⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠒⠒⠂⠒⠢⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⡍⢐⠂⡩⠐⡀⠂⠀⡀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠉⢥⠐⠌⢂⠠⢁⠠⠈⠐⠀⡀⡀⠡⠀⠠⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣁⠋⣄⠋⡄⢃⠈⠄⢂⠠⠀⠂⢈⠐⠀⠁⠂⢀⠀⠬⠅⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡰⢁⡚⠴⡁⠰⠀⡑⠠⠀⠂⠤⠁⢀⠀⠄⠀⠀⣿⣦⠀⠁⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣼⠁⢦⡙⢢⠁⠆⠡⢀⡁⢢⠁⡄⠐⡀⢂⠀⠄⡂⠬⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣏⡘⠄⡯⠐⡌⠨⡐⢢⠈⣁⢂⠡⠒⠰⡀⠒⠄⠙⢄⠀⠀⠀⠀⡅⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣗⠨⠜⡥⢃⠌⡡⢂⡐⠄⡀⣾⣿⡗⡄⠡⠁⠀⠓⠈⡀⢢⠐⠂⠠⠀⡟⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠒⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢌⡳⢌⠲⣉⠆⡱⢀⠢⠐⠤⢠⠍⡐⢀⠂⠁⢂⠠⢐⣴⡿⠈⠀⠀⢰⠃⣀⠀⠤⡒⢊⠡⢀⠂⠒⠀⠄⠀⠠⠈⠢⡀⠀⠀⠀⠀⡀⠠⠐⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠴⣊⠴⢡⠚⣄⠃⡌⡡⠈⠄⡐⢀⠂⠠⠡⠀⢲⡿⠋⠀⠀⢀⠀⢨⢁⠂⠌⡐⠄⢂⠒⠈⠠⠁⠀⠀⠀⠀⠀⠀⠘⠢⠐⠂⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣃⠞⡤⢋⡴⡁⢆⡑⠌⢂⠰⢀⠘⡠⢁⠂⠉⢀⠀⠄⠈⡀⡰⠋⠄⣈⠂⡘⢀⠂⠄⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣓⣌⠧⡜⠴⣈⠔⡸⢠⢁⠂⢆⠐⠄⢂⠡⢀⠂⢌⡐⠐⢡⠈⡔⢀⠂⡐⠠⠈⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⢰⣿⣿⣿⣷⣮⣟⣹⢦⡱⢊⡕⠢⢎⡘⢤⠃⡜⡠⠒⠆⡉⢄⠠⢁⠂⡐⢀⠂⢂⠘⠀⡁⠂⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣾⢚⡹⢣⠞⣽⣻⡿⣽⡟⣯⣓⢞⠳⣜⢋⠮⡑⢊⠌⠱⢀⠁⢂⠰⠀⣂⠈⠔⠠⡁⠌⠠⠈⡄⢀⠂⠀⠄⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⢠⡰⣶⡖⠿⣿⡙⡶⣙⢯⢾⡱⣭⢳⡙⣧⡑⠎⡌⠱⢈⠂⢂⠡⠈⠄⠁⠂⢈⠀⠄⡐⢀⠠⠊⢄⠠⠘⣀⠡⡀⠄⠠⢈⠀⠐⠀⢂⠐⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠈⠈⣀⣀⣀⣀⡙⣽⣻⣽⣾⣷⣝⣺⣧⡽⣆⡹⡐⣉⠆⡡⠊⠄⡐⠄⡐⠠⢈⢂⢈⡰⡀⣌⢠⡃⠴⣊⡔⣆⡰⡐⠌⡂⠤⠈⡈⣄⡢⠔⠂⠲⢤⡀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠤⢄⣀⡀⠀⠀⠀⣀⠼
⠀⠀⠚⠛⠛⠛⠛⠻⠿⠿⢭⣿⢯⡵⣭⣭⣍⣱⡙⢆⠓⠴⢁⠒⡀⠂⠄⣁⣂⣡⠤⠴⠴⠴⠂⠒⠒⠲⠴⠦⠖⠐⠒⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⠤⠤⠔⠒⠁⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀