⠀⠀⠀⠀⣿⡄⠀⠀⠀⣿⠀⠀⠀⢠⣿⡄⠀⠀⠀⣤⣿⠿⠛⠁⠀⠀⠀⠀⠀⣠⣶⣆⠀⠀⣶⣶⣶⣶⣶⣶⣶⠀⠀⣴⣶⣶⣦⡀⠀⠀⣶⠶⠶⣦⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⠀
⠀⠀⠀⠀⣿⠳⡄⠀⠀⣿⠀⠀⠀⡿⠘⡿⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡇⣿⡄⠀⠀⠀⠀⣿⡇⠀⠀⠀⢰⡿⠁⠀⠘⣏⣷⠀⠀⣿⠀⠀⢸⡇⠀⣼⣿⠏⠁⠀⠈⣿⡄
⠀⠀⠀⠀⣿⠀⠘⣆⠀⣿⠀⠀⢰⡇⠀⣿⠀⠀⣿⡇⠀⠀⣀⣀⣀⠀⠀⢰⣿⠇⠀⣿⣇⠀⠀⠀⢸⣿⠀⠀⠀⢸⣧⠀⠀⠀⠀⢸⣿⠀⢸⣧⣤⡿⠃⠀⢸⣿⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⣿⠀⠀⠀⣇⣿⠀⠀⡼⠻⠶⠾⡆⠀⢹⣇⠀⠀⠈⠙⢻⡇⢠⣿⡟⠛⠛⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⢻⣧⡀⠀⠀⢀⣿⠀⠀⣿⠛⣿⣆⠀⠀⢻⣧⡀⠀⠀⢰⣿⡟⠀
⠀⠀⠀⠀⣿⠀⠀⠀⠸⣿⠀⣸⡇⠀⠀⠀⣿⡇⠀⠘⢿⣶⣤⣴⠟⠀⢸⡟⠀⠀⠀⠀⣿⡆⠀⠀⢸⣿⠀⠀⠀⠀⠘⢿⣿⣾⠿⠋⠀⠀⣿⠀⠀⠛⣿⣆⠀⠈⠻⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⢒⣒⣻⣿⣿⣟⣓⣒⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⣿⡿⢹⣷⣄⡿⠿⠉⠀⣰⠟⠉⠈⠀⠀⠻⣽⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢱⣿⡇⢸⣿⣿⣤⣤⣨⡾⠋⠀⠀⠀⠀⠀⠀⠈⠹⣦⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡧⠼⠋⠉⠉⠈⠁⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣰⠃⠹⢶⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣶⣼⣿⣿⠶⣤⡀⡄⢠⡀⡀⢀⣧⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⣿⣶⣾⣿⣷⣸⣷⣻⣼⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⣿⣿⣿⣿⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢰⡟⠉⢀⣍⣛⢷⣆⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠸⡀⢰⣿⡿⣿⡏⠻⠀⠀⣾⢸⣿⡏⣀⣄⣀⣀⣿⢿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿⠀⠁⢸⣿⡶⢻⡇⠀⠀⠀⣿⢸⠟⢨⣿⣽⣿⣍⠙⠻⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡿⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠀⢰⣟⡉⣺⣿⠀⠀⣻⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣽⠁⠀⠀⠀⠀⢰⣄⣀⣀⡀⠀⠀⠀⠀⠸⢿⣏⣹⠏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⣼⡯⠟⠛⠛⠓⢦⣄⣠⡄⠀⠀⠈⠁⠀⣼⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⡀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠁⣽⣿⣿⣿⣿⣿⣿⣿⡿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠉⠉⢳⡄⠀⠸⡆⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢠⣿⣿⣿⣿⠇⣰⣿⣿⣿⣿⣿⣿⣿⡏⢧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠻⠀⠀⠀⠀⣹⣦⡀⢷⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⠇⢸⠀⠀⠀⣼⣏⣾⣟⣾⣧⣀⡀⣀⡴⢋⣀⣀⣤⣤⢴⣿⣿⣿⣿⡿⠁⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣿⡏⢀⡏⡇⢀⣾⣿⣿⣯⣿⢿⡟⣿⡫⣿⠻⠿⣟⠛⠋⠀⣼⣿⣿⣿⣿⢧⡾⠁⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⣿⡏⠀⡼⠗⠛⠛⠉⠙⣿⡟⠁⡞⠀⢳⣦⡿⡆⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋⠀⣴⠟⣡⡿⠛⣿⣿⣿⣿⣿⣿⣧⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⡿⠀⣴⠃⠉⠉⠉⠑⡄⣿⠀⡼⢁⡖⠘⣿⠁⠁⣀⡴⠊⢡⣿⣿⣿⣿⣿⠀⠀⣼⠃⣠⠇⢀⣾⠏⠁⠀⠈⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⠃⣰⠇⠘⠋⠉⠛⣆⡳⠋⢻⣧⡿⢋⣿⡋⠙⠻⣷⢦⠀⡼⣿⢻⡇⢰⡇⠀⣸⠋⣸⠃⢠⡾⠁⠀⠀⠠⣄⣀⣹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢏⡏⢀⡇⠠⠴⠶⢶⡆⣻⣇⣤⠞⢽⣧⢯⡀⠙⠶⣄⠈⢹⠀⣿⣇⣿⠀⣿⠀⢠⡇⣠⠁⢠⡟⢁⡠⢶⣿⠀⠀⠈⢻⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⠁⢸⡁⠠⣦⣤⣋⡹⠙⠀⢸⢠⡤⢧⡀⠙⢦⡀⠘⡄⠘⣧⣿⣿⢻⢸⡿⢠⣿⣶⣿⣦⣼⡵⠋⠀