⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⣒⣬⡿⣿⣿⣿⣿⣿⣭⣕⣲⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡤⣪⡷⣿⣯⣿⣽⣿⣿⣷⣿⣿⠙⠛⠿⣿⣯⣶⣙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡴⣿⣾⣷⣭⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠛⢿⡋⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡞⣼⠿⠚⠿⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠉⠛⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠢⢼⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠀⠀⢀⣴⢶⣶⣤⣀⡰⠋⠀⣀⡀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⢯⠿⢲⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡟⡇⠀⣿⣿⣿⣏⣿⡟⣀⠔⠉⠀⠈⠙⠢⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡇⡇⢠⣿⣿⣿⣿⣿⠱⠇⠀⠀⠀⠀⠀⠘⢤⠀⠀⠀⢁⣠⢤⡒⢿⢿⠀⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣹⣇⢸⣿⠿⣯⣽⡿⠀⠀⠀⠀⠀⢀⣀⡠⣬⣄⠀⠀⠽⠶⠴⠟⠋⢠⣾⠃⠀⠀⠀⠀⠀⠀
⠀⠀⢰⡏⠉⢉⣀⣀⡀⣿⣿⡇⠀⣀⣠⠖⠋⠁⠈⢦⠝⠁⠀⠀⢀⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⣢⡀⠀⠀⠀⣷⣿⡇⢀⡆⠈⠉⠒⠒⠊⠁⠀⠀⠀⠀⠈⢦⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⡏⡕⣦⣀⣿⣿⣷⣾⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣀⡀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣧⡇⣿⣿⣿⣿⠇⢠⣏⡀⠀⠀⠀⠀⢠⡤⠤⢤⠴⣾⣻⡏⠁⢠⣿⣯⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⠀⢸⣿⣿⣦⣀⡀⠀⠀⠙⢿⡛⠻⢿⣿⠃⠀⣾⣟⣿⣳⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣿⣇⣿⣿⣇⣿⡆⠈⢿⡿⠋⠳⣌⣢⢄⣀⠀⠉⠙⠉⠀⠀⡜⢹⣾⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣻⣟⣿⣿⣿⣿⡇⠀⠊⢀⠴⠋⢈⣿⡇⠹⣿⣶⣦⣤⣤⣾⣧⢸⡏⢱⣿⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡜⣿⣿⣿⢻⡏⣿⣿⣄⠀⠀⠀⠊⠁⡈⡧⠀⠀⠙⢿⡉⠉⢉⠏⢹⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣿⣿⣿⣿⣸⣿⣿⣿⣟⠳⡀⠀⠀⠈⠳⡁⠀⠀⠀⠀⢻⠴⠋⠀⢸⣿⠿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣼⣿⣿⣿⡏⢹⣟⣿⣿⡀⠱⡄⠀⠀⠀⠹⣤⡤⠒⠊⠁⠀⠀⠳⣸⠏⠀⢟⡄⠀⠀⠀⠀⠀
⠀⠀⠀⣏⣿⣿⣿⣿⠀⠉⢻⣯⢿⡗⠒⠙⢆⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠘⣵⡀⠀⠀⠀⠀
⠀⠀⢰⢹⢿⣽⡻⢿⣆⠀⠀⠹⣾⣿⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⣀⡠⠤⠒⢲⣘⡄⠀⠹⣵⡀⠀⠀⠀
⠀⠀⡟⣿⣿⣿⣥⣨⣹⣆⠀⠀⠈⠻⣇⠀⢸⠀⠀⢸⣤⠔⠒⠉⠁⠀⠀⠀⠀⢸⡗⠀⠀⠘⣷⡀⠀⠀
⠀⢰⣱⣿⣿⣿⠀⣨⣿⣿⣆⠀⠀⠀⢹⠀⢸⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢀⡞⣷⡀⠀⠀⠘⣷⡀⠀
⠀⣎⣿⢿⣿⣿⣀⣇⠀⣿⣿⡄⠀⠀⢀⢷⡷⡀⠀⠀⣿⢧⠀⠀⢀⣠⠤⠒⠋⢀⣿⠱⣄⣀⡀⠘⣷⠀
⢀⢿⣯⣿⠀⠀⠀⠀⠀⣟⣻⣿⠀⣰⣥⠤⡇⠈⠛⠉⣿⠚⠋⠉⠁⠀⠀⠀⠀⢸⣿⠊⠉⠀⠀⠀⢸⡇
⢸⣾⡿⣿⠀⠀⠀⠀⠀⣯⣿⣿⣷⣹⣡⢻⠁⠀⠀⠀⣿⢦⡀⠀⠀⠀⢀⡠⠚⠁⠈⢳⠀⠀⠀⣠⣾⠇
⣟⣿⣶⡏⠀⠀⠀⠀⠀⠉⠙⠛⣻⣷⣷⣹⠀⠀⠀⠀⣟⠀⠉⠒⠒⠊⠁⠀⠀⠀⢀⣸⣴⡶⠛⠉⠀⠀
⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠂⣼⣿⣏⠉⠇⠀⠀⠀⣇⠀⠀⠀⠀⣀⣤⡴⣶⣾⣿⢿⠁⠀⠀⠀⠀⠀
⠘⣟⣛⣷⣶⣦⣤⣤⣤⣤⣤⣤⣮⣯⣽⣶⣄⣀⣀⣠⣟⣙⡒⣛⣉⣁⣀⣀⣹⣘⣿⣾⠀⠀⠀⠀