⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠜⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠴⠒⠒⠛⠛⠓⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⡚⠉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⢴⡾⢉⡴⢀⣴⡄⠀⠀⠀⠀⢻⡄⠀⣦⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠂⣬⡾⢡⡞⢀⡞⠉⣷⠀⢠⣶⡀⠀⢻⡄⠈⣧⠀⠀⠀⠠⠤⠬⠧⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣀⠘⣽⠁⣼⠀⣼⠁⠀⡿⠀⡾⠙⡷⡄⢀⣿⠀⣿⡄⠀⢻⡀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣲⡏⣶⡇⣰⠇⡸⢿⠀⢸⠃⣰⡇⢠⣿⣿⡿⠽⣾⠏⢷⡀⠀⢳⡀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⣇⢣⣷⢻⢰⡇⠸⣤⣟⡴⡿⣻⠟⠟⢙⣀⣤⣯⣤⣄⣻⡁⠀⢻⡄⠀⠀⠀⠈⢻⣶⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⢻⣾⡏⠏⣿⣧⠴⠿⣿⣿⡷⢃⣠⣶⣿⣿⣿⣿⣿⣿⡟⠳⡄⠀⠹⣆⠀⢲⡄⠀⠻⢿⣷⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣬⣿⣿⣴⠙⠻⣤⣤⣼⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠹⣤⠀⠘⢦⠀⠹⣆⠀⠀⠙⠿⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠈⢿⠙⣷⣿⣿⣿⣿⣿⣿⠀⠀⠈⠛⠿⠿⠿⠟⠁⠀⠀⢀⣸⣦⠀⠈⢷⡀⠈⠳⣄⠀⡀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠸⣧⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣠⣿⣧⠀⠀⠹⣄⠀⠈⠳⣍⠓⠶⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢻⡎⠙⣿⠿⠟⠋⠀⠀⠀⣠⠤⠄⠀⠀⠀⠀⢠⣾⣿⠩⠘⣯⢳⡄⠀⠈⢧⡀⠀⠈⠓⢦⣄⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⢻⡄⣞⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢾⣽⢿⠘⣧⣠⡻⣿⡿⣆⠀⠀⠙⢦⣀⠀⠀⠉⠻⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⢸⡎⢷⢸⡄⠹⡖⢦⡤⣤⠤⢤⣲⣶⣍⡎⡟⠊⢹⣦⣽⣷⣉⠊⢷⣍⣤⡀⠀⠀⠉⠙⠲⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠓⣿⠹⣞⣆⢷⣀⠹⢿⣷⢼⣏⣉⣁⣠⡼⣿⠟⠚⠉⢹⠀⠈⠉⠛⠲⢽⣏⣻⣄⠀⣔⠦⠀⠀⠹⠀
⣀⣀⣀⣀⣤⣤⡀⠀⠀⠀⠀⠀⢻⡄⠙⠓⣾⡿⣄⠸⢧⡀⠳⡄⢧⡀⠀⠀⠘⣧⢞⣉⡳⢸⠆⠀⠀⠀⠀⠀⠈⠙⣏⢓⣞⠇⠀⠀⠀⠣
⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣴⠶⠤⣼⣛⣛⠻⠦⠬⢷⡀⠹⣆⠹⡄⠙⢦⡀⠀⠘⣇⠉⠀⠽⠀⠀⠀⠀⠀⠀⠀⠀⢙⣆⢨⢿⣦⡀⠀⠀
⣻⣿⣿⣿⣿⣿⣧⣾⡚⠋⠀⠀⢸⠀⠀⠉⠀⠀⠀⠀⠹⡄⠘⣆⢹⡄⠀⠉⠃⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠘⢿⠆⠙⢌⠲⢄
⠟⣻⠿⣿⣏⣻⠃⣙⣹⡀⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠹⡄⠸⣆⢿⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣳⠀⠀⠳⡄
⠀⠱⠸⠟⠛⠛⣺⠈⣆⡇⠀⠀⢸⡀⠀⠈⡇⠀⠀⠀⠀⠀⠹⡆⢹⡀⢧⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⠀⠀⠀⠘
⠀⢸⠙⢒⣂⡩⢾⣴⠿⣇⠀⠀⢘⡇⠀⠀⢹⢰⡀⢀⠀⠀⠀⠹⡄⢧⠘⡆⠀⠀⠀⢸⡄⡟⢉⡇⠀⠀⠀⠀⠀⣿⡄⠀⠀⢹⡆⠀⠀⠀
⠀⠈⠛⣶⣶⣾⢿⠁⠀⡿⠀⠀⠀⣧⠀⠀⠘⡇⠃⢸⡄⠀⠀⠀⢳⠘⡄⢹⡀⠀⠀⠈⣧⠉⠉⠀⠀⠀⠀⠀⠀⡟⣇⠀⠀⢸⠘⡄⠀⠀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣧⠀⠀⠀⢸⠀⠀⠀⢹⠀⠀⣧⠄⠀⠀⢘⡆⠱⠀⢧⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⡇⠸⡆⠀⢸⡄⢸⡄⠀