⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠖⠘⠓⠰⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⡀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢁⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣰⠃⠀⠀⠀⢠⣃⠀⠀⠀⠀⠄⣀⡄⠀⠘⣆⠀⠀⠙⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠷⡼⣿⠇⢰⢡⣤⠦⣿⠻⡀⠀⠀⠉⠀⠈⡗⡟⠒⠾⡀⠀⢠⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⢸⣿⠀⠀⣟⡄⣇⠀⠀⠀⠀⠀⣧⡇⠀⢆⡇⠀⠈⣆⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡰⢡⣾⠉⢸⣿⠠⠄⢿⢳⣾⡤⠤⠤⠴⢶⡛⠷⣆⣸⡇⠀⠀⣯⢆⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣻⡛⢹⠀⠈⣿⣠⣴⢯⣶⣥⡀⠀⠀⢨⡵⣶⣶⣶⣾⡇⠀⠀⡿⢺⡌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡰⢡⠻⠁⣸⠀⠀⢹⡟⢯⡹⡟⠇⠀⠀⠀⠀⠁⠉⠉⠉⢸⠃⠀⠀⡇⣇⢧⠸⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡜⢡⡳⢕⣺⣻⢰⠀⠘⣳⠀⠀⠀⠀⠨⠧⠀⠀⠀⠀⠀⠀⢸⡁⠀⡄⣧⡩⡈⢆⢳⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡼⣡⢃⡵⡻⠋⠸⣸⢀⠀⢣⣇⠀⠀⠀⠀⣀⡤⠔⡶⠂⠀⠀⣟⡏⡐⣧⣷⣌⠳⠈⢆⢧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡜⣱⢷⡿⠋⠀⠀⠀⣏⣾⠀⠀⢿⣦⡀⠀⠀⠈⠑⠚⠁⠀⣀⣼⣿⢧⢃⣿⢯⠻⣷⣦⣈⢫⢣⡀⠀⠀⠀⠀⠀
⢀⣜⡱⠟⠁⠀⠀⠀⠀⠀⡿⣷⣧⣠⢾⣏⠻⣶⢤⣀⡀⢀⡤⣺⢿⣸⣿⢾⠉⠏⡼⡀⠀⠉⠻⠿⣷⣕⢄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠹⣿⠁⢼⣏⢰⡧⢸⠀⠈⠁⠀⣿⣿⣿⠁⢸⣆⠀⠁⡇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢰⡿⢀⣿⣧⣿⣧⠜⠑⠢⠤⠊⠻⢅⣏⢧⠀⢟⡄⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡸⣿⡿⠿⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠗⣬⣞⣆⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⠿⢷⣶⣤⣄⡀⠀⠀⢏⠴⠋⠁⠑⠦⣧⡉⠒⠭⣑⣄⣀⣊⡁⠶⠦⠛⠚⣩⣀⠩⠧⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠙⠻⠿⣾⡁⠀⠀⠀⠀⠀⠀⠫⢖⠢⠤⠀⣀⡠⠤⠄⠒⢊⠝⠁⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠇⢣⠀⠀⠱⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠄⠂⠀⠀⠀⢰⠁⠀⡜⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⣆⡰⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⡜⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⠘⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⠇⠑⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⢱⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⢻⠀⠰⠠⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠠⡙⠘⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡎⠘⠀⠀⠡⠑⠜⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⡠⡱⠁⠀⢻⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢢⣄⣀⠀⠀⠑⡄⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡧⣊⠔⠁⠀⣀⡬⢳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣜⢸⡟⠭⡐⠂⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢠⠔⢒⠭⢺⢳⠈⡆⠀⠀⠀⠀