⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠛⠛⠟⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠿⠿⠛⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⠀⠀⠀⠀⢀⠀⠐⡄⠀⢀⡄⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⢱⡀⡇⣰⠏⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⢀⣿⣿⠄⢀⣀⣤⣤⣤⣛⣛⣋⣤⣤⣤⣄⠀⢿⣿⡇⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣤⣄⣴⣿⡿⡋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⡻⣿⣦⣀⣠⣤⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠛⠋⢈⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⡈⠻⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣀⠉⠉⠉⠛⢿⣿⣿⣿⡿⠛⠉⠉⠻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⢙⠉⡋⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⣿⣿⣿⣷⣄⡀⠀⠀⢀⣸⡿⠧⠀⠀⠀⣀⣠⣾⣿⣿⣿⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣛⣿⣿⣿⣿⣿⣫⣶⣿⡟⠉⠁⠀⠉⠙⢿⣶⣮⡻⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇
⠀⢻⣿⣦⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣧⣄⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣼⣿⠏⠀
⠀⠈⢿⣿⣿⣄⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⢿⢿⢿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⡿⠿⠿⠿⠛⠛⠉⠀⠀⢀⣴⣿⣿⡟⠀⠀
⠀⠀⠈⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠲⢩⡍⣽⠛⠛⣻⠍⣭⠱⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠀⠀⠀
⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡆⠀⠈⠀⠙⠀⠀⠙⠀⠁⠀⢀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢹⣷⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣼⡟⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⢿⣧⡑⢿⢀⣦⠀⠀⣴⠀⡾⠜⣰⡿⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣦⣀⠀⠀⠈⠻⣿⣶⣦⣬⣤⣤⣥⣶⣶⣿⠟⠁⠀⠀⣀⣴⡿⢛⣽⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⣀⣴⣾⠟⣉⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣝⡻⢿⣶⣄⡀⠀⠀⠀⠀⠀⣀⣴⡾⠟⣉⣴⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠙⠻⣿⣿⣶⣬⣙⠻⢷⣦⣄⣀⠛⠛⠁⣴⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣶⣬⣉⠛⠿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⠀⢤⣴⣾⠿⠛⣁⣠⣍⡛⠻⢿⣿⣶⣦⣬⣉⡛⠻⠿⣿⣶⣶⡦⣀⣴⣿⠟⠀⠀⠀⠀⣀⣀⡀⠀⠀
⠀⠀⠀⠀⢀⣠⣴⣄⠀⣤⣶⣶⣦⢿⣿⣿⣧⠀⣠⣶⣿⡿⠟⠛⠉⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣶⣶⣤⡄⢾⣿⣿⢃⣾⣿⣿⣿⣿⢨⣿⣿⡄⠀
⠀⠀⠀⠀⣿⠟⠿⠏⠸⠿⠿⠿⠟⠘⢿⣿⣿⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠃⢸⣿⡟⠀⠛⠛⠛⠋⣁⠹⣿⠟⠀⠀
⠀⠀⠀⠀⠈⠛⠚⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣿⡿⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠛⠛⠟⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠿⠿⠛⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⠀⠀⠀⠀⢀⠀⠐⡄⠀⢀⡄⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⢱⡀⡇⣰⠏⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⢀⣿⣿⠄⢀⣀⣤⣤⣤⣛⣛⣋⣤⣤⣤⣄⠀⢿⣿⡇⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣤⣄⣴⣿⡿⡋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⡻⣿⣦⣀⣠⣤⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠛⠋⢈⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⡈⠻⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣀⠉⠉⠉⠛⢿⣿⣿⣿⡿⠛⠉⠉⠻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⢙⠉⡋⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⣿⣿⣿⣷⣄⡀⠀⠀⢀⣸⡿⠧⠀⠀⠀⣀⣠⣾⣿⣿⣿⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣛⣿⣿⣿⣿⣿⣫⣶⣿⡟⠉⠁⠀⠉⠙⢿⣶⣮⡻⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇
⠀⢻⣿⣦⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣧⣄⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣼⣿⠏⠀
⠀⠈⢿⣿⣿⣄⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⢿⢿⢿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⡿⠿⠿⠿⠛⠛⠉⠀⠀⢀⣴⣿⣿⡟⠀⠀
⠀⠀⠈⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠲⢩⡍⣽⠛⠛⣻⠍⣭⠱⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠀⠀⠀
⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡆⠀⠈⠀⠙⠀⠀⠙⠀⠁⠀⢀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢹⣷⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣼⡟⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⢿⣧⡑⢿⢀⣦⠀⠀⣴⠀⡾⠜⣰⡿⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣦⣀⠀⠀⠈⠻⣿⣶⣦⣬⣤⣤⣥⣶⣶⣿⠟⠁⠀⠀⣀⣴⡿⢛⣽⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⣀⣴⣾⠟⣉⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣝⡻⢿⣶⣄⡀⠀⠀⠀⠀⠀⣀⣴⡾⠟⣉⣴⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠙⠻⣿⣿⣶⣬⣙⠻⢷⣦⣄⣀⠛⠛⠁⣴⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣶⣬⣉⠛⠿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⠀⢤⣴⣾⠿⠛⣁⣠⣍⡛⠻⢿⣿⣶⣦⣬⣉⡛⠻⠿⣿⣶⣶⡦⣀⣴⣿⠟⠀⠀⠀⠀⣀⣀⡀⠀⠀
⠀⠀⠀⠀⢀⣠⣴⣄⠀⣤⣶⣶⣦⢿⣿⣿⣧⠀⣠⣶⣿⡿⠟⠛⠉⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣶⣶⣤⡄⢾⣿⣿⢃⣾⣿⣿⣿⣿⢨⣿⣿⡄⠀
⠀⠀⠀⠀⣿⠟⠿⠏⠸⠿⠿⠿⠟⠘⢿⣿⣿⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠃⢸⣿⡟⠀⠛⠛⠛⠋⣁⠹⣿⠟⠀⠀
⠀⠀⠀⠀⠈⠛⠚⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣿⡿⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣠⣤⣾⣿⠃⣿⠃⢸⠟⠻⣿⣿⣿⣿⣇⠀⠀⠀⠘⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠿⠛⠙⠛⠻⢶⡄⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠿⡿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣤⣌⣀⡇⢻⣿⣿⣿⣿⡆⠀⠀⠀⢻⣷⠀⠀⢹⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣰⣾⡿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀
⠗⠀⠀⣴⣿⣿⣿⣷⣤⣄⣉⠛⢿⣿⣷⣼⣿⣿⣿⣿⣷⠀⠀⠀⠘⣿⣧⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣼⢯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣟⣿⠟⠁⠀⠀⠉⢿⣷⣆⠙⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡟⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⢸⣟⣾⠁⠀⠀⠀⠀⠀⠈⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣤⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠏⢻⡇⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⠿⠿⡟⣛⣭⣭⣶⣿⡿⣟⣯⣶⡿⠟⠋⠀⠀⠈⢿⡄⠈⢷⣤⡀⠀⠀⠤⠔⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⢟⣛⣿⡿⠷⠿⠛⠋⠁⠀⠀⠀⠀⢀⠀⠈⢿⣄⠀⠈⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⣯⠻⣧⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠙⠛⠟⠿⠿⠿⠟⠻⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠻⣿⡻⣶⣤⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣦⠉⠻⣶⣤⣴⣶⣿⢿⣟⣵⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡹⣷⣾⣿⣿⠛⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣴⣿⣷⣾⣿⣿⣿⣿⣿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡘⠿⢿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠟⠛⣻⣿⠿⠛⢹⣿⣿⣵⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢢⣴⣾⡿⠷⠶⠶⣦⡀⠀⠀⠀⠀⠘⢷⠀⠀⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠐⠿⠁⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢷⣿⣿⣋⠀⠀⠀⠀⠈⠻⣦⢰⡄⠀⠀⠘⣧⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢟⣿⡿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠙⢷⡀⠀⠀⣿⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡀⢰⠀⠀⠀⠀⠀⢠⣿⣯⡏⣷⣆⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⣀⣤⣾⣿⡟⢙⠋⠀⠀⣀⢀⠀⠀⠀⠀⠀⠘⣷⠀⣠⠏⢀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⣷⣸⣆⠀⠀⢀⣠⣾⣿⣿⣿⢿⠛⠿⣶⣦⣀⣀⠀⠀⠻⣦⣿⣴⣾⡟⠻⢿⣿⠟⣛⣤⣶⣶⣿⠿⠷⢶⡄⠀⠀⠀⢿⡦⠏⠀⢈⡀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠹⣿⡿⠷⠿⠛⠉⠀⠸⣿⣷⢸⡀⠀⠀⠈⡉⢻⣿⣿⣾⣿⠛⠛⢿⣿⡟⠉⠀⣾⡋⠙⣿⣻⣯⣴⣾⡿⠃⠀⠀⠀⣸⠁⠀⠀⢸⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⣠⣭⣿⣿⡿⢿⡏⠀⠀⠀⣿⡅⠀⠈⠛⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣶⠚⢻⣧⣿⣿⣤⣾⣧⠀⣀⣴⡿⣿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⡇⠀⠀⣾⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣿⡿⢦⣀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠉⠉⠛⠛⠛⠋⠀⢠⣿⡟⠉⠀⠀⠳⢶⡈⠉⠛⠛⠛⠻⠶⢶⣤⣄⠀⠀⠀⠋⠀⡇⠀⠀⣿⣿⠿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⠁⠀⠉⠛⠷⠶⠶⠖⠛⠉⢻⡇⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣀⢀⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣄⠀⢠⡇⠀⢀⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⠀⠀⠀⢀⣠⠾⠋⠀⢠⣴⣾⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠐⠀⠈⠛⣶⣾⢀⣠⠞⢻⡇⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣍⡻⣿⣷⣶⣶⣶⣶⣾⣿⡿⠿⠋⣿⡆⣠⡞⠋⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠿⠛⠁⠀⣸⡇⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠳⣶⣿⣿⣿⣿⣯⣭⣶⣶⣚⣿⣿⣿⡋⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣿⣿⡭⠽⠟⠋⠉⠉⠉⠀⠉⠻⣦⣀⠀⠀⠠⠀⠀⠙⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⡟⠀⠀⠀⠀⢠⢸⣿⡇⠀⠀⠀⠀⠀⢻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⣸⣯⣧⣤⣀⠀⢀⣀⣀⣀⣠⣄⣀⣨⣿⣷⣦⡀⡆⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣾⠿⢷⣿⡇⠀⠀⠀⠀⣏⣾⡟⢻⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⣴⣶⣶⡴⠶⠟⣛⣯⣿⡿⠷⠶⢾⣿⠁⠀⠀⢻⠁⠀⠀⠀⠈⣿⡟⠀⢸⣇⠤⣤⣤⣤⣧⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽⣿⣿⠉⠉⠀⠈⠉⠁⠀⠀⢀⣠⣶⣿⠏⠀⠀⠀⠀⠀⠀⠀⣀⣼⡟⠀⠀⢸⣿⡀⠀⠀⠀⠉⠛⠶⣤⣀⣀⡤⠖⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣦⣤⣤⠤⣤⣶⣾⣯⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⣼⣻⣿⠀⠀⠀⠘⢿⣿⢦⣄⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡎⠉⢛⣛⡿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣘⣵⣿⣷⠀⠀⠀⠀⠸⣿⣷⣍⡣⣄⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⣀⣀⣀⣀⣀⣤⣶⠿⠛⠛⢿⣔⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣺⣾⡿⠿⢻⣷⠀⠀⠀⡇⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠛⠋⠉⣭⣿⠟⠉⠁⠀⠀⠀⠀⣠⣿⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣿⠟⠁⠀⠀⠀⣿⡄⠀⠀⣤⣹⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡴⠟⠋⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣦⣀⡐⢄⣀⣀⣀⢀⣤⣼⣽⣿⠁⠀⠀⠀⢀⠰⠛⢿⠀⠀⠸⠟⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠁⠀⣠⣿⠋⠀⠀⠀⠀⣤⠞⠉⠀⠀⠀⠀⠀⠀⡀⠀⣼⣿⣿⣿⣿⣿⡟⠛⠿⣿⡿⣿⡿⠿⠋⠉⢣⠈⠁⢘⣋⠁⠀⠀⢸⣆⠀⠀⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⡿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣤⣌⣀⡇⢻⣿⣿⣿⣿⡆⠀⠀⠀⢻⣷⠀⠀⢹⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣰⣾⡿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀
⠗⠀⠀⣴⣿⣿⣿⣷⣤⣄⣉⠛⢿⣿⣷⣼⣿⣿⣿⣿⣷⠀⠀⠀⠘⣿⣧⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣼⢯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣟⣿⠟⠁⠀⠀⠉⢿⣷⣆⠙⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡟⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⢸⣟⣾⠁⠀⠀⠀⠀⠀⠈⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣤⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠏⢻⡇⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⠿⠿⡟⣛⣭⣭⣶⣿⡿⣟⣯⣶⡿⠟⠋⠀⠀⠈⢿⡄⠈⢷⣤⡀⠀⠀⠤⠔⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⢟⣛⣿⡿⠷⠿⠛⠋⠁⠀⠀⠀⠀⢀⠀⠈⢿⣄⠀⠈⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⣯⠻⣧⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠙⠛⠟⠿⠿⠿⠟⠻⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠻⣿⡻⣶⣤⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣦⠉⠻⣶⣤⣴⣶⣿⢿⣟⣵⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡹⣷⣾⣿⣿⠛⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣴⣿⣷⣾⣿⣿⣿⣿⣿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡘⠿⢿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠟⠛⣻⣿⠿⠛⢹⣿⣿⣵⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢢⣴⣾⡿⠷⠶⠶⣦⡀⠀⠀⠀⠀⠘⢷⠀⠀⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠐⠿⠁⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢷⣿⣿⣋⠀⠀⠀⠀⠈⠻⣦⢰⡄⠀⠀⠘⣧⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢟⣿⡿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠙⢷⡀⠀⠀⣿⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡀⢰⠀⠀⠀⠀⠀⢠⣿⣯⡏⣷⣆⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⣀⣤⣾⣿⡟⢙⠋⠀⠀⣀⢀⠀⠀⠀⠀⠀⠘⣷⠀⣠⠏⢀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⣷⣸⣆⠀⠀⢀⣠⣾⣿⣿⣿⢿⠛⠿⣶⣦⣀⣀⠀⠀⠻⣦⣿⣴⣾⡟⠻⢿⣿⠟⣛⣤⣶⣶⣿⠿⠷⢶⡄⠀⠀⠀⢿⡦⠏⠀⢈⡀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠹⣿⡿⠷⠿⠛⠉⠀⠸⣿⣷⢸⡀⠀⠀⠈⡉⢻⣿⣿⣾⣿⠛⠛⢿⣿⡟⠉⠀⣾⡋⠙⣿⣻⣯⣴⣾⡿⠃⠀⠀⠀⣸⠁⠀⠀⢸⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⣠⣭⣿⣿⡿⢿⡏⠀⠀⠀⣿⡅⠀⠈⠛⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣶⠚⢻⣧⣿⣿⣤⣾⣧⠀⣀⣴⡿⣿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⡇⠀⠀⣾⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣿⡿⢦⣀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠉⠉⠛⠛⠛⠋⠀⢠⣿⡟⠉⠀⠀⠳⢶⡈⠉⠛⠛⠛⠻⠶⢶⣤⣄⠀⠀⠀⠋⠀⡇⠀⠀⣿⣿⠿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⠁⠀⠉⠛⠷⠶⠶⠖⠛⠉⢻⡇⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣀⢀⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣄⠀⢠⡇⠀⢀⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⠀⠀⠀⢀⣠⠾⠋⠀⢠⣴⣾⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠐⠀⠈⠛⣶⣾⢀⣠⠞⢻⡇⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣍⡻⣿⣷⣶⣶⣶⣶⣾⣿⡿⠿⠋⣿⡆⣠⡞⠋⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠿⠛⠁⠀⣸⡇⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠳⣶⣿⣿⣿⣿⣯⣭⣶⣶⣚⣿⣿⣿⡋⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣿⣿⡭⠽⠟⠋⠉⠉⠉⠀⠉⠻⣦⣀⠀⠀⠠⠀⠀⠙⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⡟⠀⠀⠀⠀⢠⢸⣿⡇⠀⠀⠀⠀⠀⢻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⣸⣯⣧⣤⣀⠀⢀⣀⣀⣀⣠⣄⣀⣨⣿⣷⣦⡀⡆⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣾⠿⢷⣿⡇⠀⠀⠀⠀⣏⣾⡟⢻⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⣴⣶⣶⡴⠶⠟⣛⣯⣿⡿⠷⠶⢾⣿⠁⠀⠀⢻⠁⠀⠀⠀⠈⣿⡟⠀⢸⣇⠤⣤⣤⣤⣧⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽⣿⣿⠉⠉⠀⠈⠉⠁⠀⠀⢀⣠⣶⣿⠏⠀⠀⠀⠀⠀⠀⠀⣀⣼⡟⠀⠀⢸⣿⡀⠀⠀⠀⠉⠛⠶⣤⣀⣀⡤⠖⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣦⣤⣤⠤⣤⣶⣾⣯⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⣼⣻⣿⠀⠀⠀⠘⢿⣿⢦⣄⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡎⠉⢛⣛⡿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣘⣵⣿⣷⠀⠀⠀⠀⠸⣿⣷⣍⡣⣄⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⣀⣀⣀⣀⣀⣤⣶⠿⠛⠛⢿⣔⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣺⣾⡿⠿⢻⣷⠀⠀⠀⡇⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠛⠋⠉⣭⣿⠟⠉⠁⠀⠀⠀⠀⣠⣿⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣿⠟⠁⠀⠀⠀⣿⡄⠀⠀⣤⣹⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡴⠟⠋⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣦⣀⡐⢄⣀⣀⣀⢀⣤⣼⣽⣿⠁⠀⠀⠀⢀⠰⠛⢿⠀⠀⠸⠟⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠁⠀⣠⣿⠋⠀⠀⠀⠀⣤⠞⠉⠀⠀⠀⠀⠀⠀⡀⠀⣼⣿⣿⣿⣿⣿⡟⠛⠿⣿⡿⣿⡿⠿⠋⠉⢣⠈⠁⢘⣋⠁⠀⠀⢸⣆⠀⠀⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀