⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⡽⠿⠿⠟⠛⠛⠻⠿⠯⣍⡉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠀⠈⠙⠢⡀⠀⠈⢻⣿⣿⣿⠀⠀⠀⠿⢅⡀⠀⠀⠀⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠢⡀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⡀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠘⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡄⠀⠈⠉⡏⠉⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠸⡄⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠢⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢡⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⠀⢀⡞⠙⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠸⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⠙⢿⣿⣿⣿⠿⢿⣿⡆⠀⠀⠀⠀⠸⡼⠀⠀⠀⠀⠀⢀⣤⣆⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⠀⢣⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠁⠀⠀⠈⣿⣿⠃⠀⠀⢹⣷⠀⠀⠀⠀⠀⡇⢳⠀⠀⣤⡎⣿⣿⣿⣦⠀⠀⠀⠀⠀⡇ ⠒⠈⠁⠒⠒⠧⠀⠀⠀⠀⠈⠢⣀⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠉⠀⢀⡀⠀⣴⣿⣿⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⢇⠀⢳⠀⠹⣿⣾⣿⣿⣿⣧⠀⠀⠀⠀⡇ ⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⡀⠀⠀⠠⠈⣁⣴⠋⠀⠹⣆⠐⠂⠠⠀⢡⡀⠀⠀⠀⠘⣆⠀⢣⠀⠙⣿⣧⢻⣿⣿⡇⠀⠀⢰⠇ ⠀⠀⠙⠲⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⢈⣅⢲⣬⠓⣰⠒⠛⠻⠿⣤⣦⣤⣿⡷⠬⢠⢤⠬⢑⡀⠀⠀⠀⠸⠔⠋⠀⠀⠈⠻⣷⣦⢻⣧⣤⡀⢸⠀ ⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣔⣛⠦⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣝⡛⢧⡘⡄ ⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⠀⠀⠀⠀⠀⢀⣤⣾⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⡀⠀⠀⠈⠙⠒⠡⠘ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⡜⠉⠁ ⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣱⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣔⢊⣀⣀⣀⣀⣀⣀⣀⣤⣤