⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⢖⣶⣶⠶⣤⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠻⠛⠉⠛⠛⠙⠝⠋⠙⢿⣍⣯⣿⡷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠿⡽⣥⢏⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠃⠀⢹⣧⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡠⠫⢶⠀⠀⠀⢻⡧⠰⠉⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⢿⣿⣷⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⣀⣸⣏⠀⠀⢹⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠒⢄⠀⢀⠞⠁⠀⠈⣿⣿⣿⣦⠀⠀⠀⠀

⠀⠀⠀⠀⠎⠀⠀⠈⠀⣠⣾⠟⠛⠛⠉⠑⢮⡁⡿⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣾⣷⣧⣄⡀⠀⠀⢹⣿⣿⣿⣷⡀⠀⠀

⠀⠀⠀⢀⠆⢀⠀⢀⡴⠋⠀⣠⡄⢠⡀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢿⣿⣿⣿⣷⡀⠀

⠀⠀⠀⡸⠀⡸⠀⡼⠀⠀⠀⣻⡏⠀⣾⡇⠀⢀⠇⠀⢤⣶⣤⡈⢦⡀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣇⠀

⠀⠀⢰⣇⢠⠇⠀⡇⠀⠀⠀⡿⡧⡽⡟⡆⢠⠞⠀⣼⣿⣿⣿⣿⡄⠹⣄⣈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣿⣿⣿⣿⣿⠀

⠀⠀⣼⣿⠏⠀⢠⣇⣀⠀⣘⣤⢤⣧⣴⠖⠋⠀⢀⣿⣿⣿⣿⣿⣿⠀⣿⡏⢀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿

⠀ ⢿⣿⠀⠀⠖⣛⣹⠛⠛⠛⠋⠀ ⢀⡢⠀⢸⣿⣿⣿⣿⣿⣿⣷⠘⣇⠀⠁⠠⠤⢅⡀⠉⣉⣛⣋⡉⢀⣿⣿⣿⣿⣿

⠀ ⢿⡏ ⠀⠀⠈⠀⠀⠀⠀⠐⠒⠋⠉⠀⠀⠀⠀⢿⡿⠻⣿⣿⣿⠇⡈⣄⠀⠀ ⠀⠀⠈⠑⠾⠿⣿⣿⣿⣿⡟⣿⣿

⠀ ⣿⠃ ⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠚⠁⠀⡈⠛⡅⠀⡇⢸⣟⠂⠀⠀⠀⠀⠀⠀⠀⠋⠛⢋⣼⣿⣿⣿

⠀ ⡼⠃⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀ ⠀⠐⡏⠀⠀⠀⠀⡇⠀⠀⣧⠀⢢⠀⢱⠸⣿⣯⣠⠀⠀⠀ ⠀⠀⣀⣴⣠⣺⣿⣿⣿⠀

⢠⠃⢀⣀⠤⠐⢉⣩⣉⠁⠀⠀⠀⠀⡜⢀⣄⣀⠦⡘⠛⢂⠜⠛⢧⠞⠳⢘⡀⢹⣿⣷⠀⠀⢀⡀⣊⡁⠈⠙⣿⣿⣿⣿⣿⠀

⣸⠐⢁⣴⢶⣶⣿⣿⣿⣿⣄⠉⢆⠀⣑⡜⠉⣟⣀⣤⣀⣤⠦⠤⢼⣅⣨⢸⢸⣿⣿⣿⣇⣠⣤⣿⣥⣾⣷⣶⣌⠉⠙⢻⠀

⠙⠷⣾⠣⣿⣿⡿⢿⣿⢻⣿⣷⡜⠀⡛⢿⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠙⣶⠙⣿⣿⣏⣿⠟⣿⣿⣿⣿⣿⣧⠀⢸⡇⠀

⠀⠀⠀⢳⣿⣿⡆⠘⣿⢨⣿⣿⡗⢰⠿⠶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢉⣹⣿⣿⡿⢰⣿⡇⣼⣿⣿⡿⠀⢴⠅⠀

⠀⠀⠀⠀⢳⡀⠀⠘⣿⠘⣿⣿⣿⠸⡀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠖⢊⡝⡿⠃⢸⣿⠀⣿⣿⣿⣷⡆⡇⠀⠀

⠀⠀⠀⠀⠈⣧⠀⢸⣿⠀⣿⣷⢻⣻⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠋⠁⠀⣿⡇⢠⣿⣿⣿⡿⠀⣇⠀⠀

⠀⠀⠀⠀⠀⣸⠀⢨⣿⡇⣽⣿⠟⣷⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢸⣿⣿⣿⠇⢀⡎⠀⠀

⠀⠀⠀⠀⡀⢸⠀⠀⣿⡏⣿⡿⠷⠻⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣾⣿⣿⠟⠀⣿⠀⠀⠀

⠀⠀⠀⠀⢼⣼⡆⢀⡙⢷⣿⣷⡞⣾⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠐⣿⡟⠁⠀⣼⡿⠀⠀⠀

⠀⠀⠀⠀⠸⣿⡇⠀⠘⢾⣿⣯⠗⢿⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⣿⣷⣾⣿⡿⠃⠀⠀⠀

⠀⠀⠀⠀⠀⠈⣏⠂⠀⠀⠹⢷⣿⠿⣿⣧⡤⢶⢲⣦⣤⠤⢤⡠⢄⣀⣀⣤⢤⡦⡴⡆⠀⣿⡃⠄⢀⣻⣿⣿⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⣖⠀⠀⠀⢀⠉⡀⢈⠀⢻⡉⢹⠁⡷⠀⠸⠀⠘⡀⢻⡄⢸⣇⣿⡅⢀⣿⠋⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣦⣆⠀⠀⠈⠐⠄⠘⠉⠉⢻⠞⠒⣾⠲⡴⠒⠾⠓⢺⠙⠉⡿⣿⣶⣾⡿⠂⠀⠐⣿⡿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆⠀⠀⠀⠀⡀⠀⠀⠘⠀⠀⠈⠀⠇⠀⢘⠀⠚⠀⠀⠇⢻⣿⣿⡧⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠁⠐⠶⠆⠐⠀⠀⠀⠒⣀⣠⣆⣀⠀⢤⣠⣾⡿⠉⠀⠀⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⢿⣿⣿⡿⠿⡿⣯⣶⠆⢠⠌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠒⠒⠖⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀