⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠤⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠦⠤⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⣀⣀⠤⠤⠖⠒⠒⠒⠈⠉⠉⠉⠁⠒⠒⠢⠤⢄⣀⠀⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⣀⡤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢄⡀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⣡⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠘⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡜⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢣⡘⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡞⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣤⠀⠀⠈⡏⢣⠀⢳⡈⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡞⢀⡎⠀⠀⡴⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢸⠹⡄⠀⠈⢧⠀⠀⢱⠘⡆⠀⢣⠘⡄⠀⠀⠀⠀
⠀⠀⠀⠀⡼⠀⡜⠀⠀⠸⠀⢰⠃⠀⠀⠀⡴⢲⠀⠀⠀⠀⠀⠿⡄⠀⠀⠀⢀⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢧⠇⠀⠀⠘⡆⠀⠀⠳⠇⠀⠈⡆⢳⠀⠀⠀⠀
⠀⠀⠀⣼⠃⢰⠁⠀⠀⢠⣠⠏⠀⠀⠀⠀⣅⡼⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⡜⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠉⠀⠈⠃⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢹⠈⡇⠀⠀⠀
⠀⢀⡞⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢰⠇⠀⠀⢸⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠈⡆⠃⠀⠀⠀
⢠⠎⢠⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⢧⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠃⠀⢸⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⡇⠀⠀⠀⠀⠘⡆⠀⠀⢠⣽⣧⣄⣀⣀⠀⢹⡀⠀⢸⡀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢧⢸⠀⠀⠀
⠀⠀⡈⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢹⡄⠀⠀⢸⡘⣆⠀⠀⠀⠘⣷⠀⠀⡇⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠘⣆⢣⡀⠀
⠀⠀⡇⢀⡿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⡇⠘⡄⠀⠀⠀⢯⢣⡀⣇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠢⣙⠢
⠀⠀⢧⢸⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢹⢳⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢷⠀⠹⡄⠀⠀⢸⠀⢳⣻⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⢸⢸⠀⢸⡀⠀⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠸⡄⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⢸⠀⠀⠙⡄⠀⠘⡇⠀⢹⠀⠀⠀⠀⠀⠀⠸⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣼⠀⣸⢧⠀⠀⠸⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣀⣇⣀⣀⣀⡸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣼⣀⣀⣀⣘⣦⣀⣇⣀⢸⠀⡄⠀⠀⠀⠀⠸⠀⣟⢦⡀⠀⠀⠀⣦⠀
⠀⠀⠀⢹⣴⡇⠈⢧⠀⠀⡄⠀⠀⠀⢠⡐⠛⣿⠛⠛⢻⣿⣿⣛⢛⣟⣳⡇⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⠿⠿⠿⠿⢿⣿⣿⠟⠓⢺⠀⡇⠀⠀⠀⠀⢸⣸⡇⠀⢷⠀⠀⠸⡄
⠀⠀⢠⣞⡵⢻⡀⠈⣳⡀⡇⠀⠀⠀⠸⠷⡶⠿⠶⢖⣚⣉⠉⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣋⣉⣉⣉⣙⠿⠋⡀⠀⡜⠀⡇⠀⠀⠀⠀⢸⡿⠀⠀⢸⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠑⢤⡏⠻⣇⠀⢀⡠⠔⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⡇⢸⠇⠀⠀⠀⠀⣸⣤⠀⠀⢸⠴⠃⠀⠀⢰⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⠋⣁⡤⠖⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⣿⠀⠀⣀⡤⡤⠟⣛⡠⠞⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠋⠁⠀⣀⡤⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⢿⣿⠞⠉⠁⠀⠀⠀⠃⠀⠠⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠖⠋⣡⠔⠛⢳⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⢹⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠖⠋⠀⠀⠀⣸⠀⠈⢦⣿⠙⠳⣶⡠⠤⣤⣤⣀⡀⠀⢀⣠⠤⠀⣴⣶⣶⣿⢿⣿⣿⣷⣴⣷⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡄⠀⣠⠞⠁⠀⠀⠀⠛⠀⠀⢀⣽⣿⣿⡏⢹⢿⣿⡅⠀⠀⢠⡿⣿⣿⡏⠀⣿⡿⠟⢻⣷⣿⡚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠻⠚⠁⠀⠀⠀⠀⠀⠀⢀⡔⠛⠻⠿⣿⡄⢀⡟⠛⣿⣆⣠⠟⠀⠛⣷⡁⠀⣱⣧⠴⠛⠋⠉⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠈⢻⣼⠃⠀⠀⠙⠋⠀⠀⠀⠀⠳⣼⠋⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⣿⠓⠲⠤⠤⠤⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠤⠤⠤⢴⡆⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀