⣠⠴⠒⠋⠉⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣰⡿⣋⣁⡰⣄⡷⠹⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡶⢶⢿⣿⣿⣦⣀⡀⠀⢴⠛⣆⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠉⢲⡞⠛⢯⣏⡏⠉⠒⣷⠙⠁⠀⠀⠀⠀⠰⡤⣿⡆⠀⣠⠄⠀⠀⠀⠀⠀⡔⣆⣶⠁⣄⣆⣤⢶⡗⢿⣏⠻⡿⡉⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢸⡇⣠⣿⠋⣿⢦⣴⢿⡀⠀⠀⠀⠀⠀⠀⠛⠃⡞⣴⠏⠀⠀⠀⠀⣄⣞⠶⡳⠋⢦⠝⠛⠁⠸⣏⠸⡿⡄⡅⡇⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠘⠚⠚⣿⠀⣿⡆⢠⡈⢳⡀⠀⠀⠀⣧⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⣯⢻⠜⠀⣰⠋⢀⠀⠀⡄⡿⡀⡿⣟⡽⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⢀⣄⠀⠀⢠⣦⢰⣟⠀⢸⣟⠈⣷⡄⢳⡀⠀⠀⣯⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡜⡇⢀⡾⠀⣼⠁⢗⣇⠸⡽⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣧⡺⢹⠀⢠⠏⠿⡟⠙⡖⢺⢿⠤⣧⣻⣆⡷⣄⠀⡏⡏⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⣸⣠⣏⣇⡼⡟⣇⣴⣣⠆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠏⠁⠘⠀⠈⠀⠰⡟⠀⢳⡸⣈⢧⣿⠀⠙⢷⣮⢦⣸⢱⠈⢿⡄⠀⣧⢠⠆⠀⣪⣿⢷⣧⢞⠝⠩⠫⢻⣷⡿⣾⡁⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡿⣈⣻⣾⣭⣽⣯⠥⠹⣏⢧⠀⣧⣰⡏⣞⢐⣾⣯⡭⣿⣵⣁⡀⠀⠀⠋⠉⠊⡇⠉⠀⢠⣣⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡿⣿⡽⠿⠛⠛⡛⣟⣯⡁⠈⠻⣷⣿⣾⣿⡽⣫⣿⡵⠛⠛⠺⠽⣏⣳⢦⣤⡄⢸⠀⠀⢠⣿⠃⣸⠃⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠈⠙⢿⡏⢸⡀⠸⡸⡿⡹⣸⢹⠉⠂⠀⠈⠋⠹⠉⠀⠀⢿⡁⢾⠾⠇⡧⣸⠀⠉⣻⠋⡇⠀⢠⣻⠃⢠⡏⡄⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠈⡧⣀⠳⣄⣀⣀⡳⠎⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣳⣄⣀⣀⡲⠏⢀⡠⠃⣸⠀⣠⡷⠃⢀⡞⠈⣡⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢹⠀⣇⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠃⣰⡿⠁⠀⣸⢁⡔⢹⢠⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢀⠀⠀⠀⠘⡆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⣴⠟⠀⠀⢠⠻⠊⠀⠸⠃⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢸⠀⠀⠀⠀⣿⡈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡾⡟⠀⠀⢠⠃⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠘⡆⠀⠀⠀⢸⢧⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⢲⠁⠀⢠⠃⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢳⠀⠀⠀⠈⡎⣇⢷⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⡏⠀⢠⠃⠀⠀⢀⠄⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⣆⠀⠀⠀⢱⠘⣯⣧⡀⠀⠀⠀⠀⠀⡇⢀⣠⠴⠒⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⡠⢃⠔⠀⣴⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣽⣣⡀⢰⡀⢇⠈⢿⣿⢦⡀⠀⠀⠀⢳⡋⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣠⠞⣹⠃⡴⡵⠋⢠⠞⡟⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠳⣜⡄⠈⢿⣧⠙⢦⡀⠀⠀⠉⠉⠙⠉⠁⠀⠀⠀⠀⣠⠴⠋⠀⢠⢃⣾⣾⢃⡴⠋⢸⡱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣿⣷⣽⣿⢤⡀⠳⡄⠀⠙⠳⣄⡀⠀⠀⠀⠀⢀⣠⠔⠋⠁⢀⡴⢲⣯⣿⣧⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠉⠻⢧⡉⠳⢽⣆⠀⠀⠳⣿⠓⠤⣖⣚⣉⠎⠉⢿⠶⠚⢠⢟⣩⡟⠋⠀⠀⠀⠀⠀⠀⠀�