⠀⠀⠀⣠⣾⣿⣿⡿⠟⠋⢁⠔⠀⡠⠊⠀⠀⠀⠈⠩⠉⠙⠻⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⠉⠀⠀⠐⠁⡀⠞⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠹⢿⣿⣿⣿⣿⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠡⠀⠀⠀⠎⠹⣿⣿⣿⣿⣇⠀⠀
⠀⠀⠀⠀⠀⠀⣿⡟⢡⠂⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⢁⠀⠀⠀⠀⢈⢻⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⣸⡿⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡇⠀⠘⠀⠀⠀⠂⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀
⠀⠀⠀⠀⠀⣿⠇⡏⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⡐⣐⠀⢷⠀⠀⡆⠀⠀⠈⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀
⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠰⠀⠀⢀⠆⠀⠀⠰⠁⡅⠀⢸⠀⠀⡟⠀⠀⠀⠠⠀⠀⠃⠀⡀⢸⣿⣿⠀
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢰⠀⠀⣀⡀⠀⠠⠁⢰⠃⠀⠈⡇⠀⡁⢁⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⠀
⠀⠀⠀⠀⣠⢿⣿⠀⢸⠀⠀⢀⢿⢠⣧⣄⣇⡔⡥⠂⡄⠀⠀⠀⢷⠀⡁⠚⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀
⠀⠀⢠⠎⠱⠀⣿⡀⢸⠀⠀⡼⠛⡞⣃⣄⡙⠳⡀⠈⠀⠀⠀⠀⠘⣤⢀⡤⠸⡶⠀⢠⠀⠀⠀⠀⢠⡟⡑⢄
⠀⠀⠸⡀⠀⠀⢹⢣⡈⡀⢰⠁⠀⣾⣿⣽⣿⡆⢱⠀⠀⠀⠀⠀⠀⠀⠁⢠⣴⣦⣌⠺⡆⠀⠀⢀⠟⠃⠀⠈
⠀⠀⠀⢇⠀⠀⠀⢾⣷⠠⡌⠆⠀⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣾⣿⠀⢸⣴⣸⡟⠀⠀⠀⢰
⠀⠀⠀⠘⡀⠀⠀⣼⠻⡆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⠻⠿⠟⠀⠈⢹⣿⠁⠀⠀⢀⡆
⠀⠀⠀⠀⠱⠀⠀⡙⢶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢻⠀⠀⠀⡞⠀
⠀⠀⠀⠀⠀⠱⡀⠠⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⡜⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠢⠄⣼⣯⡧⣀⠀⠀⠀⠀⠀⠀⠀⢐⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃⢀⠎⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⡇⠀⡇⠀⢀⠀⠀⠀⢀⡤⠊⠀⠈⠉⠉⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⢶⢤⡀⠀⠃⠀⡇⠀⢀⡀⢤⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡇⢙⠤⣈⢹⠀⠀⠗⠊⢁⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⣰⠍⡂⠍⣐⠏⠀⢰⠃⠍⠀⠀⠀⢸⠑⢄⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⠉⠀⠀⠐⠁⡀⠞⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠹⢿⣿⣿⣿⣿⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠡⠀⠀⠀⠎⠹⣿⣿⣿⣿⣇⠀⠀
⠀⠀⠀⠀⠀⠀⣿⡟⢡⠂⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⢁⠀⠀⠀⠀⢈⢻⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⣸⡿⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡇⠀⠘⠀⠀⠀⠂⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀
⠀⠀⠀⠀⠀⣿⠇⡏⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⡐⣐⠀⢷⠀⠀⡆⠀⠀⠈⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀
⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠰⠀⠀⢀⠆⠀⠀⠰⠁⡅⠀⢸⠀⠀⡟⠀⠀⠀⠠⠀⠀⠃⠀⡀⢸⣿⣿⠀
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢰⠀⠀⣀⡀⠀⠠⠁⢰⠃⠀⠈⡇⠀⡁⢁⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⠀
⠀⠀⠀⠀⣠⢿⣿⠀⢸⠀⠀⢀⢿⢠⣧⣄⣇⡔⡥⠂⡄⠀⠀⠀⢷⠀⡁⠚⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀
⠀⠀⢠⠎⠱⠀⣿⡀⢸⠀⠀⡼⠛⡞⣃⣄⡙⠳⡀⠈⠀⠀⠀⠀⠘⣤⢀⡤⠸⡶⠀⢠⠀⠀⠀⠀⢠⡟⡑⢄
⠀⠀⠸⡀⠀⠀⢹⢣⡈⡀⢰⠁⠀⣾⣿⣽⣿⡆⢱⠀⠀⠀⠀⠀⠀⠀⠁⢠⣴⣦⣌⠺⡆⠀⠀⢀⠟⠃⠀⠈
⠀⠀⠀⢇⠀⠀⠀⢾⣷⠠⡌⠆⠀⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣾⣿⠀⢸⣴⣸⡟⠀⠀⠀⢰
⠀⠀⠀⠘⡀⠀⠀⣼⠻⡆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⠻⠿⠟⠀⠈⢹⣿⠁⠀⠀⢀⡆
⠀⠀⠀⠀⠱⠀⠀⡙⢶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢻⠀⠀⠀⡞⠀
⠀⠀⠀⠀⠀⠱⡀⠠⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⡜⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠢⠄⣼⣯⡧⣀⠀⠀⠀⠀⠀⠀⠀⢐⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃⢀⠎⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⡇⠀⡇⠀⢀⠀⠀⠀⢀⡤⠊⠀⠈⠉⠉⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⢶⢤⡀⠀⠃⠀⡇⠀⢀⡀⢤⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡇⢙⠤⣈⢹⠀⠀⠗⠊⢁⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⣰⠍⡂⠍⣐⠏⠀⢰⠃⠍⠀⠀⠀⢸⠑⢄⠀