⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣾⣿⣿⣿⠻⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣾⣿⡿⠛⢻⠛⠻⣿⡿⣷⣽⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣰⣿⣿⣿⡿⠋⠙⣧⣸⡄⠀⠙⣷⣿⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⡯⠤⢄⣀⣝⣿⡍⠀⢠⣿⣷⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣮⣿⣿⣿⣿⡧⣍⠀⠘⡄⢳⠹⢲⣼⣿⣏⢠⡑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣿⣿⡿⠉⠀⡿⠀⠀⠀⠀⢳⣿⣿⡿⠽⠙⢯⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠈⣹⣷⣦⣀⠁⠀⠀⢡⠠⡟⠀⠀⠀⠀⠀⠈⠳⡄⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣿⣿⡶⣀⣠⣾⡷⠀ ⠀⢠⣿⣿⣿⣿⣿⣶⣤⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠫⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡳⣾⡿⡏⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⠗⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠺⡷⡀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣿⡿⣿⣿⣿⡿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠇⢹⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⡥⡇⠀⠀⠀⠀⢀⣀⣀⣿⡿⠃⢹⣿⡏⡏⠀⠀⠀ ⠀⠉⠉⢻⣽⣿⣿⣦⣾⡧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⣸⡄⠀⡠⠂⢁⢀⣽⣿⢷⣀⢼⣿⣇⢃⠀⠀⠀ ⠀⠀⠀⢸⣹⠀⣤⠇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠋⠀⢀⡏⣸⣿⣿⢿⡧⣼⣿⣿⣮⢆⠀⠀ ⠀⠀⠀⣾⡇⠈⡟⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡈⢧⡀⣘⡿⣿⣿⡟⡾⢣⣿⣿⣿⠀⢸⠀⠀ ⠀⠀⠀⣿⡄⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠞⠋⣹⠁⢹⣿⢁⠃⣿⣿⣿⣿⠀⠈⡇⠀ ⠀⠀⠀⢸⡇⠀⢳⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣟⡅⢺⡿⠈⠀⢿⣿⣿⣯⣤⡶⠟⠀ ⠀⠀⠀⠀⢿⣄⢹⣇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠈⠱⢾⣿⣿⣇⡷⣾⣶⣶⢟⢟⣹⠟⠁⢨⡆ ⠀⠀⠀⠀⣸⠳⠎⡓⠚⠎⡑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⣀⠀⠉⠛⠿⣥⣾⣡⠴⠉⢀⣀⣠⣤⡾⠁ ⠀⠀⠀⠀⣗⣫⡖⢉⣀⣀⣤⣤⣬⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣪⣽⡻⠓⠒⢻⣿⣷⢾⣿⣿⣆⣼⡏⠀⠀ ⠀⠀⠀⠀⠈⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠿⠛⠳⠟⠛⠛⠻⣿⠿⠿⠿⠛⠋⠁⠀⠀