⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢤⡤⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠁⡠⠒⠉⢀⣠⣴⣶⣾⣏⠱⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⡠⡞⠁⡠⢒⣥⣴⣤⣶⣶⣿⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡎⠀⠀⡜⢰⣠⣾⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢾⠀⣀⡜⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠫⡀⣷⣿⣿⣿⣿⣿⣿⣛⡛⠛⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢦⣀⣤⠒⠁⡷⠛⠏⣿⣿⣿⣿⠙⠿⢿⡷⠗⡇⠀⠀⢈⣿⣿⣿⣿⣿⣿⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⣡⠆⠀⣯⡐⠒⣿⣿⣿⣿⣆⠀⠐⠀⣤⢇⠠⢴⣿⣦⣹⣿⣿⣿⣿⡇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⡘⢻⣀⢠⣛⣿⣿⣿⣿⣿⣿⣿⠿⢇⡀⠀⠉⠀⠀⠉⡋⣿⣿⣿⣿⣿⣇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⠡⣗⢻⣌⣿⣿⣿⡿⣿⣿⣟⣏⠀⠀⠙⠿⠦⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠛⠿⠭⠘⢫⣿⣿⣏⣸⣷⣄⠀⢀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⠤⠾⢿⣿⣛⣛⣻⡿⢿⣿⣿⣿⣏⠉⢧⣿⣿⣿⣿⣿⡿⠿⠖⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠤⢲⠏⡀⠀⣠⠋⠀⠀⠈⠑⠢⡒⠙⠉⠛⠫⣭⠩⠭⠵⠦⠬⣉⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡌⠀⡰⠁⠀⢻⣠⣍⢰⠇⠀⠀⠀⠀⠀⠀⠈⢆⠀⠔⠈⠀⠀⠀⠀⠀⠀⠈⠹⣄⠈⠳⡦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠀⠰⠁⠀⠀⢻⠫⠟⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⡼⣌⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡌⠀⡇⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⠁⡏⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠃⠀⢇⠀⠀⠀⠘⣆⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡰⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢰⠀⠀⠀⠀ ⠀⠀⠀⠀⠎⠀⠀⠘⢄⠀⠀⠀⠘⢦⡹⡄⠀⠀⢀⣠⠄⠀⠉⢀⠇⠈⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⠋⡜⠀⠀⠀⠀ ⠀⠀⠀⡘⠀⠀⠀⠀⠈⣓⣤⣤⡴⢾⣿⣿⣿⣭⡔⠁⠀⢀⡠⠊⠀⠀⠀⠀⠘⠑⠢⢀⠀⠀⠀⢀⢎⣴⣋⠜⠀⠀⠀⠀⠀ ⠀⠀⢠⠁⢀⡀⠤⠒⠉⠀⣿⣿⠭⠽⢿⣿⣿⣿⣟⠓⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣶⠶⣿⣿⣮⡧⣀⠀⠀⠀⠀⠀ ⠀⠀⣬⠒⠁⠀⠀⠀⢀⢄⣽⣿⡿⢶⣾⣿⣿⣛⡤⢇⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⢴⠾⢻⣿⣿⣿⡏⠓⡆⠀⠀⠀ ⠀⢠⠁⠀⠀⠀⠀⠰⢁⣺⣿⣿⣿⣄⠈⠻⢴⡡⣇⡜⡼⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣐⡡⡒⠭⠛⣿⣿⠛⣯⡇⠀⠀⠀ ⠀⠘⡀⠀⠀⡰⠀⢠⣲⣿⣿⣿⣿⣿⠛⠉⠹⣷⠟⠀⠁⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⡟⠱⡉⡏⠉⠉⠉⢁⠃⠀⠀⠀ ⠀⠀⢇⡀⢊⡠⢲⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠻⣆⡖⠘⠁⠀⠀⠀⢠⣀⠀⠀⠀⠀⠠⣸⠈⠄⠱⣱⡀⠀⡀⠌⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢠⠃⠀⠘⢄⠀⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⣀⣠⡴⢿⣿⢿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠘⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⠿⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀ ⣠⣴⣾⣯⣄⡴⣪⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⢮⣯⠴⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀ ⠐⠛⠛⠉⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡎⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀ ⠀⠀⢀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀ ⠀⡔⢩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⣇⠀⠀⠀⡰⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀ ⢸⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⢸⡷⠶⢶⡇⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀ ⢸⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡄⠀⠈⡇⠀⢸⠀⣼⠂⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀ ⠘⡄⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⣸⣷⣶⠇⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀ ⠀⡷⡀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠛⠛⡻⠊⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀ ⠀⡇⠱⣄⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢄⣰⠁⠐⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⡇⠀⠈⠳⣄⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⡇⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⡆ ⠀⡇⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠈⠐⠤⡀⠀⠀⠀⠀⠀⠀⣷⠀⠒⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀ ⠀⠇⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣀⠀⠀⠈⠳⣤⣀⠀⠀⠀⡟⡀⣰⣿⣿⣿⣿⣯⣯⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆ ⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣼⣿⣿⣷⣦⡀⡇⠣⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣧⡀⣿⣿⣿⣿⣿⣿⢿⣽⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠟⠸⣿⣿⣿⣿⡿⣿⣿⣽⡷⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀