⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⣀⠀⣠⡴⠾⠋⠁⠀⠀⠀⠀⠈⠉⠒⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⢀⣀⡀⠀⠉⠈⠙⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣗⠒⠠⢄⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⡎⠈⠑⢢⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⢆⠀⠀⠈⠉⠒⠤⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡟⠀⢠⠃⡀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⣶⣄⡀⠀⠀⠈⠷⠄⠀⠠⡤⢤⣤⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣠⠇⡰⠁⠀⣠⣴⣿⣿⣿⠃⢸⣿⠈⠻⣿⣿⣷⣄⠀⠸⠀⠀⡔⣳⡾⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣰⠁⣠⣾⣿⣿⣿⡟⠁⠀⠀⣿⠀⠀⠙⣿⡟⣿⣷⣔⠐⣾⠟⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠇⣠⣿⣿⡿⣿⣁⣀⣀⠀⢠⡏⠀⢀⣤⢼⣷⣿⣹⠋⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣰⣿⣿⣿⣿⡻⣿⣿⡟⠀⠚⠀⠀⣾⣿⡇⢹⣿⣿⠀⣸⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣇⠙⠋⠁⠀⠀⠀⠀⠈⠉⠠⣿⣿⡃⣸⡿⠁⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣼⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠀⠈⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣍⣻⠿⣹⠛⠳⢄⡀⠛⠛⣀⣠⣾⡿⠛⢹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⢀⣿⠗⠋⠙⡅⠛⢦⡀⡀⠈⠉⠉⡠⠞⡟⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣼⠇⠈⠢⡀⠘⡄⠀⠑⣄⠀⠠⠊⢀⡜⠳⣤⡼⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠈⠳⢼⠀⠁⠘⣧⣀⣠⣾⠃⠀⡞⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢣⡄⠀⠘⢻⡟⠁⠀⢸⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈⡆⠀⠀⠀⡇⡆⢠⡟⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣀⠀⠀⠀⠀⠀⢠⡟⡦⣀⠀⠀⠀⢸⠀⡈⢀⣇⣥⠯⡇⡆⢀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣦⣀⡴⠋⠱⣥⠈⠓⠤⠀⠀⣷⡧⣿⠋⠰⡗⠙⠛⠋⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⠁⠀⠀⠘⣯⠢⣄⠀⢀⣯⠀⠻⡄⡸⡟⠀⠠⢚⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡴⠋⠀⠀⢣⠀⡄⢼⠳⣄⠉⠉⠈⡆⣠⠏⣧⠁⠀⠀⠞⡿⢮⣷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⡎⢣⡹⣾⡀⠀⠑⠄⠀⣿⡿⢾⠃⠀⠀⠀⢰⢀⡼⢿⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠇⠀⠀⠀⠀⡇⠀⠑⢽⣧⠀⠀⠀⠀⡟⣧⡼⠀⠀⠀⠀⣼⠞⣠⠎⠱⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣶⣿⣯⣽⡿⠿⣿⣇⠀⠀⠀⢀⠉⠒⠠⠌⢻⣧⠀⠀⠀⡇⠸⣳⠀⠀⠀⣰⣿⠞⠁⠀⠀⠘⢄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠈⢿⣧⡀⠀⢸⠀⠀⢀⣀⡨⣮⣷⡀⠀⣧⠀⢻⡀⠀⣼⡿⠃⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⣠⢴⣺⠯⠤⠤⠬⠿⣷⡄⠀⠙⢋⣷⣴⣾⣿⣆⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣡⠞⠁⠀⠀⠀⠀⠀⠈⢿⣷⣾⢭⠿⣋⠙⡀⠘⢦⡀⠀⠀⠀⠀⡸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⡄⠀⠀⠀⠀⠀⠀⠘⡏⢆⣂⠳⠛⠒⠛⠚⠉⠈⠒⠤⠤⠚⠀⠚⡂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡅⠘⢆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡳⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠤⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀