⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⢸⡛⠛⢶⣴⠟⢻⣤⣤⡤⠶⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠷⠞⠓⠒⠛⠋⠀⠀⢻⣄⠀⠀⣾⡧⠤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⣠⣤⣤⣄⢰⣾⣿⣿⡷⣠⣿⣦⣼⠏⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⢨⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⠛⠛⢻⣿⣶⣀⡉⠁⠀⠿⢿⣿⠛⢷⡄⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⢀⣼⢣⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣷⡀⠀⠙⣿⣛⣻⡇⠀⠀⠀⠸⢯⣤⡾⠃⠀⠀⠀⠀⠀⠀⠈⣿⣤⣤⡤⠶⢛⣱⠟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⣷⣤⣤⣬⣽⣿⡆⠀⠀⠈⠉⠉⠀⢀⣶⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢀⣿⡤⠤⣴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠉⢹⣇⢶⣄⠀⠀⠀⣠⡾⠃⠀⣀⡀⢿⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠁⣰⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣶⠌⢿⣌⣛⣶⠤⣾⣋⣀⣠⡾⠿⠥⠼⠷⣤⣄⣀⣤⡴⠞⠋⢹⡟⠀⣿⣀⣿⣍⣛⠛⠛⣻⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣴⠞⠋⠁⠀⣀⠀⠉⠉⠁⠀⠈⠉⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⢠⣄⠀⠀⣾⠃⠀⣿⠉⠁⠈⢹⡟⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣴⠟⠁⠀⢀⠀⣰⠟⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠈⢻⡄⠀⣿⠀⠀⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⠟⠁⣠⣴⣾⠟⠀⣿⠀⠀⠀⢠⡿⣷⠀⠀⠀⠀⠀⢸⠌⢻⣆⠀⠀⠀⠀⠘⣷⡄⢿⡄⠘⣇⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣼⣋⣴⢾⣿⣿⠃⠀⢸⡏⠀⣤⡀⣼⠁⢿⠀⠀⠀⠀⠀⢸⠀⠀⢻⣆⣠⡤⠀⠀⣿⣿⠈⢿⡀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣼⠿⠋⠀⢸⣿⢃⣶⡆⢸⡇⠀⠈⢛⣿⠦⠼⣇⠀⠀⠀⠀⢸⠀⠠⠼⢿⡏⠀⠀⠀⢸⣿⡆⠈⣷⣿⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⣼⣧⡿⢹⡇⠸⣧⠀⠀⢸⡇⣀⡀⢻⣆⠀⠀⠀⢸⠀⠀⣠⣌⣷⡀⠀⠀⢸⡏⣧⠀⠈⢹⡄⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⠟⠀⢸⡇⠀⣿⠀⠀⣾⠷⡿⣧⠀⠻⣦⠀⠀⢸⡀⠀⣿⢻⣻⣧⠀⠀⢸⡷⢿⣄⢀⣿⡇⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⢻⠀⠀⠘⣷⢀⣽⡀⠀⣿⠀⣇⣿⠀⠀⠙⢷⣄⠸⡇⠀⣿⣸⡇⣿⡀⠀⣸⣧⡄⢹⣿⠏⡇⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⠀⢿⣾⡟⣧⠀⡏⠀⠻⠟⠀⠀⠀⠀⠙⠻⣿⡀⠹⠿⠁⢹⣇⠀⣿⣡⡇⣸⠏⠀⣿⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⠀⠀⠀⠘⣿⣸⣿⣧⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢸⣿⣴⣏⣉⣴⠟⠀⠀⣿⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀
⠀⠀⠀⢰⡟⠀⠀⠀⠀⣠⣼⠖⠻⣿⣷⣤⣄⣀⣀⣠⣤⣤⣤⣄⠀⢀⣀⣠⣿⣽⡿⠛⠛⠛⠓⠶⢤⣿⡇⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀
⠀⠀⠀⣿⠁⠀⠀⣴⣾⣿⠀⠀⠀⠙⢿⣷⣿⣉⣙⣿⢻⠛⣻⣿⣿⡟⠉⠁⣿⠟⠀⠀⠀⠀⠀⢀⣴⣿⠿⢦⣄⠀⠀⠀⠈⣷⡀⠀⠀⠀
⠀⠀⢠⡏⠀⠀⠀⣯⣿⣿⡀⠀⠀⠀⣠⡿⠛⠉⠉⣿⣾⠚⣿⠉⠘⣷⣴⡞⠿⣤⣄⣀⠀⠀⠀⣾⣻⡏⠀⢀⣽⠀⠀⠀⠀⠸⣷⠀⠀⠀
⠀⠀⣼⠁⠀⠀⠀⠙⠻⣿⣷⡤⠶⠛⠋⠀⠀⠀⠀⡾⠁⠀⣿⠀⠀⠈⠉⢿⡄⠀⠈⠉⠛⠲⢶⣿⣿⣷⣶⡟⠋⠀⠀⠀⠀⠀⠹⣆⠀⠀
⠀⢰⡿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢰⣧⣀⣼⠏⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠉⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀
⠀⣿⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣰⡟⠙⠛⠁⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⣸⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣴⡞⢿⣴⣿⣷⡀⠀⠀⠀⠀⣰⠶⢴⡟⣻⣦⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⣿⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠘⣿⣿⣿⣹⠇⠈⣿⣦⣤⣶⠛⠻⣆⣨⣿⣏⣿⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⡇⢀⣄⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⣼⣟⢿⣿⣓⠶⣿⠥⠤⣿⣶⣾⣿⠽⣾⡋⠁⠀⠀⠀⠀⠀⠀⢻⡆⠀⣴⣦⠀⠀⠀⠀⠀⠀⢸
⣧⡾⣿⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢀⣼⠋⢹⡿⠉⠙⠛⠛⠛⠛⠛⠉⠙⢷⡤⠾⣷⠀⠀⠀⠀⠀⠀⠀⠘⣇⢠⡟⠻⣦⡀⠀⠀⠀⠀⢸
⣿⠁⢿⡀⠀⠀⢀⡾⠃⠀⠀⠀⠀⣼⠃⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⣿⣼⠁⠀⠘⠻⣦⡀⠀⠀⣼
⠛⠀⠘⣿⣄⢠⡾⠁⠀⠀⠀⠀⠀⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠙⠻⣆⣀⡿
⠀⠀⠀⠈⢻⣿⠁⠀⠀⠀⠀⠀⠀⣿⣄⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁