⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⢿⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠿⠛⠋⠉⠉⠙⠛⠻⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣶⣿⠟⠁⠀⠀⠀⠀⠀⠉⠻⣿⣿⣦⡀⠀⠀⠀⣀⣠⣤⣶⣶⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⣀⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⢿⣿⣶⣄⠀⠀⠀
⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣴⣾⡿⠿⠛⠉⣽⣿⣶⣾⣷⣶⣿⠿⠛⠛⠻⢿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠙⢿⣿⣷⠀⠀
⠀⠀⣠⣿⠟⠁⠀⠀⠀⢠⣤⣤⣤⣀⣀⣀⢀⠀⠀⢿⡟⠋⠀⠀⠀⠀⠐⣿⡟⠁⠀⠙⠉⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⡿⠿⢿⣷⣤⡀⠀⠀⠀⠀⢻⣿⣧⠀
⢀⣼⣿⠋⠀⠀⠀⣰⣿⣿⠟⠛⠛⠛⠛⣻⣿⣿⣷⢄⣠⠴⠒⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠛⠉⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⢻⣿⡇
⢸⣿⠃⠀⠀⠀⣼⣿⡟⠁⠀⢠⣶⣦⣾⡿⠻⠿⠿⠧⠤⠖⠛⢦⡛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣻⣿⣤⣄⠀⠀⠀⠀⢈⣿⡇⠀⠀⠀⠀⠀⠈⣿⡇
⢸⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠘⣿⣯⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣈⡙⠒⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣹⣿⡄⠀⠀⣀⣾⡿⠁⠀⠀⠀⠀⠀⠀⣸⡇
⢸⣿⡀⠀⠀⠀⢿⣿⣶⣤⣀⣀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠤⠤⠤⢄⡉⢓⣶⣶⣿⣧⣤⣀⡀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⣴⣿⡇
⠈⣿⣧⠀⠀⠀⠀⠉⠛⠿⠛⠛⢻⠙⡆⠀⠀⠀⢀⣰⣶⣶⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⣾⣾⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀
⠀⢸⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⡾⢰⠃⠀⠀⣠⣾⡿⠃⠀⣰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣼⣿⡟⠁⠀⣻⣿⣿⣿⣿⣿⣿⠆⠀⠀⠠⣤⣄⣀⣀⣀⣠⣄⣠⣶⣿⣿⠿⠋⠀⠀
⠀⠀⠙⢿⣿⣦⣤⣀⣀⣀⣠⣶⣗⣸⠀⠀⣰⣿⣿⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣿⣏⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠸⣿⣿⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⢛⣿⡿⠋⠀⠀⢿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢢⡄⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠈⠉⠛⠛⠟⠛⠟⠛⠛⠉⠀⠹⡌⢱⡀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣳⡈⡇⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⣀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻⡿⢿⣶⣶⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣾⡿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡀⠙⣿⣿⠿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡏⠁⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⣿⣇⣴⣾⡿⠿⣿⣿⠿⠿⠇⠀⠀⠀⠀⠰⠿⢿⣷⣶⣦⣵⢠⡇⢀⣿⣿⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣴⣿⠟⠋⠀⢻⣿⡄⠀⣠⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣧⣀⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⢟⣜⣡⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⣿⣷⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣡⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⠛⢿⣷⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣷⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠿⠋⠁⠀⠀⠉⠉⠛⠻⠿⠿⢿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀