⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⡄⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡔⠁⡀⢠⢀⡇⡀⠀⡀⣀⠀⢀⣼⣿⢏⡴⣹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠗⠀⠀⡠⠔⣻⣧⣦⠔⢘⣦⣾⡿⢃⠞⡼⣡⢏⡿⣖⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠚⣿⠿⢦⠀⣸⠀⠀⡁⣿⠏⠉⣵⣿⡿⢡⢯⡞⡴⢣⡟⡴⢻⡼⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠉⠀⠳⠤⠁⠀⣠⣾⣿⡿⢱⢇⡎⡼⣡⢟⡞⠠⣿⣷⠁⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⠧⡄⠀⠀⢰⠃⠀⠀⢀⣀⣀⣶⣶⣶⡆⠀⢀⣾⣿⣿⣿⢡⣏⡎⡸⢱⢏⡞⣰⣤⣿⡿⣡⠼⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⢸⢻⣶⣿⣿⣷⣌⣿⣶⣿⣿⣿⣿⠟⢡⡔⣿⣿⣿⣿⠇⠈⠀⠀⠁⠀⠈⠀⠀⢰⡟⠀⢸⡀⢀⠀⠁⢰⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣀⣀⣸⣸⣤⠿⢏⡷⣾⣟⢹⣿⠿⠻⠋⡠⣼⢹⢰⣿⣿⣿⣿⡸⠤⠄⠀⠀⠀⠀⠀⣀⡀⢠⠀⠀⠀⡄⣰⠀⠘⠀⠀⠀⠀⠀⠀
⠀⠀⠹⡀⠈⠉⢿⣸⢲⣄⣳⣇⢸⣿⠶⠲⡖⡏⣇⣿⠚⠊⠉⡩⠁⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠁⠙⠳⢄⡀⡁⢻⢰⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⣄⠀⠈⢿⣯⡑⠿⣿⠸⣿⣿⡄⣲⡻⠿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠻⣼⡎⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠳⢄⡈⢳⣧⢺⣸⡤⢟⢁⣮⡿⠛⠀⠀⠀⠀⠀⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢢⠀⠀⠀⠀⠀⢹⠀⠀⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡈⠉⠙⣯⣏⣔⣾⠿⠋⠀⠀⠀⠀⠀⠀⠊⠤⠳⡄⠀⠀⠀⠀⠀⠀⡐⠁⠒⠀⢣⠀⠀⠀⠀⠘⠗⠒⡛⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣆⢰⢀⣀⣾⣯⡝⠛⠀⠀⠀⠀⠀⣀⠄⠀⠀⣀⣠⡿⡀⠀⢀⠀⢀⣔⣁⣤⣤⣴⣘⠀⠀⠀⠀⠀⡀⠀⡙⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠂⠀⡏⠛⡏⠉⢹⠁⡇⠀⠀⠀⠀⠀⠀⣧⣴⣾⣿⣟⠛⢻⡧⠔⠉⠳⢺⢿⣿⡍⠉⢻⣻⠀⠀⠀⠀⠀⣇⠠⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢱⡸⢅⡀⡜⠀⡇⠀⠀⠀⠀⠀⠀⠸⣼⠘⠛⠃⠀⠈⡇⠀⠀⠀⢸⡘⠋⠀⠀⣸⠃⠀⠀⠀⠀⢰⠀⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⡇⡠⢣⡀⠀⠀⠀⠀⠀⠀⠸⡷⣄⡀⣀⠜⠁⠀⠀⠀⠀⠛⠤⠤⠴⣁⡀⠀⠀⠀⢀⡏⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠁⠀⠑⠤⠄⣀⠀⠀⠀⠀⢡⡀⠉⠁⠀⠀⠀⠀⢀⠀⠀⢀⣠⡖⠁⠀⠀⠀⢀⠞⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠘⠁⡀⠀⠀⠀⠀⠀⠀⡟⠳⡄⠀⡏⢻⢲⢶⣦⣤⡖⠒⠚⢉⡅⠂⠀⢀⠀⢀⠔⠃⠂⠸⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣀⣠⡱⡉⠺⠤⡧⡟⣷⢤⣈⠓⠒⠒⠂⠸⠤⢀⠀⠀⠀⠐⠸⢆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠃⠒⠦⡄⣄⣀⣀⡤⠄⠂⠀⠐⢽⢹⠒⣯⣤⣌⣄⣰⢧⢣⣟⡞⣳⣟⣲⣀⠀⠀⠀⠈⠑⠤⡄⣀⣀⠤⠵⢄⠀⠀⠀⠀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⡄⠀⡇⠀⠀⠀⠀⠰⣏⣽⡿⣇⣿⣿⠁⠿⣮⣿⢻⣥⣗⡯⠼⠿⠿⢶⣀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢢⠀⠀⠀
⠀⠀⠀⡌⠀⠀⠀⠀⢀⠁⠀⡇⠀⠀⠀⠀⠀⢈⡏⡏⢸⣿⣟⣵⠶⣣⢫⠟⠈⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠘⡆⠀⠀⠀⠀⠀⡆⠀⠀
⠀⠀⠀⢧⠀⠀⠀⠀⠀⡄⠀⠡⠀⠀⠀⠀⠀⡎⢸⠡⣿⠋⠐⣹⢷⣄⠀⠀⡀⠀⠀⠀⣀⡂⠤⣀⡀⠈⠄⠀⠀⡇⠀⠀⠀⠀⣰⠀⠀⠀
⠀⠀⠀⠈⢳⣀⠀⠀⠀⢧⠀⠀⠡⢀⠀⠀⣸⠁⠈⠀⢃⡞⡿⣡⡟⠉⠑⡂⠸⠉⠜⠁⠀⠀⠀⠀⠀⢱⠀⢣⠐⠀⠀⠀⢀⠐⠀⠀⠀⠀