⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡀⠀⣠⠴⠃⣠⣴⣾⣷⣄⠀⠂⣤⣶⣶⣤⡀⠀⢀⣤⣶
⠀⠀⠀⠀⠈⠙⡇⠈⢦⡀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⡇⠀⢰⣿⣿⣻⣿⣿⣷⣼⣿⣿⣿⣿⣷⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⢿⣀⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⠿⣿⣿⣿⠟⠈⢻⣿⣿⣿⣿⠏⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢰⠈⡟⣇⠀⠀⠀⠳⡈⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢱⡿⠀⢣⠸⡄⢀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⣀⠀⠀⡜⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢧⠀⡜⢠⢧⠈⣧⠀⠀⠘⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣸⣉⠳⣼⣱⡥⢧⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⡄⡇⡜⢸⡀⢹⢧⠀⠀⠸⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡴⢻⠋⠙⢄⠘⡆⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⢣⠇⠈⡇⠈⡆⠳⡀⠀⢹⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡇⠀⠀⠈⢧⢹⡄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⣯⠤⠒⠒⠒⠽⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢳⠎⠀⠀⡇⠀⢹⠀⠙⢆⠀⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣸⠀⠀⠀⣀⢀⣑⠷⡀⠀⠀⠀⠹⡷⢄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠉⠀⠀⢸⠀⠀⠀⡇⠀⠀⢧⠀⠀⠑⠾⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣇⡇⠀⢀⠞⡡⠔⠚⠋⠹⣆⠀⠀⠀⠱⡄⠙⠦⣄⠀⠀⠙⣟⡶⠤⣄⣠⡤⠤⠤⣈⠙⠫⣅⢳⠀⠀⠀⠀⠀⢸⠀⠀⢸⠃⡄⠀⠈⢇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡄⠈⣇⠀⠀⢻⠀⠀⡾⠋⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠙⣄⠀⠀⠙⠢⢴⣉⡷⣟⣽⣿⣿⡯⣭⡉⠛⢯⡁⠸⡆⠀⠀⠀⠀⠘⣆⣀⡎⠀⢷⡀⠀⠘⣆⠀⠀⠀
⠀⠀⠀⠀⠀⢧⠀⠸⡄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠠⠴⣶⡄⠈⠢⡀⠀⠈⢦⠀⠀⠀⠠⢿⣿⠏⠘⠉⠈⢷⣞⢹⣿⣦⡙⣖⡇⠀⠀⠀⠀⠀⣇⡙⡇⠀⢸⠙⣄⠀⠘⣆⠀
⠀⠀⠀⠀⠀⠸⡆⠀⠹⡄⠀⡇⠀⠀⣠⡴⠒⠚⠓⠲⣯⣄⣀⠀⠈⠲⣄⠀⢳⡀⠀⠀⠀⢻⢠⡄⠀⣠⣠⣿⢿⢿⡏⢷⣽⡇⠀⠀⠀⠀⠀⣇⡱⢹⠀⣼⠀⠈⠳⢄⡘⣆⠀
⠀⠀⠀⠀⠀⠀⢱⡀⠀⡟⢦⢳⢤⡼⢏⣾⠟⠛⣿⣶⢿⣿⡀⠀⠀⠀⠀⠙⠲⠽⠀⠀⠀⠘⠈⣿⡽⢻⣿⣾⣿⠈⡇⠘⢉⡇⠀⠀⠀⠀⠀⡇⠀⢸⠀⡇⠀⠀⠀⠀⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠣⠀⡇⠈⠙⢸⣣⡟⡁⠀⠀⣸⣿⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠉⠛⠁⣰⠃⠀⢸⠁⠀⠀⣠⠀⠀⡇⢀⡏⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠚⢻⣼⡅⢰⣤⣾⣿⣳⣿⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢒⣲⡎⠁⠊⠀⡼⠀⠀⡰⡏⠀⠀⣧⡎⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⡄⠈⠻⠇⠈⣿⡘⠿⠵⠟⠐⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡼⢹⠃⠀⠀⡇⢣⡜⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠱⡄⠀⢲⡀⠀⠀⠳⡜⣆⠀⠀⠀⠈⠳⢤⣀⣤⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⢺⢠⠏⠀⠀⠀⡇⠘⣇⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⢆⡀⢷⣄⠀⠀⠘⢮⣆⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡎⠀⠀⠀⢀⡇⠀⠘⣇⢀⣀⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠺⠈⢳⠢⢄⣀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢸⡇⢀⠴⠚⠉⠀⠀⠈⢳⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⡇⠀⠀⠀⠀⢸⠞⠁⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠹⣶⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣇⠀⠀⣴⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡞⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠈⢹⣠⡀⠘⡄⠀⠈⢷⡶⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠔⠚⠉⠀⡼⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⣇⠱⣄⠹⡄⠀⠀⠳⡀⠀⣾⠀⠀⠈⠉⠉⢿⣍⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡀⠈⠲⣹⡄⠀⠀⢳⢰⢻⠀⣀⡀⠀⠀⠀⠉⠳⠤⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠀⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⡇⠀⠀⠈⢱⡀⠀⠈⣿⣌⡿⠁⢹⠀⠀⠀⠀⠀⡼⠛⠋⠱⡄⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢁⡜⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⢀⣠⢿⣰⠃⠀⢠⠀⠀⠀⠀⣸⡁⠀⠀⠀⣼⣆⣠⠤⠖⠒⣚⢺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡤⠚⠉⠉⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠈⣇⠀⠀⢀⡽⠋⠀⠀⠈⢧⠀⢸⠓⠉⠉⣉⡙⠛⠲⠉⢙⠋⠁⡀⠤⠖⠋⠁⣸⠇⠀⠀⠀⠀⠀⠀⠀⢠⠞⡡⠞⠁⠀⠀⠀⠀⢸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡰⠋⢦⣀⠀⣀⠀⢹⠀⡰⠋⠀⣀⡤⠤⡄⠘⡇⣸⡀⠀⠀⠀⣉⣩⢷⠤⡞⠓⣖⠒⠒⠒⠒⢤⢿⠀⠀⠀⠀⠀⠀⣲⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣌⡉⠻⡙⠦⣷⠁⠐⠋⠀⠀⠀⠹⡄⢣⢹⠙⠒⠚⢉⡏⠀⡟⠀⢸⡀⠘⢆⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠳⠧⢤⠃⠀⡠⠖⠋⠉⢳⡀⢰⡜⠘⡄⠀⠀⡜⠀⢀⡇⠀⠈⢇⠀⠈⢧⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀