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