⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⢴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⠇⠀⠈⢯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢼⣷⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢱⡏⠀⠀⠀⠀⣋⣾⣴⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⠉⠙⢿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⠇⠀⠀⠀⠀⣿⢻⡏⢿⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⡇⠀⠀⠀⠙⢯⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣿⠀⠀⠀⠀⠀⣿⠈⣷⠀⠻⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣟⠁⠀⠀⠀⠀⠀⠻⣞⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢠⡏⠀⠀⠀⠀⠀⣿⠀⢸⡆⠀⠹⣧⠀⠀⠀⠀
⠀⠀⠀⢀⣿⡆⠀⠀⠀⠀⠀⠀⠘⢿⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⠇⠀⠀⠀⠀⢀⡿⠀⠈⣷⠀⠀⠹⣧⠀⠀⠀
⠀⠀⠀⣿⣿⣮⡄⠀⠀⠀⠀⠀⠀⠈⢿⡌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⣿⠀⠀⠀⠀⠀⡸⡁⠀⠀⣿⠀⠀⠀⢻⡧⠀⠀
⠀⠀⢠⣿⢻⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠹⣦⠀⠀⠀⠀⠀⠀⠀⣀⣰⣷⣿⣾⡷⣠⢠⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⢠⢷⠁⠀⠀⣿⡇⠀⠀⠀⣿⡆⠀
⠀⠀⢸⡏⢸⡇⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡘⣷⠀⠀⠀⠀⠀⠀⣽⣿⠿⠟⠛⢿⣿⣿⡄⠀⠀⠀⠀⠸⡇⢾⠁⠀⠀⠀⠀⣼⠃⠀⠀⠀⢹⡇⠀⠀⠀⢹⡇⠀
⠀⠀⢸⡇⠈⣧⠀⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣽⣷⠀⠀⠀⠀⢠⣿⣿⣤⡀⠀⢀⣿⣿⣿⠀⠀⠀⠀⣿⣽⠃⠀⠀⠀⠀⣤⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀
⠀⠀⢸⡇⠀⢿⡀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⡀⠀⠀⢸⣿⣿⣷⣴⢀⢼⣿⣿⣯⠇⠀⠀⠸⡾⠃⠀⠀⠀⠠⣺⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣷⠀
⠀⠀⣾⡇⠀⢸⣧⠀⠈⢏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⣪⠿⠟⡿⡯⠏⣼⣾⣿⠃⠀⠀⢀⣼⠃⠀⠀⠠⠲⠩⠃⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣿⠀
⠀⠀⢻⡇⠀⠘⣿⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠄⣶⣃⢸⢷⣿⡀⠀⢈⢼⣦⠀⠀⣌⠇⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⣿⠀
⠀⠀⢸⡇⠀⠀⠸⣇⠀⠀⠀⠙⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⣿⣾⣧⢧⣶⣼⣮⡏⣰⢡⠕⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠏⠀⠀⠀⠀⠀⣿⠀
⠀⠀⠈⣿⠀⠀⠀⢿⡀⠀⠀⠀⠈⠘⢂⢤⡀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣏⡻⣿⣚⣏⢟⣿⡣⢏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠢⠁⠁⠀⠀⠀⠀⠀⣮⠀
⠀⠀⠀⣿⡀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠈⢙⠗⡄⡀⢀⠀⣀⡄⣴⡯⢿⣞⡿⣭⠹⣳⣗⢻⣷⣌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀
⠀⠀⠀⢹⡇⠀⠀⠀⠱⣧⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠟⠛⠑⠉⠁⠀⠘⢧⣿⣿⠚⠿⡯⣡⠙⡻⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀
⠀⠀⠀⠈⣿⠀⠀⠀⠀⢻⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣛⠛⣯⡆⢿⣢⠀⢀⣆⠀⠉⣵⣿⣏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀
⠀⠀⠀⠀⢙⠄⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡟⢻⣷⢺⣿⣷⣖⡖⠀⠀⠈⠙⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀
⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣻⢈⣷⣿⣿⣿⠼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠨⣦⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⣝⠆⣿⣿⣿⣿⡿⣟⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢷⡜⣿⣿⣯⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢷⡯⣵⡿⣿⣯⣏⣤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢚⣭⣃⢾⡏⣿⣿⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢾⢽⡹⡣⣿⣿⡿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡁⠸⣿⡪⢊⣿⣿⡏⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀⠈⣿⣱⣗⣿⣿⠂⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣤⠀⢹⣷⡇⣿⡏⠀⢠⣿⣿⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣿⣿⣿⡀⠈⣯⣶⡛⠃⢠⣿⣿⣇⠀⠀⠀⠀⠠⣹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡼⣿⣿⣿⣿⣤⣃⠈⢘⣧⣾⣻⣿⡟⠀⠀⠀⠀⢄⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗⢻⣿⣿⣿⣿⣯⣀⣡⣽⣿⣿⣿⣇⣀⠀⠀⢀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⡟⠶⢹⣿⣿⣿⣿⣿⣿⣤⣼⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡯⠽⢻⣯⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⡦⢤⣻⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣷⢿⣿⢶⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠯⢿⡿⠿⠿⠿⠿⠛⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⢴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⠇⠀⠈⢯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢼⣷⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢱⡏⠀⠀⠀⠀⣋⣾⣴⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⠉⠙⢿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⠇⠀⠀⠀⠀⣿⢻⡏⢿⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⡇⠀⠀⠀⠙⢯⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣿⠀⠀⠀⠀⠀⣿⠈⣷⠀⠻⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣟⠁⠀⠀⠀⠀⠀⠻⣞⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢠⡏⠀⠀⠀⠀⠀⣿⠀⢸⡆⠀⠹⣧⠀⠀⠀⠀
⠀⠀⠀⢀⣿⡆⠀⠀⠀⠀⠀⠀⠘⢿⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⠇⠀⠀⠀⠀⢀⡿⠀⠈⣷⠀⠀⠹⣧⠀⠀⠀
⠀⠀⠀⣿⣿⣮⡄⠀⠀⠀⠀⠀⠀⠈⢿⡌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⣿⠀⠀⠀⠀⠀⡸⡁⠀⠀⣿⠀⠀⠀⢻⡧⠀⠀
⠀⠀⢠⣿⢻⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠹⣦⠀⠀⠀⠀⠀⠀⠀⣀⣰⣷⣿⣾⡷⣠⢠⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⢠⢷⠁⠀⠀⣿⡇⠀⠀⠀⣿⡆⠀
⠀⠀⢸⡏⢸⡇⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡘⣷⠀⠀⠀⠀⠀⠀⣽⣿⠿⠟⠛⢿⣿⣿⡄⠀⠀⠀⠀⠸⡇⢾⠁⠀⠀⠀⠀⣼⠃⠀⠀⠀⢹⡇⠀⠀⠀⢹⡇⠀
⠀⠀⢸⡇⠈⣧⠀⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣽⣷⠀⠀⠀⠀⢠⣿⣿⣤⡀⠀⢀⣿⣿⣿⠀⠀⠀⠀⣿⣽⠃⠀⠀⠀⠀⣤⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀
⠀⠀⢸⡇⠀⢿⡀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⡀⠀⠀⢸⣿⣿⣷⣴⢀⢼⣿⣿⣯⠇⠀⠀⠸⡾⠃⠀⠀⠀⠠⣺⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣷⠀
⠀⠀⣾⡇⠀⢸⣧⠀⠈⢏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⣪⠿⠟⡿⡯⠏⣼⣾⣿⠃⠀⠀⢀⣼⠃⠀⠀⠠⠲⠩⠃⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣿⠀
⠀⠀⢻⡇⠀⠘⣿⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠄⣶⣃⢸⢷⣿⡀⠀⢈⢼⣦⠀⠀⣌⠇⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⣿⠀
⠀⠀⢸⡇⠀⠀⠸⣇⠀⠀⠀⠙⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⣿⣾⣧⢧⣶⣼⣮⡏⣰⢡⠕⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠏⠀⠀⠀⠀⠀⣿⠀
⠀⠀⠈⣿⠀⠀⠀⢿⡀⠀⠀⠀⠈⠘⢂⢤⡀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣏⡻⣿⣚⣏⢟⣿⡣⢏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠢⠁⠁⠀⠀⠀⠀⠀⣮⠀
⠀⠀⠀⣿⡀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠈⢙⠗⡄⡀⢀⠀⣀⡄⣴⡯⢿⣞⡿⣭⠹⣳⣗⢻⣷⣌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀
⠀⠀⠀⢹⡇⠀⠀⠀⠱⣧⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠟⠛⠑⠉⠁⠀⠘⢧⣿⣿⠚⠿⡯⣡⠙⡻⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀
⠀⠀⠀⠈⣿⠀⠀⠀⠀⢻⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣛⠛⣯⡆⢿⣢⠀⢀⣆⠀⠉⣵⣿⣏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀
⠀⠀⠀⠀⢙⠄⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡟⢻⣷⢺⣿⣷⣖⡖⠀⠀⠈⠙⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀
⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣻⢈⣷⣿⣿⣿⠼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠨⣦⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⣝⠆⣿⣿⣿⣿⡿⣟⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢷⡜⣿⣿⣯⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢷⡯⣵⡿⣿⣯⣏⣤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢚⣭⣃⢾⡏⣿⣿⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢾⢽⡹⡣⣿⣿⡿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡁⠸⣿⡪⢊⣿⣿⡏⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀⠈⣿⣱⣗⣿⣿⠂⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣤⠀⢹⣷⡇⣿⡏⠀⢠⣿⣿⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣿⣿⣿⡀⠈⣯⣶⡛⠃⢠⣿⣿⣇⠀⠀⠀⠀⠠⣹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡼⣿⣿⣿⣿⣤⣃⠈⢘⣧⣾⣻⣿⡟⠀⠀⠀⠀⢄⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗⢻⣿⣿⣿⣿⣯⣀⣡⣽⣿⣿⣿⣇⣀⠀⠀⢀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⡟⠶⢹⣿⣿⣿⣿⣿⣿⣤⣼⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡯⠽⢻⣯⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⡦⢤⣻⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣷⢿⣿⢶⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠯⢿⡿⠿⠿⠿⠿⠛⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
