⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠗⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⡖⢶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡿⣠⠖⠉⣀⡤⢖⣂⣤⠤⠖⢲⡆⠀⠀⠀
⠀⠀⠀⠀⠀⣏⠁⠀⣏⠙⠳⢬⡛⠢⣀⣀⣀⣠⠤⢤⣧⡀⣿⠃⢠⣾⠿⢛⡭⠟⠃⠀⡠⠈⢹⠆⠀⠀
⠀⠀⠀⠀⠀⡏⠀⣠⠼⠆⠀⠀⠉⠳⣄⡉⠀⠀⠀⠀⠈⠳⣾⣶⡤⠤⠔⠻⠤⢤⣀⠀⠁⣶⢸⡆⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠙⢦⡀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⢦⣀⠀⠀⠈⠳⣌⠁⠀⡇⠀⠀
⠀⠀⠀⠀⠀⡇⠀⢖⡉⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠀⠀⠀⠀⠠⡄⠀⠈⠳⣄⡀⠀⠘⢦⢀⡇⠀⠀
⠀⠀⠀⠀⠀⢹⠀⠀⠉⡗⠀⡀⠚⠁⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⠙⣦⣄⠈⢿⠀⠀⠀
⠀⠀⠀⠀⠀⡼⢧⠀⠰⠀⡞⠀⠀⡀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⢧⠙⢺⡷⠀⠀
⠀⠀⠀⠀⡼⠁⠀⠀⢠⢼⠁⠀⣰⠃⠀⠀⠀⢀⣾⡀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⢸⡄⠀⢷⠀⠀
⠀⠀⠀⣸⠃⠀⠀⢀⡏⡸⣀⠜⢹⡀⠀⠀⢠⠞⠀⡇⠀⠀⠀⢠⡄⠀⢰⠹⣆⠀⢀⣷⣄⡅⠀⠘⣇⠀
⠀⠀⢠⠇⠀⠀⠀⠸⠁⠛⠁⠀⢈⣧⠴⣶⣿⡖⠒⠻⢦⣀⢀⡞⢑⣠⣷⡄⠘⠲⢾⣿⠈⠁⠀⠀⢹⠀
⠀⠀⡾⠀⠀⠀⠀⢸⠀⠀⠀⢰⠋⠀⠀⣿⣿⣷⠀⠀⠀⠈⢯⣰⢻⣿⣿⡇⠀⠀⠀⠈⣧⠀⠀⠀⠀⡆
⠀⢸⠃⠀⠀⠀⠀⢸⠀⠀⠀⢸⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣸⣇⢸⣿⣿⡇⠀⠀⠀⢀⡞⠀⠀⠀⠀⢠
⠀⠘⠐⢺⠀⠀⠀⢰⡀⠀⠀⠀⣷⢤⣀⠹⣿⠃⠀⢀⣠⠞⠁⠈⠳⢿⡿⠀⢀⣠⠴⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠸⡆⠀⢀⡼⣧⠀⠀⢠⣿⡆⠈⠉⠛⠛⢻⡏⠀⠀⣠⣄⠀⢀⡀⠉⠀⠀⣠⢿⡀⠀⠀⣰⠀⠀
⠀⠀⠀⠀⢳⡴⢻⡆⠘⡆⠀⣼⠈⠻⢦⣀⠀⠀⠀⠙⠓⠚⠁⠈⠉⠉⠀⢀⣠⠞⠁⣼⠳⣄⠀⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠧⠞⠻⣴⠿⣆⠀⣸⣯⠙⣲⣦⡤⣤⣤⣤⣤⣴⠶⠛⢹⢷⡄⢠⠏⠀⠈⠛⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢁⡼⢟⠉⠀⠀⠄⣤⠼⠁⠙⠳⣦⡿⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀
⣰⠋⠁⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡃⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⢐⡏⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠘⣇⠀⠀⠀⠀⢰⣧⣤⡀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⣴⡷⠀⠦⣄⠀⠀⠀⠀
⠹⡄⠀⠀⠈⠣⢤⡴⠚⠉⠉⠉⠙⣧⣀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡟⡴⠂⠀⠀⠀⢳⡀⠀⠀
⠀⠙⢦⡀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠘⣿⢹⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⡿⠃⠀⠀⠀⠀⢠⡇⠀⠀
⠀⠀⠀⠈⠛⠲⣇⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠉⣿⡟⠛⣿⡟⠛⠉⠙⢿⡀⢷⣤⣀⠀⠀⣠⡞⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠹⣷⣤⡀⠀⠀⠀⣠⡟⠀⠀⠀⠛⠀⠀⢸⠃⠀⠀⠀⠈⠀⠘⣿⠛⠛⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠚⠉⠙⢲⣦⣤⡀⠀⠀⢈⣤⣀⠀⢀⣠⡄⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠘⠉⠀⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⠉⠀⡿⠀⠀⠀⣴⡟⠋⠁⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠻⠦⣤⣼⣧⠀⠀⢸⠛⠷⢤⣤⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠦⠤⢀⢠⡟⠀⠀⢸⠳⠤⡀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣸⠃⠀⠀⣾⠀⠀⠀⠀⠈⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⣯⠀⠀⠀⠻⣶⣤⡀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀