⡀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⣻⠻⢾⣯⣌⠛⠩⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠶⠾⢿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣕⡒⣄⣘⠏⠓⠦⣙⣿⠀⣤⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣚⣋⢷⡒⠁⠀⠀⠀⢠⡀⠉⠩⠟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠛⢿⣿⣿⣶⣦⡄⠙⢷⣼⠠⡶⡈⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⢔⠯⠛⠊⠁⠀⠀⠀⠀⠀⢨⡟⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣏⠙⠿⠿⣿⣷⣦⣷⣾⣽⣝⣲⣘⣝⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⡪⢂⡀⠀⠀⣀⡤⠀⠀⠀⠪⠑⡺⠦⠀⢄⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠀⠀⠀⠘⠛⠈⠀⠀⠏⠀⢹⢰⡋⠉⠒⠌⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⢀⣴⠡⣂⠰⠊⠕⣀⢄⠤⢚⣐⣾⠎⡂⡀⠀⠳⠁⢣⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠸⢿⣷⣦⣄⡀⠉⠓⠤⣍⡓⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢃⡟⢁⡴⠏⠡⠂⢠⣾⢋⣴⠛⠉⠉⢻⢃⢰⠃⠀⠀⠐⠈⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠈⠉⠛⠿⣿⣶⣤⣀⠈⠑⠢⢬⣙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⢯⣞⡵⢋⡄⡤⢞⣤⢿⢯⡟⠁⠀⠀⠀⣸⢸⣸⠈⠀⢰⢴⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⠀⠈⠐⢀⣠⣤⣄⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣶⣦⣄⡈⠉⠒⠬⣍⡒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣭⡝⠃⡠⣀⢞⡟⠋⠕⠋⢸⠅⠀⠀⠀⢀⡧⢳⡻⠀⠃⣾⠘⠰⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠛⠀⠀⠀⣻⢽⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣦⣄⠀⠉⠓⠢⢍⣓⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣭⠷⠑⠛⣋⣴⠋⠀⠀⠀⠀⠀⠉⠠⠀⢀⣾⠁⠎⡅⢠⣼⣏⢦⡋⣼⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⢁⣀⣄⡀⠀⢠⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣁⠂⠀⣀⠈⠑⠒⠭⣉⢱⡏⠳⢤⣀⠀⠈⢛⣯⣵⡴⠂⠀⠞⢿⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⠙⡦⡨⠁⣿⡿⡋⢃⣗⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⡆⠀⠈⠉⠀⠀⠀⠸⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢒⡮⠼⠿⣭⡉⠒⢿⡿⣍⣯⣿⡷⢤⡀⠀⠁⠀⢀⠀⠀⠘⡆⠀⠀⠀⠸⡄⠀⠀⢠⠃⠀⡇⡇⠝⣽⡽⢱⣓⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢠⠟⢟⢶⢤⡤⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢠⣺⠭⠉⢳⡈⡿⡄⠀⠻⡌⠻⢝⢥⣄⣉⣻⠀⠀⢾⣆⢘⢠⣹⠀⠲⢤⣀⠀⠁⠒⠋⠀⡀⢳⢁⣾⣿⡈⢧⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠴⠋⠀⠈⢦⡇⡝⢦⠹⢷⢦⣤⣤⡀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠴⠚⠉⠀⠀⠉⡒⣏⣿⢫⠑⠊⠑⠀⠀⠻⣟⢿⡊⢱⡄⠸⣿⡄⡟⢾⡇⠀⠐⠮⠓⠦⠤⣠⠊⢀⣼⣸⣿⡏⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢸⢰⣿⣧⡲⣿⡿⣦⢾⣧⣤⠚⠋⢡⡀⠀⠀⠀⠀⠀⠠⣀⠱⣷⢸⢸⡀⠀⠀⠀⠀⢀⡿⠈⢻⡷⡵⣜⣿⠃⠩⢻⡇⠀⠀⠀⠀⠀⢘⣡⡴⣻⣷⢯⠏⡷⠡⠃⢀⡴⣶⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡜⢸⣿