⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⢖⣶⣶⠶⣤⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠻⠛⠉⠛⠛⠙⠝⠋⠙⢿⣍⣯⣿⡷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠿⡽⣥⢏⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠃⠀⢹⣧⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠫⢶⠀⠀⠀⢻⡧⠰⠉⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⢿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⣀⣸⣏⠀⠀⢹⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠒⢄⠀⢀⠞⠁⠀⠈⣿⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠎⠀⠀⠈⠀⣠⣾⠟⠛⠛⠉⠑⢮⡁⡿⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣾⣷⣧⣄⡀⠀⠀⢹⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⢀⠆⢀⠀⢀⡴⠋⠀⣠⡄⢠⡀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢿⣿⣿⣿⣷⡀⠀ ⠀⠀⠀⡸⠀⡸⠀⡼⠀⠀⠀⣻⡏⠀⣾⡇⠀⢀⠇⠀⢤⣶⣤⡈⢦⡀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣇⠀ ⠀⠀⢰⣇⢠⠇⠀⡇⠀⠀⠀⡿⡧⡽⡟⡆⢠⠞⠀⣼⣿⣿⣿⣿⡄⠹⣄⣈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣿⣿⣿⣿⣿⠀ ⠀⠀⣼⣿⠏⠀⢠⣇⣀⠀⣘⣤⢤⣧⣴⠖⠋⠀⢀⣿⣿⣿⣿⣿⣿⠀⣿⡏⢀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿ ⠀ ⢿⣿⠀⠀⠖⣛⣹⠛⠛⠛⠋⠀ ⢀⡢⠀⢸⣿⣿⣿⣿⣿⣿⣷⠘⣇⠀⠁⠠⠤⢅⡀⠉⣉⣛⣋⡉⢀⣿⣿⣿⣿⣿ ⠀ ⢿⡏ ⠀⠀⠈⠀⠀⠀⠀⠐⠒⠋⠉⠀⠀⠀⠀⢿⡿⠻⣿⣿⣿⠇⡈⣄⠀⠀ ⠀⠀⠈⠑⠾⠿⣿⣿⣿⣿⡟⣿⣿ ⠀ ⣿⠃ ⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠚⠁⠀⡈⠛⡅⠀⡇⢸⣟⠂⠀⠀⠀⠀⠀⠀⠀⠋⠛⢋⣼⣿⣿⣿ ⠀ ⡼⠃⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀ ⠀⠐⡏⠀⠀⠀⠀⡇⠀⠀⣧⠀⢢⠀⢱⠸⣿⣯⣠⠀⠀⠀ ⠀⠀⣀⣴⣠⣺⣿⣿⣿⠀ ⢠⠃⢀⣀⠤⠐⢉⣩⣉⠁⠀⠀⠀⠀⡜⢀⣄⣀⠦⡘⠛⢂⠜⠛⢧⠞⠳⢘⡀⢹⣿⣷⠀⠀⢀⡀⣊⡁⠈⠙⣿⣿⣿⣿⣿⠀ ⣸⠐⢁⣴⢶⣶⣿⣿⣿⣿⣄⠉⢆⠀⣑⡜⠉⣟⣀⣤⣀⣤⠦⠤⢼⣅⣨⢸⢸⣿⣿⣿⣇⣠⣤⣿⣥⣾⣷⣶⣌⠉⠙⢻⠀ ⠙⠷⣾⠣⣿⣿⡿⢿⣿⢻⣿⣷⡜⠀⡛⢿⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠙⣶⠙⣿⣿⣏⣿⠟⣿⣿⣿⣿⣿⣧⠀⢸⡇⠀ ⠀⠀⠀⢳⣿⣿⡆⠘⣿⢨⣿⣿⡗⢰⠿⠶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢉⣹⣿⣿⡿⢰⣿⡇⣼⣿⣿⡿⠀⢴⠅⠀ ⠀⠀⠀⠀⢳⡀⠀⠘⣿⠘⣿⣿⣿⠸⡀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠖⢊⡝⡿⠃⢸⣿⠀⣿⣿⣿⣷⡆⡇⠀⠀ ⠀⠀⠀⠀⠈⣧⠀⢸⣿⠀⣿⣷⢻⣻⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠋⠁⠀⣿⡇⢠⣿⣿⣿⡿⠀⣇⠀⠀ ⠀⠀⠀⠀⠀⣸⠀⢨⣿⡇⣽⣿⠟⣷⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢸⣿⣿⣿⠇⢀⡎⠀⠀ ⠀⠀⠀⠀⡀⢸⠀⠀⣿⡏⣿⡿⠷⠻⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣾⣿⣿⠟⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⢼⣼⡆⢀⡙⢷⣿⣷⡞⣾⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠐⣿⡟⠁⠀⣼⡿⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡇⠀⠘⢾⣿⣯⠗⢿⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⣿⣷⣾⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣏⠂⠀⠀⠹⢷⣿⠿⣿⣧⡤⢶⢲⣦⣤⠤⢤⡠⢄⣀⣀⣤⢤⡦⡴⡆⠀⣿⡃⠄⢀⣻⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣖⠀⠀⠀⢀⠉⡀⢈⠀⢻⡉⢹⠁⡷⠀⠸⠀⠘⡀⢻⡄⢸⣇⣿⡅⢀⣿⠋⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣦⣆⠀⠀⠈⠐⠄⠘⠉⠉⢻⠞⠒⣾⠲⡴⠒⠾⠓⢺⠙⠉⡿⣿⣶⣾⡿⠂⠀⠐⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆⠀⠀⠀⠀⡀⠀⠀⠘⠀⠀⠈⠀⠇⠀⢘⠀⠚⠀⠀⠇⢻⣿⣿⡧⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠁⠐⠶⠆⠐⠀⠀⠀⠒⣀⣠⣆⣀⠀⢤⣠⣾⡿⠉⠀⠀⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⢿⣿⣿⡿⠿⡿⣯⣶⠆⢠⠌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠒⠒⠖⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀