⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠟⠿⠿⠿⠿⠿⠿⠿⠿⠻⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠟⡿⣾⣶⣤⣤⣀⣀⣀⠀⣿⣿⠀⣀⣀⣀⣤⣤⣶⣷⢿⠻⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡿⣾⣿⣹⢀⠀⠀⠀⠀⠀⠉⠉⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⣏⣿⣷⢿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣴⣠⠀⣆⣿⠻⠀⠀⠀⣧⣿⣾⣶⣴⣤⣤⠀⠀⠁⣿⣿⠿⠛⠙⠟⣿⣰⠀⣄⣦⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠟⣿⣴⢀⠀⠀⠁⠛⡿⣿⢰⠀⠀⡄⣿⢹⠀⠀⠀⠀⠀⠀⡏⣿⢠⣀⣄⣦⣿⢠⠀⠀⠀⠀⡀⣦⣿⠻⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠋⡿⣾⢀⠀⠀⠁⠟⣿⣴⣠⠀⠀⠀⠀⠀⣧⣿⠘⠀⠀⠀⠀⠃⣿⣼⠀⠀⠀⠀⠀⠀⠀⠋⠻⠈⠀⠀⡀⣷⢿⠙⠀⠀⠀⠀
⠀⠀⠀⠏⣿⣻⠙⠈⠀⠀⠀⣄⣷⢿⠙⠀⠀⠀⠀⠀⡄⣿⢻⠀⠀⠀⠀⡟⣿⢀⠀⠀⠀⠀⠀⠋⡿⣾⣦⣿⠹⠀⠁⠋⣟⣿⠹⠀⠀⠀
⠀⠀⠏⣿⣰⣄⣦⣿⠿⠛⠀⠀⠀⣄⣷⢿⠙⠀⠀⠀⠀⣇⣿⠛⠛⠛⠛⣿⣸⠀⠀⠀⠀⠋⡿⣾⣠⠀⠀⣄⣿⢿⣿⣴⣠⣆⣿⠹⠀⠀
⠀⠃⣿⣸⠀⠀⠁⡿⣾⢀⠀⠀⠀⠀⠀⣄⣷⢿⠙⠟⡿⣾⣿⣿⣭⣭⣿⣿⣷⢿⠻⠋⡿⣾⣠⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⣇⣿⠘⠀
⠀⡿⣿ ⠀⠀⠀⡟⣿⢩⠀⠀⠀⠀⠀⠀⠀⠁⣟⣿⣿⢛⠿⣿⣿⣿⣿⣿⣿⠿⡛⣿⣿⣻⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠀⠀⠀⣿⢿⠀
⠇⣿⢸ ⠄⣤⣦⣶⣷⢿⠿⠻⠛⠙⠉⡿⣾⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣷⢿⠉⠋⠛⠟⠿⣿⣾⣶⣷⣿⠘⠀⠀⡇⣿⠸
⡇⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⣀⠀⠀⠀⡆⣿⢸⠀⠀⡆⣿⢸
⡇⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸
⡇⣿⠘ ⠀⠀⡇⣿⠘⠀⠀⠀⠁⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢸
⡆⣿⢸ ⡄⣿⢿⠿⡿⣿⣶⣴⣤⣠⣀⣿⢿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡿⣾⣀⣄⣤⣦⣶⣿⢿⠿⠻⠛⠀⠀⠀⡇⣿⢰
⠀⣷⣿ ⠀⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⣯⣿⣿⣬⣶⣿⣿⣿⣿⣿⣿⣶⣥⣿⣿⣽⢀⠀⠀⠀⠀⠀⠀⠀⣃⣿⣼⠀⠀⠀⣿⣾⠀
⠀⡆⣿⢹⠀ ⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠋⡿⣾⣠⣦⣷⢿⣿⣿⣛⣛⣿⣿⡿⣾⣴⣄⣷⢿⠙⠀⠀⠀⠀⠀⠁⡿⣾⢀⠀⠀⡏⣿⢠⠀
⠀⠀⣆⣿⠹ ⠋⠟⣿⣷⢿⠙⠀⠀⠋⡿⣾⣠⠀⠀⠀⠀⡏⣿⣤⣤⣤⣤⣿⢹⠀⠀⠀⠀⣄⣷⢿⠙⠀⠀⠀⣤⣶⣿⠻⠙⠏⣿⣰⠀⠀
⠀⠀⠀⣆⣿⣽⣠⢀⠀⣦⣿⠻⡿⣾⣠⠀⠀⠀⠀⠀⠁⣿⣼⠀⠀⠀⠀⣧⣿⠈⠀⠀⠀⠀⠀⣄⣷⢿⠙⠀⠀⠀⡀⣄⣯⣿⣰⠀⠀⠀
⠀⠀⠀⠀⣄⣿⢿⠈⠀⠀⡀⣧⣤⠀⠀⠀⠀⠀⠀⠀⡟⣿⢠⠀⠀⠀⠀⡄⣿⢻⠀⠀⠀⠀⠀⠋⠟⣿⣴⢀⠀⠀⠁⡿⣿⣠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⣦⣿⠻⠈⠀⠀⠀⠀⠃⢿⠻⠙⠉⠃⣿⣸⠀⠀⠀⠀⠀⠀⣇⣿⠘⠀⠀⠇⣿⣾⣠⢀⠀⠀⠁⠟⣿⣴⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⠻⠙⠀⠏⣿⣴⣄⣦⣶⣿⣿⢀⠀⠀⠛⠛⠛⠿⡿⣿⢿⠀⠀⠀⣦⣿⠹⠀⠋⠟⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⢿⣿⣹⠈⠀⠀⠀⠀⡀⠀⠀⠀⣿⣿⣀⣀⣀⠀⠀⠀⠀⠀⠁⣏⣿⡿⣾⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣷⢿⠿⠛⠛⠉⠉⠉⠀⣿⣿⠀⠉⠉⠉⠛⠛⠿⡿⣾⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⣴⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀