⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⡞⡏⡅⠀⢠⡟⣹⣏⠻⣄⠀⠘⢿⣿⡲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⡾⠋⣸⣿⣿⠀⢸⢁⣿⠙⢷⣌⢳⡀⠈⢿⣷⡲⡝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⣠⣶⣿⣿⠇⢀⣏⣾⠏⠀⠀⠹⣆⢳⡀⠘⣧⣧⡙⢦⣽⡲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⡟⠀⣰⡿⡿⣱⠋⣠⣿⡿⣿⠟⢷⣄⠀⠸⡄⢧⠀⢿⢸⢧⠀⠹⣿⣿⣿⣿⣒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡞⠀⣴⢋⣞⣙⣁⣴⠟⡏⣼⠃⠀⠀⢿⣆⠀⢻⣸⡄⣸⢸⣿⣆⠀⢿⣷⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠃⣸⠇⣼⠀⠀⣿⡀⢀⡇⡟⠀⠀⠀⠈⣿⡄⢸⣿⠇⡟⡞⠙⣿⢦⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⣿⠀⣿⡄⢸⡿⢿⣼⣿⡇⠀⠀⠀⠀⣿⡇⡾⣿⣦⠿⣿⠀⢹⢿⣷⣼⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡇⢸⣿⠀⣿⣧⣾⣷⣶⣿⣿⣿⡀⠀⠀⢀⣿⣿⣿⡿⣿⡆⢸⡄⢸⢸⡌⠛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⣧⢸⢿⡄⣿⣿⡿⢔⣒⡺⣿⣍⠓⠀⣠⢾⣿⣗⣒⣀⣸⣿⣼⡇⢸⠈⣇⣄⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⣿⢿⣸⢸⣇⣇⠩⠟⠛⠛⣻⢿⡿⠀⠀⡇⠘⣟⠿⠭⠉⠙⠛⠙⣇⣼⢰⣿⢸⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⡿⢸⠟⢸⣿⣿⡆⠀⠀⢀⣤⡞⠁⠰⠶⡷⠦⡌⠳⣄⠀⠀⠀⠀⣿⣇⡏⡟⢸⣷⣮⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⣿⡇⢸⠀⢸⣿⣿⣿⠀⠀⠉⠉⠀⠀⠀⠀⢻⠀⠀⠀⠙⠒⠶⢦⣄⣿⣿⠇⡇⣿⣿⡌⠛⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡄⢸⣿⡙⠛⣧⠀⠀⠀⠀⠀⣶⡦⣾⣶⠀⠀⠀⠀⠀⠀⠈⠉⣿⠀⢡⡟⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢻⡇⢸⣿⣇⠀⢻⣆⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⣸⠃⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡟⣷⣿⣿⣿⡆⢤⣿⡆⠰⢷⣖⣶⡷⠛⠻⣿⡾⠆⠀⠀⠴⣾⣿⣿⣠⡏⣧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡇⣿⣿⣿⣿⣿⣏⠈⣿⡀⠀⠈⢩⣉⣩⣍⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⣿⣆⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡀⢸⣿⣿⣿⣿⢿⣷⣼⣷⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀⣾⡟⣿⣿⣿⣿⠀⣿⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡇⢸⣿⣿⣿⣿⡇⠹⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠁⣿⣿⣿⣿⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠟⣿⣿⣿⣿⢿⡀⠹⣏⠻⢿⣦⣤⣤⣤⣶⡿⠋⣸⠃⢸⣿⣿⡿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣾⡿⠹⣧⠀⢻⡄⠀⠉⠉⢉⣸⡿⠀⢠⠏⠀⣼⠀⠻⣷⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⣤⣶⣿⣿⣿⣧⣀⠙⣆⠀⢳⡀⠀⢶⣿⡿⠁⠀⡾⠀⣰⠏⣠⣴⣿⣿⣿⣿⣷⣶⣤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⣾⣿⣿⠏⢻⣿⣿⣿⣿⣿⣿⣿⣦⣽⣧⠈⣧