⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡇⠀⠑⠤⠤⠤⠤⠤⠤⠤⠄⣀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠏⠉⠒⠢⢇⣀⣀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⡄⠀⠀⠀⠀⢀⡱⠄⡀⢀⠔⡖⠀⠒⢄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⠔⠊⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⣣⡀⠀⠀⢠⠃⡔⠂⣎⡿⡄⠱⣠⢢⡈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡝⢄⠀⠘⠤⣱⠰⠃⠀⠈⡆⠈⢳⣏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠠⠄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⡆⠀⠉⠀⠀⠀⠸⡄⠀⢇⠀ ⠀⠠⡀⢀⠀⢠⠒⠢⡀⢰⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠀⠀⠀⠀⣠⠚⣦⠀⠀⠀⠀⠀⠀⠀⠐⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡼⠀ ⠀⠀⠗⠧⢀⠸⡄⠀⡷⡸⢀⡠⠔⠀⠀⠀⠀⠀⣠⡾⠶⠾⡄⠀⢀⡜⠁⠒⠚⠦⡀⠀⠀⠀⠀⠀⠀⢙⡿⡀⠀⠀⠀⢆⠀⠀⠀⢀⡁⠀ ⠀⠀⠀⠀⡘⠀⢰⢸⠀⣠⠈⢓⡆⠀⠀⠀⠀⣼⠁⠀⠀⠀⠱⣆⡞⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠈⢗⠑⠒⠲⣀⠀⠑⠢⠤⠉⠀⠀ ⠀⠀⠀⢠⠃⠀⠈⡄⡚⠹⡀⢸⠁⠀⠰⡄⠀⢇⠲⠶⠖⠋⠀⠀⡄⠀⠀⠙⠶⠶⠖⠘⣆⠀⠀⠀⢱⠀⠀⢉⠇⠒⢢⠑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢣⠈⣆⡀⢠⡟⢦⠌⠢⠄⠀⠀⠀⠀⠇⠀⠀⠀⢀⣤⣴⢏⢮⢻⣦⠇⡸⢠⠒⠉⠀⠀⠀⠃⠀⢄⠒⠢⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠂⠈⢣⡈⡷⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⠘⡄⡇⢿⠖⠁⠀⡇⠀⠀⠀⠀⠈⠀⠀⠁⠀⠸⠀ ⠀⠀⡄⠀⠀⡠⠤⢬⣄⣠⠎⠀⠀⠀⠈⠁⠀⢳⡀⠀⠀⠀⠐⠂⠠⠐⠋⠀⠀⢀⡜⠀⠀⠈⡸⠀⠀⠀⡏⠂⠄⠀⠀⠘⠀⡀⠀⢠⠃⠀ ⠀⠀⢨⠔⠁⠠⠀⠉⡳⢄⣀⡀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⢰⠃⠀⢀⣜⡀⠀⠄⠀⠀⢄⠔⢁⡴⠃⠀⠀ ⠀⠀⠃⠀⠀⡄⢀⡰⠕⡕⠈⠳⣄⣀⣀⣀⣄⠀⠀⠀⠈⣹⣖⠤⠤⠤⣔⡮⣝⡄⠀⣀⠤⠛⢢⡒⠓⠢⢌⡓⢔⣠⠖⠥⢂⠝⠁⠀⠀⠀ ⠀⠀⠀⢀⠔⠱⠁⠀⡜⡠⠣⢄⣀⠀⡠⠬⠈⢓⣶⠞⢩⢣⠀⠀⠀⠀⠀⠀⠸⣟⠉⠀⠀⢀⡴⠋⠑⠲⣄⠘⢌⢧⡀⠔⠁⠀⡄⠊⢠⠀ ⠄⠴⠤⠯⢤⣧⠀⠚⠊⠀⣐⣎⣠⠟⠺⡍⠀⠱⡀⡏⠑⡮⣄⠀⠀⠀⠀⠀⠀⢹⣒⠒⠉⠁⠀⠀⠀⠀⠈⢧⡘⣼⠁⢀⣠⠎⡄⠀⠀⣠ ⣦⡄⠀⢠⡞⠀⠑⠢⣴⠩⢤⠜⠁⠀⠀⣈⠓⠚⠁⠣⠞⣀⠈⢢⠀⠀⠀⠀⠀⣼⣿⣷⣄⣀⣀⠀⠀⠀⠀⠀⢣⣻⡖⠁⠀⡧⡇⠘⣰⠃ ⣇⡉⠀⠀⠙⣏⠲⢄⣈⣶⡘⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀⠈⠀⠀⠋⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠻⡉⠒⢫⡧⠼⣠⠃⢤ ⠹⣷⠆⢤⡄⡈⠑⣦⢀⣀⠇⠀⠀⠀⠀⠀⠀⠠⠋⠀⠈⠂⠀⠀⠸⡤⢤⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠱⣐⡿⣇⠀⢸⠀⣿ ⠴⠛⢷⣶⣿⣾⣿⡟⠢⡼⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⣇⢸⠙⠦⠤⠃⠘⣍⠉⣀⣿⣿⡟⠁⠀⠀⠀⠀⠹⡀⢹⠑⢺⠀⢻ ⣐⣮⠃⣿⣿⣿⣯⣖⢲⠇⢰⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡯⠊⢀⡵⡷⡀⠀⠀⠀⠀⠉⠁⠈⡿⠃⠀⠀⠀⠀⠀⠀⡇⠎⠀⠈⡆⠈ ⠀⠀⠀⣧⣿⣿⠟⠣⢿⠀⠸⡎⠁⠑⡖⡄⠤⡴⠚⠋⢄⠀⠀⠀⠀⠈⠚⣱⣾⣷⣦⣤⣤⣤⣾⣿⣿⡄⠀⠀⠀⠀⠀⢰⠣⢉⣲⢤⡹⡀ ⠀⠐⢴⣿⣿⡿⠓⢢⡇⠀⠀⠉⠒⠊⠀⠑⠚⢦⣀⣀⣈⠦⠔⠚⢤⡴⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡠⠃⠀⠈⠀⠢⠀⠱ ⠀⣰⣿⠿⠹⡈⢣⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠴⠋⢹⡟⠛⢿⣿⡿⠿⠿⢿⣿⢦⢴⡖⠉⠀⠃⠀⢠⠊⠀⠀⠀ ⠛⠃⠘⢧⣇⣈⣪⣄⡞⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡜⠁⠀⠀⠚⠛⠁⡰⡷⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀