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