⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⣄⣀⡀⡒⢒⣲⣿⡿⠛⠉⠉⠀⠈⠙⣏⣭⣭⣭⣭⣄⡈⣽⣿⣷⣿⡷⠖⠋⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⢁⠜⠀⢉⢮⣾⣥⡴⢟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢫⣾⣷⣿⣿⣿⣿⣇⠀⠀⠀⢹⣧⣶⣠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠂⣔⠃⠀⡀⠀⣘⠋⣽⢣⠃⢀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢘⣿⣿⠿⣿⣾⠞⠿⠋⠉⠹⣎⠑⠢⢀⠀⠀⠀⠀⠀ ⠀⠀⢰⠯⢜⠘⠀⠀⣿⡷⣿⣿⣿⣘⡖⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣷⣞⣿⣿⣿⣤⣻⢃⡏⠀⠀⠀⢠⠇⠀⠀⠘⣣⠀⠀⠀⠀ ⠀⠀⣿⡈⡌⠁⠀⢸⣿⡧⣿⣿⣧⡟⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣷⠻⣗⠀⣠⣴⣶⡦⠯⠓⠒⠄⠧⡀⠀⠀ ⠀⠀⢹⣷⣧⢅⣀⣾⣳⣻⣝⢿⣿⣯⡠⡀⡀⠀⠀⣀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⡿⢻⠟⢻⡿⣿⣻⡛⣳⣆⡀⠀⠀⠀⢈⢦⠀ ⠀⠀⢸⣿⣿⣿⣿⣶⣾⠋⠀⠉⠛⠯⠿⣿⣕⠴⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠏⡿⣽⣦⡯⢾⢁⣼⠟⣙⠽⢿⣭⣽⣿⣛⡢⡶⠿⡀ ⢀⣤⢿⣿⣿⣟⡼⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⡗⣿⡿⢿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣼⣿⣿⣿⣷⣿⡟⡺⡁⣰⠯⠿⣵⣾⢿⣍⣀⠀⣧ ⢸⢯⣧⡴⠋⠋⠛⠫⣵⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⣝⢿⣿⣿⣿⣿⣿⣷⣦⣀⣈⣿⣿⣇⣿⣿⡿⣿⣙⢿⣿⣿⣿⣿⣿⣾⢇⠿⣆⠀⡜⡅⠀⠸⠀⠀⣝ ⢨⢬⣟⠀⠀⣠⣠⣄⣸⠇⠀⠀⠀⠀⠀⠀⠀⠈⢽⣝⣿⣷⣿⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣺⢿⣿⣿⢿⡏⠉⣡⣾⣿⣿⣷⣟⡹⣽⣾⣏⣣⠞⢳ ⠀⢻⣴⣤⢾⣿⣿⡟⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢿⣿⣿⣿⣿⣷⣿⣯⣭⣭⣽⡿⣿⣿⣿⣾⡿⡓⣞⡝⣽⡷⣟⣻⣿⣿⣿⣿⣿⣾⣾⣿⣿⡟⠀⢀⡜ ⠀⠀⠉⠻⣿⡷⠽⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⡇⣚⢿⣿⣿⣿⠓⠿⠋⠀⠈⠳⣾⣯⣛⣿⡿⣿⣿⡿⢟⡲⠐⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⣷⣿⣿⣿⣿⣿⣿⣿⠟⠚⣻⣿⣯⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⠛⠛⠊⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣾⠸⣿⣿⡏⠈⢿⣿⣿⣿⣻⠽⣻⣾⣿⣿⣿⣿⣿⣟⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢰⣿⣧⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⡎⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠸⣿⣿⣿⡿⠇⠀⠀⠀⠸⡿⡄⢀⣸⣿⣿⣿⣿⣿⣿⣹⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣿⣿⣿⣷⠦⠀⠀⠀⠀⡇⡇⣿⣾⣿⣿⣿⣿⣿⣿⣿⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣜⣿⣿⣿⣯⠄⢰⣿⣤⡧⠇⣿⣿⣿⣿⣿⣿⠃⠈⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢠⣻⣿⣳⣿⣷⠀⢸⣿⣿⡟⠀⣷⣿⣿⣿⣿⣿⣤⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡇⢸⣸⣿⣿⣾⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢿⣿⣯⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢗⣿⣿⣿⣿⣿⣿⣷⣾⣟⠏⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⢿⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⣿⣿⣿⣟⢉⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢏⣿⣿⣏⣀⠀⣀⡙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣻⣿⣿⣿⣿⠿⢧⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡓⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀