⡘⢆⠀⠈⢿⡄⠀⢱⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀
⡏⢸⡇⢠⠘⢡⠀⢸⡇⠀⠘⡇⠀⠀⠀⠀⠈⢿⡄⠘⢆⠙⢾⣿⣾⣧⡀⠘⢌⣆⠀⠸⡹⡄⢈⡄⡆⢡⠀⠀⠀⠀⠀⠀⠀⠀
⡇⢸⠀⢸⢰⠸⡀⠸⡇⠀⠀⢹⡄⠀⠀⠀⠀⠈⢿⡄⠀⠑⢌⠋⠻⣿⣙⢦⡈⢻⡆⠀⢳⢻⡼⡇⢰⣸⡀⠀⠀⠀⠀⠀⠀⠀
⡇⢸⠀⣿⠐⡀⡇⢸⡇⠀⠀⠀⠳⡀⠀⠀⠀⠀⠈⢷⠀⠀⢀⡱⠖⠋⠛⢧⡉⠢⣿⡀⠸⡞⣷⣧⢸⣷⣧⠀⠀⠀⠀⠀⠀⠀
⣧⢸⡆⣿⢠⣇⢹⠈⣷⠀⠀⠀⣀⠵⠤⠤⠤⠀⠀⠈⢧⠀⠉⠀⠀⠀⠀⠀⠉⠂⠀⡇⠀⡇⣿⡟⢸⡇⠙⣆⠀⠀⠀⠀⠀⠀
⣿⡈⣿⣏⢸⠛⡌⣧⢹⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢔⣒⣒⣒⣦⢸⠀⡇⣿⢿⣾⡇⠀⠈⠀⠀⠀⠀⠀⠀
⣿⡇⢻⣿⠸⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⠋⠉⠉⠉⠁⣾⠀⡇⣿⣯⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢹⡸⣿⡆⢧⢸⣿⣿⡹⡄⣠⣤⣾⣿⠿⠿⣦⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠀⢧⡟⠂⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢹⢸⣧⠸⣧⢰⣾⡙⣿⡧⠈⢻⡿⠉⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠈⣿⢷⡹⣿⠻⢭⡛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⢀⣤⠂⠀⢸⢸⣼⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⣿⠀⢿⣾⡟⠜⢿⣌⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣠⣤⣶⠿⡿⠛⠀⠀⢸⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⢹⠀⢸⣿⣿⡦⣈⠻⣒⠷⡄⠀⠀⠀⠀⢶⣒⣊⡭⠟⠛⠉⣁⠤⠊⠁⠀⠀⢠⣾⡗⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠀⢸⠀⢸⣿⣿⣿⡈⢻⡾⣭⣙⣦⡀⠀⠀⠀⠈⠉⠉⠉⠩⠭⠔⠋⠁⠀⣠⣴⡏⢈⠹⣿⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⢿⣧⠀⣷⠘⣇⠈⠻⣗⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠇⢸⠀⠹⣿⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⣿⢸⣿⠀⣸⠀⢹⠀⠀⢻⣿⠈⠻⣿⠷⣶⣶⣶⣶⣾⣿⣿⣿⣷⡃⢨⣇⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⢸⣿⣴⡿⠀⡼⢠⡄⠈⣿⠀⠀⠹⣧⠀⠉⠉⠹⣿⣿⣿⠸⣯⡻⣜⣟⠟⠒⠒⠛⠀⣀⡤⠤⣄⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⣴⠛⢁⢃⠜⡿⡄⢀⡴⣿⡆⠀⠀⠀⠀⠀⠀⠀⢻⣭⡭⠭⠔⠚⠿⣿⡻⢵⡄⠀⠀⢃⠉⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠐⠋⠉⠙⠓⢗⠳⢲⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠉⣩⠟⠛⠃⠀⢱⠈⠢⠙⠀⠀⠀⠀⠀⠀