⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⠒⠒⠒⠒⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⣽⡿⢋⡩⠟⠋⠀⠀⡠⠐⠋⠈⠳⣄⠀⠀⠀⠀⠀⠉⢛⡋⠉⠉⠛⠛⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣠⡾⠋⡰⠋⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠈⠳⣄⡠⠔⠒⠉⠉⠉⠑⢦⡀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣠⠎⠀⠀⡠⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠀⠀⠀⠀⠀⠀⠈⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡣⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢀⡀⠀⠀⠀⠀⠹⣶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠘⣦⠙⢷⡦⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⣀⠤⡲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀⠘⣧⠸⣧⠈⢻⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⡠⢚⡿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡘⣆⣽⢀⡞⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠊⡠⠋⠀⠀⠀⠀⠀⠀⠀⠂⠀⡄⠀⠀⢠⠏⡰⠋⡅⠀⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣿⡏⡾⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⡰⠀⡰⠁⠀⠀⠀⢀⣴⠃⠀⢠⡎⡔⠀⠀⡇⠀⣿⠀⠀⠀⠘⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠈⢿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡠⠁⣰⠃⠀⠀⢀⣼⠟⡧⢀⡤⢹⡟⠀⠀⠀⡇⡄⣿⡇⠀⠀⠀⡷⡄⠀⠈⣧⡀⢠⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⢧⣤⣴⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡰⠃⢠⠇⠀⠀⢠⣾⠋⡜⡤⠋⠀⣘⣀⠀⠀⠀⢣⣿⡏⢿⢤⠀⠀⡇⠘⡄⠀⢸⠱⡄⣏⠀⠀⠀⠀⠀⠈⣷⡀⠀⢄⠀⢸⡀⢿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⢸⠀⣼⠀⠀⢀⣾⢯⡼⠚⠉⠉⠉⠉⠉⠉⠉⠀⠘⢿⡇⠸⣷⠃⠀⡇⠀⠈⢦⡀⡅⠘⣿⣇⠀⠠⡄⠀⠀⠈⢷⣄⢸⡄⢸⡇⠈⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠏⡞⠀⣸⡐⠛⠀⠀⣾⠃⠀⠀⠀⠀⠀⣠⣤⣦⡀⠀⠀⠀⠘⡇⠀⠻⣧⢠⡇⠀⠒⠚⠿⣿⡦⢼⣿⣦⠀⠸⢆⠀⠀⢸⡏⢿⡇⢸⡇⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⣼⠃⠇⢀⠀⣰⣿⡀⠀⠀⠀⣴⠟⡛⠀⢘⣷⡀⠀⠀⠀⠃⠀⠀⢻⣧⡇⠀⠀⠀⠂⠘⠃⠀⠘⣿⢧⡀⠈⠃⠀⢸⣿⠈⢿⣼⠃⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡘⠀⠀⣼⠃⠀⠀⠸⡀⣿⠙⡇⠀⠳⣿⠁⢸⣀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⣠⡶⠛⣿⣆⠀⠘⡇⠻⡄⠀⠀⠀⣿⡀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⠃⠀⠀⣿⠀⠀⠀⠀⣿⣇⠀⠨⡀⠀⠇⠀⠸⡿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣉⠀⢀⣾⣿⣧⠀⠀⠀⠱⡄⠀⢀⠇⢷⡀⠸⡄⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡎⠀⠀⢰⠃⠀⠀⠀⢀⡿⡆⠐⠀⠆⠀⠀⠀⠀⢈⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⢳⣦⡤⠀⢠⣿⡀⢸⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⠁⠀⠀⢸⡘⠀⠀⠀⢸⡇⠈⢦⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡁⠏⠀⢸⠋⠀⣠⡾⠛⣷⡼⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡟⠀⠀⠀⢸⠁⠀⠀⠀⢘⠇⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡸⢻⠠⢿⣿⠇⠀⠸⡇⠀⠀⠘⡄⠀⠀⠀⠀⠀
⠀⠀⠀⢠⡇⠀⠀⠀⢸⠀⠀⠀⠰⢸⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠴⠋⢰⡿⣧⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⢁⣠⠔⠉⢀⡟⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠸⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸⡇⠀⡄⠀⠀⡅⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⡍⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⢱⠀⠀⠀⠀⠀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⢳⠀⠀⠀⢸⡇⠀⣷⠀⠀⡇⠀⣤⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⡏⠀⡇⠀⠀⠀⠀⣸⣧⠀⠀⠀⡇⢀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⡆⠀⠀⢸⡇⠀⢹⠀⠀⠇⠀⣿⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠀⢸⡇⠀⡇⠀⠀⠀⠀⡇⡏⠀⠀⠀⢃⢸⠀⠀⠀⣇⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢱⡀⠀⢸⠁⠀⠈⡄⢰⠀⠀⢹⠀⠀⠀⠀⢀⡅⠲⢄⠀⠀⠠⠄⠒⠉⠁⣿⠀⠀⠀⢸⠃⠀⡇⠀⠀⠀⢰⡇⡇⠀⠀⠀⢸⠘⡆⠀⠀⢸⠀⠀⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢳⠀⢸⠀⠀⠀⡇⠘⡀⠀⠈⣇⠀⠀⣠⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠤⣀⠀⠀⠀⢰⡇⠀⠀⠀⡾⢀⡇⠀⠀⠀⢸⠀⠃⠀⠀⠀⡆⠀⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⠀⠀⠀⢰⡈⣧⠀⠀⢙⡶⠉⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠱⡀⠀⡼⠀⠀⠀⢠⡇⢸⠇⠀⠀⠀⢸⡄⢠⠀⠀⠀⢱⡀⠀⠀
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠈⠇⢹⣆⠴⠃⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠸⡀⠈⠳⢥⡀⠀⠀⣼⠀⣼⠀⠀⠀⠀⠀⡇⠘⡀⠀⠀⠈⠇⠀⠀
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⡇⣿⢰⠀⠀⡀⠤⠊⠁⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣠⠁⠀⠀⠀⠈⠙⠚⠧⠤⣿⠀⠀⠀⠀⠀⡇⠀⢧⠀⠀⠀⢸⠀⠀
⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢀⣷⠤⢿⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠁⠀⠀⠀⠀⠀⠀⠀⣠⡔⠛⠙⠒⠲⣤⣀⣇⠀⠈⡄⠀⠀⠀⡆⠀
⠀⠀⠀⠀⠀⣷⡀⠀⠀⢸⡍⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠁⠀⠈⠉⠉⣹⡇⠀⢣⠀⠀⠀⢹⠀
⠀⠀⠀⠀⠀⠙⢇⠀⢀⠎⢡⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠈⢲⠤⢀⠀⠀⠀⠀⠀⣀⠤⢰⠂⠀⠀⠀⠀⠀⠀⣀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⡇⠀⠈⡄⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠈⠀⡈⠀⠈⢇⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠑⡀⠉⠀⠀⠀⠁⠀⡐⠁⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⢱⠀⠀⢹⠀⠀⠀⢃
⡇⠀⠀⠀⠀⡆⠀⠀⠇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⢲⠀⣀⡀⠀⠀⠀⠈⠢⠀⠀⠀⢀⠈⠀⠀⠀⢀⡠⢴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠸⡀⠀⠈⡄⠀⠀⢸
⠘⢆⠀⠀⡰⠁⠀⡈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⠠⡐⠒⠠⣄⡀⠠⡀⠠⠂⢀⡤⠔⠈⣡⠔⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠸
⠀⠈⠲⢎⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠉⣲⠦⠌⣑⡾⣷⣎⣑⠐⠀⠉⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢧⡀⠀⠃⠀⠀⢸
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠔⠉⠀⢀⡀⠸⠇⣷⢄⡀⠈⠓⠤⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠄⠀⠀⠸⡃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡄⠀⡐⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢀⠤⡖⡛⠟⣦⡈⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠁⠀⡘⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠸⠁⡴⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⡏⠉⠁⣠⢣⠇⡇⢸⠉⠐⠂⠤⡖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠐⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠃⡈⠀⡇⠸⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠘⠋⠀⠀⠀⠀⠀⠈⡄⠀⠀⢠⠇
⠀⠀⠀⠀⣰⡠⠀⠀⠀⠀⠀⠀⠀⠄⠈⢇⠀⠀�