⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠢⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⣀⡠⠔⠒⠉⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠉⠓⠲⢤⣀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣈⠳⡀⡠⠚⠀⢀⣠⠤⠒⠚⠉⠉⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣑⢿⣁⡠⠒⠉⠀⠀⠀⣀⠤⠒⠒⠤⢌⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⣁⣠⠤⠤⢄⡀⠑⢌⠶⢄⠀⠀⣠⠞⢁⠴⠒⠒⠢⠤⢌⣉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⣁⠴⠚⠉⠀⠀⠀⠀⠀⠙⠢⣄⣀⣨⠏⠑⢁⡴⠃⠀⠀⠀⠀⠀⠀⠀⠉⠺⣄
⠀⠀⠀⠀⠀⠀⠀⣀⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠔⠊⣁⠴⠊⠁⢀⣠⡴⣶⣿⣯⠉⠉⠉⠉⠒⠢⠤⣐⠒⠉⣠⣤⣴⡤⠤⠤⠤⣀⣀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⢀⠞⠁⢸⡀⠀⠀⠀⠀⠀⠀⣠⠶⠯⠤⠖⠒⢉⣁⠤⢴⣾⣿⣿⣧⣾⡋⢻⡇⠀⠀⠀⠀⠀⠀⠀⣧⣿⣯⣩⡿⢿⡆⠀⠀⠀⠀⠉⠑⠢⣄⠈⠆
⠀⠀⠀⠀⢀⠏⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⠒⠦⡎⠉⠉⠁⠀⠀⠈⢿⣿⣿⣧⣿⣿⣾⠇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣏⣿⣧⣴⡿⠀⠀⠀⠀⠀⠀⠀⣀⣑⡃
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠭⠭⢭⣉⣙⡛⠿⠥⣀⣀⠀⠀⠀⣀⡠⢺⢿⣿⣿⣿⣿⡿⠃⠀⣀⡠⠔⠊⠉⠉⢀⠇
⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠬⣝⣒⠦⠤⠭⣭⡭⠤⠖⠋⠀⠀⠈⢉⣉⠉⣉⣉⡤⠔⠒⠀⢠⠏⠁
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡩⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣠⢤⡤⠒⠁
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⢀⡠⠴⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢝⢦⠈⢦
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠃⠃⠀⢣
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⣄⣀⡀⠀⠓⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠒⠒⠒⠢⠤⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⣀⣴⣶⣶⣶⣶⣤⣄⣀⠀⠀⠈⠙⠒⠲⠤⠤⠤⠤⠤⠴⠒⠉⠀⠀⠀⣀⣠⣄⣀⠀⣠⠃
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣠⣾⡿⠟⠛⠛⠉⠛⠛⠛⠿⢿⣷⣶⣦⣤⣄⣀⣀⣀⣀⣀⡤⠤⠴⠒⠚⠉⠉⠉⠉⠉⢙⠄
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⠔⠊
⠀⠀⠀⠀⣀⣀⣱⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠈⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠋⠉⠁⠀⠀⠀⠀⠀⢀⠔⠁
⡤⠖⠋⠉⠁⠈⠀⠑⠦⣉⠒⠤⣄⡀⠀⠀⠀⠀⠑⠲⠤⣄⠉⠉⠒⠒⠦⠤⠤⠤⠤⠤⠤⠖⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠈⠙⠒⠢⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠦⣄⣀⠀⠀⠉⠉⠙⠒⠒⠲⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠒⣒⠶⠟⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠲⢤⡤⣄⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠖⠒⠉⠉⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄