⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠒⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠳⠶⢤⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢼⣀⣀⣀⠀⠈⠙⢷⣄⡈⠀⠀⠐⢄⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⡞⢛⣫⢗⡪⣉⡤⠌⣑⣲⠦⢌⣛⢦⣄⠀⠈⠢⡀⠀⠀⠀⠀⠈⢆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣽⣾⡿⢫⢖⡽⣪⢕⣴⠟⣩⣤⠴⡲⠊⠉⠛⠳⣄⠀⠘⢄⠀⠀⠀⠀⠈⢢⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⡟⣌⡾⡱⣳⢏⠞⣵⡻⣣⣾⡟⣡⠊⣠⢔⣶⣾⡆⠈⠢⡀⠀⠑⠤⡀⠀⠀⠀⢇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣹⢹⢱⣹⢃⡏⣼⢳⢳⣿⡟⣼⢃⡼⣵⢏⠙⠻⢷⣿⡇⡌⣦⡀⠀⠈⠈⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣾⣸⡟⣸⢠⣿⣿⣾⣿⣿⡟⡽⣽⡇⠘⢦⡀⠀⠈⡇⡇⡏⣿⡷⢄⡀⠀⠀⢠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣧⢿⡜⣿⣿⢻⣿⣿⣿⣧⣿⠀⠀⡀⠙⠦⣤⣷⢳⣧⣿⣿⠀⢸⣿⡏⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣾⣿⣿⡟⠿⠿⠿⠇⠻⡏⠐⣿⣿⣦⣴⣿⢿⠃⡏⣿⣿⠀⢸⣯⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⣒⡽⢛⣼⣾⣿⣟⣿⣿⣟⠆⠀⠀⠀⠀⠁⠀⠈⠙⠿⡿⠃⡼⢠⣿⣿⣏⣄⣿⢹⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢪⢊⡵⣡⣾⣿⣿⣿⢿⣾⣿⣿⣎⠂⠀⠐⢤⣀⣀⡀⠀⠀⠀⣀⡾⢡⣿⣿⣿⡿⣿⢧⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⣎⣾⣏⣿⣿⢿⣻⣟⣿⣿⣭⣽⣷⣤⡀⠸⢄⡠⠃⠠⢤⣽⣿⣶⣽⣿⣽⣿⣽⣡⠊⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⠴⠒⠛⠉⠙⠓⠦⣌⢹⣾⢻⢯⣿⣿⣿⠿⠛⣿⡏⠀⠀⢁⣀⣙⣢⣤⣤⣄⣐⣲⢟⡿⣫⣾⣿⣿⣟⣿⠃⠀⠀⠀⠀⠀
⠀⠀⡤⠖⠛⡡⠄⠀⠀⠀⠀⠀⠀⠘⣆⠛⢺⣸⢿⣧⡿⠀⢀⠷⠇⠴⡙⠉⠁⠀⠀⣨⣯⣳⠟⠛⠿⠵⠿⢿⣿⣿⣼⡇⠀⠀⠀⠀⠀⠀
⠀⠘⠀⠀⢰⠁⠀⠀⡔⠉⠉⠀⠀⠀⢻⠀⠈⣿⠀⢿⡧⠞⠁⢈⡀⢤⠁⠀⠀⠀⢊⣴⡻⠃⠀⣠⠔⠢⠀⠀⠈⠻⡍⠁⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⣸⠀⠀⢰⠀⠀⠀⠂⠀⠀⢸⡅⢠⠔⠉⠁⠀⢠⠊⠁⠸⣼⠀⠀⢀⢴⠟⣾⣇⣀⠜⠁⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀
⠀⠈⠓⠔⠻⣀⠀⢸⠀⠀⠀⡆⠀⣠⣾⣄⣇⣤⡤⠤⡀⠃⠀⠀⠀⢻⠒⢋⣵⠋⢸⠟⠉⡎⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⣦⠤⠚⠁⡰⠋⠘⡟⠉⠀⠈⠑⢼⡄⠀⠀⠀⠀⠑⢊⡯⠤⣘⠦⢀⣘⣦⡀⠀⠀⠀⢀⠄⠀⣼⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠀⡠⠃⠀⠀⠱⡀⠀⠀⠀⢘⠇⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠈⠉⠀⣱⢦⣤⠠⠏⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠀⠀⠀⠀⠀⠃⠀⢀⣴⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⠢⢈⣉⠭⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣆⣴⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠎⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣀⣀⣠⠞⢉⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⢀⡴⠛⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡹⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⡀⠀⠀⠀⠀⠀⠑⠀⠀⠒⠉⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡤⠊⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠒⠒⠒⠒⠂⢄
⠀⠀⠀⠀⢀⠔⠉⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀
⠀⠀⢠⠔⠁⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀
⢀⠔⠁⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀
⠏⢀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣃⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀
⡆⠀⠱⡀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡄⠀⠀⠀⠀⠀⣠⢶⡀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀
⠘⡄⠀⠘⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠱⡀⠀⠀⠀⡜⠁⠀⠙⢦⡀⠆⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⣠⠂⠀
⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⡀⠀⠀⢳⠀⠀⠀⠀⠉⠒⠤⠤⣀⠀⡤⠒⠉⠐⠒⠀⠤⠐⠊⠁⠀⠀