⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣠⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠢⠋⠃⠈⠀⠀⠈⠁⠒⠚⠾⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠇⠀⠀⠀⠀⠀⠀⢀⢀⠀⠤⠀⡊⠳⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⡤⠴⡃⠀⠀⠀⡠⠞⢈⣊⠙⡃⠄⡔⣑⡅⣻⣾⢧⢀⣄⡠⡤⢀⠀⠀⠀⠀⠀
⠀⠀⢀⢄⠪⠃⠀⠀⠢⣳⢀⠀⣼⠁⣔⠋⠁⢘⡍⠀⡸⠋⠀⠷⡸⢿⢨⡂⣄⡀⢠⢣⠀⠀⠀⠀
⠀⢠⡫⠁⠀⠀⣤⡠⠀⡈⣶⢹⠁⠀⢥⣤⢤⣐⣾⠆⠷⣤⣤⣸⡇⢷⠃⠨⢃⡝⢸⢀⠆⠀⠀⠀
⠀⣯⠁⢀⣤⡍⠁⠈⠁⢊⢚⠘⢵⠀⠐⢉⣱⣍⡅⣀⣹⣏⣩⣅⣀⣗⠀⣰⡜⠃⡐⡼⠀⠀⠀⠀
⠀⢃⢄⢸⠟⠂⠀⠀⢀⠋⢸⣱⠀⠘⢘⠸⠛⠑⠉⠖⡜⠶⠚⠳⡅⡎⠑⠉⢀⠜⣰⠁⠀⠀⠀⠀
⠀⠀⠻⡢⣹⣦⠄⡀⡀⢁⡆⠃⠀⢀⡂⠀⠀⠀⠃⠀⠐⠀⠸⠂⢷⡒⢀⡂⢥⠴⠰⢤⣀⠀⠀⠀
⠀⠀⠀⠈⠈⠃⠦⢄⣹⢏⠅⠀⠀⡚⠀⠀⠀⠀⠀⠀⠀⢑⡀⠀⠈⡿⠁⢠⡍⠀⠀⠀⠪⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢙⠅⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢸⡃⣒⠀⠀⠀⠀⠀⡛⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡰⡀⠀⠀⢻⠆⡀⡀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠜⣑⠘⣷⣄⠀⢰⢾⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠞⡑⣤⢚⢢⡉⠃⡄⣠⣤⣴⡄⠤⠔⠤⣤⣬⡋⠀⠋⡻⡿⠪⠗⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢩⠑⠀⠩⠑⠲⢸⣷⣀⠀⠰⡆⠁⠂⡺⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠐⠨⠆⠳⡆⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⢀⠀⠀⠛⠦⢄⣤⣠⣼⠀⠀⠀⠀⠀⡿⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠁⡟⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠂⠀⠀⠀⠀⠀⢐⠆⠀⠀⠀⠀⢀⡄⢣⠀⠀⠀⠀⠀⠀⠇⡤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢤⠪⠃⠀⠀⠀⠀⠀⠀⠀⠀⠺⢦⢀⡔⠋⠀⠈⠻⣣⠀⠀⠀⠀⠼⢿⢿⡀⠀
⠀⠀⡐⠄⣠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡀⠀⠀⠀⠀⠙⡅⠀⠀⢰⣿⣿⡛⠂⠀
⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢦⠤⠀⢤⠄⠴⠠⠐⠚⠛⠈⠒⠀⠀