⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣻⣿⣿⣟⣷⠒⠤⣄⡀⣉⣱⣦⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣀⣀⣀⣠⣖⣿⣿⣿⣷⣿⣿⢯⢳⣽⣵⣆⠀⠙⢿⣿⣫⠿⠿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠇⠻⢧⠹⣯⠛⢧⠀⠀⠙⣾⠻⠢⣘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣟⣻⢻⣯⣿⣼⣴⣿⠁⠀⠀⠀⢸⣇⠫⡆⠀⢣⠀⠀⠘⣦⢹⣿⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣛⣿⣧⣿⣯⣿⡟⠁⡟⠀⠀⠀⠀⡆⣿⡄⠸⡆⢨⣆⠀⠀⠸⣼⣿⠟⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⣿⣼⡇⣿⣿⠀⠀⢀⡄⠈⡏⢀⢁⣿⢣⢀⢳⡎⣾⡄⠀⠀⢻⣹⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢻⡿⣽⢸⠀⠀⢸⡇⠀⡇⠈⡏⡷⣯⡎⣿⣿⢸⣿⠀⠀⠘⣇⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣺⡇⣿⢿⠀⢠⠸⣧⠀⣇⠀⡟⡗⠺⣷⣿⣿⣧⢿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⡇⢹⣸⣇⣼⢾⢻⣘⣿⣶⣿⡇⣠⣼⣿⣿⣾⣿⣧⣸⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣼⣿⣿⣾⣿⣾⣿⡿⠿⠟⠈⠟⡉⢿⣿⣿⣿⡏⣸⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣿⣿⡹⣿⣿⣿⠀⠀⠀⠀⠀⠈⠛⣓⣮⠏⣇⠏⠀⣾⡇⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣯⠙⠚⢓⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⣰⡽⠀⠀⣿⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣍⠓⣴⢹⠏⣿⣷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⡇⢠⠀⣼⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡈⠳⣌⢿⢠⡧⣿⣿⡛⣷⣄⡀⠀⠀⠒⠈⠉⠀⠀⢀⣤⣾⣇⣾⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠙⢷⣸⣾⠞⢱⡟⣾⢻⢻⡅⣿⢳⠢⣄⡀⣀⡤⡶⠋⡜⣿⢪⢿⢸⡃⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⢸⠇⢀⣿⡿⣿⠈⡸⠑⠻⣬⠧⢿⡏⠁⠀⠀⠰⢡⣿⡿⡌⣿⠃⡇⢸⡀⠀⡇⠀⠀⠀⢀⡴⣺⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣼⣴⢿⣿⡿⣿⠄⡇⣠⣞⣁⡴⠿⠀⠀⠀⠀⢠⡿⣿⠁⠀⡇⡀⢡⠙⡟⣄⡇⠀⠀⣴⣯⣾⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⣧⣿⡿⠁⣿⢰⠞⠁⣠⠎⢱⡄⠀⠀⠀⡴⠋⠀⢸⡇⢸⡿⠁⣼⡠⢿⢻⢱⠀⠀⣿⣿⣿⣿⠛⠁⠈⢻
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⢸⣻⣿⠉⣳⣿⣿⢖⡝⠁⠀⠈⠹⠃⡤⠴⠒⠢⠤⡾⠀⣾⡹⣻⠛⠓⠺⢯⡞⡆⠀⢿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣿⡽⠀⠀⠀⢸⢏⣿⣿⠟⣿⣭⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣾⣿⣳⠃⠀⠀⠀⠀⢳⢱⠀⠈⠙⠛⠋⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⣿⢯⠃⠀⠀⠀⢸⡿⠛⠓⣼⣿⡀⠙⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠻⣽⣃⠀⠀⠀⠀⠀⠈⡇⢇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣾⢋⣯⡟⠀⠀⠀⠀⠈⡀⠀⣰⣏⡇⠉⠢⢄⡀⠀⠉⠉⠑⠒⠤⢄⡀⡞⡏⠀⣷⠃⠀⠀⠀⠀⠀⢠⣷⡘⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⡿⣱⣿⣿⠇⠀⠀⠀⠀⠀⡇⢀⣿⢻⠁⠀⠀⠀⠀⠀⠉⠑⠒⠦⣄⠀⣸⣧⣇⢠⠃⠀⠀⠀⠀⠀⠀⣼⢿⣷⡘⢆⠀⠀⠀⠀⠀⠀
⠀⢠⡿⡱⣿⠏⣿⠀⠀⠀⠀⠀⠀⣷⣼⣿⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣽⢚⡟⠒⠒⠤⣀⠀⠀⣰⡹⡜⣿⡷⡈⢣⡀⠀⠀⠀⠀
⠀⣾⠃⠹⡟⢠⣷⠀⠀⠀⠀⠀⣰⢙⣵⣿⣷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⣟⣿⣿⠓⣖⢤⣄⠈⢣⣰⢛⡇⡷⢿⢣⠙⣦⡑⢄⠀⠀⢀
⠀⣿⣻⢠⠃⢸⣏⣆⠀⠀⢀⡜⡿⡄⢳⡹⡿⣿⣀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣞⣾⡿⠃⣸⣿⡟⡼⣷⣠⣇⡇⠀⡇⢸⠘⣄⢱⡙⠢⣕⡄⣾
⠀⡟⡏⢸⠀⠘⣿⣼⣧⡤⡎⢡⣿⣇⠀⠹⣵⡟⣿⢧⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⠇⣰⣫⡾⠸⢱⢏⢿⣿⡇⠀⠁⢀⠀⣿⡌⣷⡀⠀⣽⣿
⠀⢳⣷⣾⠀⠀⣿⣹⣿⢸⣷⢸⢸⣿⡆⠀⠘⠹⣼⣷⡁⠀⠀⠀⠀⠸⡰⣿⡋⠸⣰⡗⢱⠁⡰⢃⣞⢼⡷⡇⠀⠀⢸⠀⣟⢷⢸⣷⣾⣿⣿
⠀⠈⣿⡟⡄⢀⣿⣿⢻⡾⡟⣼⠀⡟⠹⣆⡀⠀⠈⢻⣱⡄⠀⠀⠐⢞⣿⠓⢥⣰⠋⢀⢏⡔⡵⣿⣏⣾⣧⡇⢠⠆⣿⠀⡏⠘⡇⣿⣿⣿⣿
⠀⠀⠘⡟⢿⣾⡇⣿⠀⣇⣿⣿⠀⡧⠀⢹⡵⢦⡀⠈⢧⠙⠀⠀⢀⣾⠃⠠⢀⡙⠢⣄⡞⠀⣼⡿⣼⢃⣿⡇⡜⣲⡏⠀⣇⣴⡇⢸⣧⢿⡿
⠀⠀⢠⠃⣰⣿⡏⣿⡇⢸⣣⢻⡀⢱⠀⠈⠻⡌⢣⠀⠈⠀⠀⠀⣾⠃⠀⠀⠀⠈⠲⡼⢻⣶⣻⣿⣞⢿⣿⣳⢣⣿⡇⢸⣿⣿⣿⢸⣿⡿⡀
⡀⠀⠀⣰⡿⠁⢸⢻⣿⡀⢻⣮⢷⣼⡇⠀⠀⠘⡄⠱⡄⠐⡆⣸⠃⠀⠀⠀⠀⢠⣾⢖⣾⢼⣿⣿⡻⡟⣾⢏⣾⣽⢆⣿⣿⣿⣿⡼⠁⢸⠁
⠻⣤⠴⠃⠀⠀⢸⢯⣯⢳⡌⢻⣯⣻⣷⢳⡀⠀⠀⠀⠙⢄⣸⠋⠀⠀⠀⠀⡰⠋⢳⢟⡿⣿⡿⢋⣿⠿⣏⣾⣿⣿⣾⣿⡿⠟⣧⠃⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠈⡎⢿⣷⣌⡢⣯⣻⢿⣏⠛⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⡼⠁⠀⠐⢿⣸⡿⠁⣼⣿⣾⣿⣿⣿⡿⠟⠋⠀⣰⠏⠀⠠⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢄⡈⠛⠿⠯⡿⠹⡼⡄⠀⠀⠀⡰⠁⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢻⡁⡼⠹⣿⣿⡿⠟⠉⠳⠀⠠⠞⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇⢳⠀⠀⣰⠃⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠹⡟⢦⣽⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠸⡄⢧⣰⠃⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⠙⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀