⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣶⠶⢦⣄⠀⠀⠀⠀⠀⠀⠠⣽⣿⣿⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⣤⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠻⠉⠉⠁⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢠⣿⠁⠀⣦⠀⢹⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢧⡀⣀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⢀⡀⠀⠀⢿⣄⠀⣸⠀⢀⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⢷⣤⣿⣶⣟⣁⠀⠀⠀⠈⠉⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣤⣄⠙⠷⣄⠀⠀⠀⠀⠀⡄⠀⠀⢠⡼⠁⠀⠀⠀⠀⠀⠀⠒⢻⢿⡿⠉⠉⠀⠀⠀⠀⢠⡶⠋⣡⣤⣶⣶⣤⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠈⠹⣷⡄⠈⢷⠀⠀⠀⠀⣿⣄⣴⣿⠃⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡼⠋⢠⣾⠟⠉⠀⠀⠈⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⠘⣿⡄⠀⠧⠈⠙⠷⣿⣿⣿⣧⣤⣤⠄⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠅⢠⣿⠋⠀⢀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⣤⠇⠀⠀⣿⡇⠀⠀⠀⠀⠈⢩⠟⣿⢿⣯⠀⠀⠀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠀⠀⠘⣆⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⣿⡇⠀⣷⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢸⣿⠀⠀⠀⠈⠉⠙⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⢀⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⣼⠃⠀⠀⠙⣶⣤⣀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⡴⠂⠈⣷⡀⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⣼⠏⠀⠀⠀⠀⠸⣿⣿⣿⣦⣄⠀⣿⣿⣿⣿⠀⢀⣠⣶⣿⣿⡿⠀⠀⠀⠹⣷⡀⠹⣷⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢠⡾⠋⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣿⣿⣿⣯⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠘⢷⣄⠙⢿⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠈⠻⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⡟⠀⡼⠃⠀⠀⠀⠀⠀⠀⢀⡴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠧⠀⢹⠂⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠙⢦⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢩⣿⣿⠟⣿⠻⣿⣷⡍⠉⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠁⢠⣴⣶⣶⣶⡦⢄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⠀⠀⠈⠳⠀⠀⠀⠀⠀⣀⠴⢒⣾⣿⣿⣿⣶⡄⠠⠶⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠆⠉⠳⣤⣀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠀⠀⢀⣠⡴⠛⠁⢀⣻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⠙⢿⡲⢦⣄⡀⠀⠀⠀⢀⣠⠴⢚⡽⠋⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠅⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⣓⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢤⣤⣤⡄⢀⣠⣤⣶⠾⠛⠁⠀⠀⠀⠀⠀⢠⠤⢤⣤⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠛⠁⠀⠀⠈⠛⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⢀⣠⣤⡶⠖⠋⠹⢷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠋⠀⠀⣀⣀⣠⠤⠶⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠶⠦⢤⣀⣀⡀⠀⠈⠉⠳⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠒⠿⠛⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀