⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⣄⡀⠀⠀⢿⡿⢿⡝⣿⣿⢿⢋⠀⢀⣠⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡋⢒⠚⠿⣿⣷⠦⠜⢿⣿⡅⢽⡇⠀⠀⣼⡟⢉⢈⣼⠿⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠉⠂⣸⣿⢿⣧⣬⠛⡁⡀⠉⠀⡾⠋⠤⠚⣉⣵⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⣷⣽⣻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠌⡛⠿⣿⡿⠿⠴⡁⡇⠀⠀⠀⠆⣘⣛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣮⣟⣿⡧⢤⣤⣀⣀⣤⠔⣶⣦⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣁⣠⣷⣤⠀⢰⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣦⣤⣄⣀⡀⠀⢿⣶⣿⣻⡼⣾⣯⢷⢸⣮⡝⣿⡄⠀⢸⣏⠀⢸⣿⣿⣿⣧⣀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⠇⠘⠻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣇⡀⠻⣿⢻⣷⡿⣻⣷⣽⢿⣿⣿⣧⡀⢾⡏⢀⣼⢟⠿⣿⣿⣿⡇⠀⠀⠀⠉⠒⠶⠶⠬⡿⠋⠀⣠⣴⣾⣯⣟⠛⠋⢉⡙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢹⣿⣿⣿⣿⣯⣻⣞⢷⠙⠀⢙⠃⢿⣿⣿⣿⣽⣯⣽⠃⢸⡷⠏⠑⣋⣸⡿⣛⠿⠁⠀⠀⠀⠀⠀⠀⣴⢃⢶⠛⠃⣭⠲⣾⣝⡿⠛⡶⠩⠍⢛⣳⣶⣦⠀⠀⠀⠀⠀⠀⣠⣮⣴⣶⣶⣦⠀⠀⠀⠀⠀
⠈⢻⣿⣿⣿⣿⣿⣿⠶⣄⢢⠈⠀⠀⠘⠿⣯⣹⣷⠻⠀⠀⠀⡴⠟⢋⣁⣴⣞⣀⣀⠀⠀⠀⠀⠀⢸⣟⡸⠂⠀⠳⡍⠀⠀⠈⠡⢜⡳⢳⣺⣿⣭⢿⣾⣧⠀⠀⠀⢀⡜⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⣙⠛⠛⢛⣋⣡⣤⣮⣤⣼⣾⣿⣿⣶⣤⣈⠩⡄⠀⠀⠀⢁⣲⣻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⢁⠘⢷⣤⣅⠀⠀⠀⠂⠻⣿⣾⣻⢿⠿⣣⣬⡙⣤⠀⠀⣾⢁⣴⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⢸⣤⣠⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠁⠀⠀⢀⣸⣛⣻⣿⣿⣿⣿⣿⣿⢀⡆⡀⠀⠀⣤⠺⡔⠊⡙⣿⡄⣀⣄⢶⣤⣭⠻⠿⣾⣶⣿⣿⡧⢹⡆⠀⣋⣸⡿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠙⠛⠛⢻⣿⣿⣿⣯⡛⢿⣿⣿⣿⣿⣯⣶⣿⣿⣦⣝⡽⢿⣿⣿⣿⡿⠿⠃⡜⡜⡄⠀⢸⢢⠳⣌⠃⢡⣿⡇⢿⡌⣧⣻⡰⣄⠰⣿⣿⣿⠟⣡⣿⡇⠘⢿⣿⣤⣿⣿⠟⣁⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣭⣭⣿⡻⢿⣿⣿⣿⣿⣿⢏⡶⢛⣉⣥⢶⡲⡹⡜⠡⠀⠀⠘⢦⣻⠼⢀⣿⠟⢁⣾⣷⣾⣷⣽⡿⠀⠻⣿⣣⣼⣿⡿⠋⠀⠈⠁⠁⢩⣤⣬⣭⣿⣿⣿⣷⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⡆⣙⠛⠉⣩⡾⣋⠰⣿⣽⡿⠓⡉⢱⡙⠀⠀⠀⠀⠀⠉⠃⠊⠉⠀⠸⣿⣿⣿⣿⠿⠁⠀⠀⢀⣩⣤⣀⣐⠀⠀⠀⠀⠀⠥⡐⠶⠾⢭⣭⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⣿⣿⡿⣿⠟⠹⣿⣙⣻⣵⢟⣻⣶⣿⡮⠁⢚⣰⣈⠶⠃⠤⠄⠂⠀⠀⠀⠀⣀⣠⣾⣥⠶⠯⠙⠉⠁⠀⠀⢀⡼⠳⠈⣿⣯⡿⠀⠠⣀⡀⡀⠑⠢⢤⣬⣝⠛⠋⠁⠀⠀
⠀⠀⠀⠀⠀⣤⣶⣿⣿⣛⣟⢲⣍⡃⠁⠀⠀⠘⠋⢉⣉⣝⣏⠹⠟⢀⣀⡊⠈⣡⣤⣞⠻⢿⣿⣦⣤⡀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⢡⠍⡙⢿⣿⠇⣴⠒⣿⣿⣬⣅⣀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣽⢸⣿⣿⣿⣿⣿⣛⡻⢿⣀⠀⠀⢠⣶⣛⣿⣿⣿⣿⡆⠀⠉⠁⠈⠓⠬⢭⣋⣟⣷⣶⣶⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢩⠀⢼⡿⢡⣿⠀⢹⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠹⣆⠙⣿⣿⣿⣿⣿⣿⣶⣾⣯⣷⣄⢯⣽⣿⣿⣿⣿⣷⣦⠈⠲⡄⠛⠛⠶⣶⣬⣭⣛⡻⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠈⢟⡇⢺⣿⣿⣛⣻⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠓⠺⠿⠿⠛⡛⣿⣿⣿⣿⣿⣿⡏⣿⣏⣿⣿⣿⣿⣿⣤⠱⠌⠣⠈⣷⡢⣍⡻⢿⣿⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠛⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡓⠼⢿⣿⣿⣿⣟⠃⠈⠻⣿⠟⢻⣿⡟⣧⣅⠒⠧⠀⠈⠙⠛⠻⠆⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠉⠝⠉⠀⠀⠀⠀⠀⠀⠀⢙⡃⢿⣿⣷⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
