⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡞⠁⠀⢰⠁⠀⠀⢸⣠⡖⡯⠵⡦⡄⠀⢸⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡜⠀⠀⠀⠀⡯⠂⠛⢯⣭⠔⣃⣸⠀⠀⠀⡟⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠤⣄⡇⠀⠀⢠⠇⠀⠀⠀⠈⠑⠢⠤⠤⠬⠵⠃⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠎⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠸⡖⠉⠁⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⡀⡀⡀⠄⠤⠤⠤⠠⢀⣀⠀⠀⠀⠈⢇⡈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠃⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⠽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⢠⠔⠊⠉⠉⠲⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣁⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡀⠀⠀⠀⠀⠀⠤⠊⠁⠈⢣⠀⠀⠙⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⢇⠀⠀⠀⠉⠑⠢⣀⠀⠀⡎⠉⠳⠀⠀⠀⠀⠚⠀⠀⠀⢧⠀⠀⠀⠃⠁⡴⠃⡀⠀⠀⡇⠀⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡇⠀⢄⠹⡕⠒⠦⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⡜⠀⠀⠠⠚⢡⠇⣼⠀⠀⢠⠃⠀⠀⠀⠸⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢧⠀⠹⡀⠙⠦⡀⠀⠑⠒⠁⣠⠴⠒⠲⢄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠃⠀⢇⠀⡞⠀⠀⠀⠀⠀⠸⡀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠱⡀⠱⡄⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠑⠤⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠤⠤⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀ ⠀⠀⠀⠀⠀⠀⢣⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⡎⠀ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠂⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠃⠀⠀⠀⠀⡴⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⠔⠩⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⣌⠉⢷⢦⣄⣀⣄⠤⠖⠂⠂⠂⠂⠇⠐⠐⠐⠐⠐⢳⡒⣂⣒⣂⣊⡉⠩⠁⡥⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠞⢝⣃⠏⢱⣬⠉⡇⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡜⢧⣘⡗⡂⠢⠆⣠⠃⠙⠄⠥⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡎⠁⠨⠈⠸⡕⠋⡿⡿⠁⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣥⠭⡍⠂⢾⠯⠎⢂⠈⠽⠀⡱⡄⠀⠀ ⠀⠀⠀⠀⡔⠋⡃⡠⡋⣈⡮⠥⡾⠁⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡢⠹⠆⠇⠴⡷⣽⣄⠑⠇⠀⠋⡀⠅⠀ ⠀⣀⣴⠋⠀⡨⡒⠆⡟⢙⡁⠪⡢⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡃⠡⠅⠀⠈⠁⢣⡁⠔⢀⡣⠱⡏⣿ ⠿⠋⢙⠷⠮⠓⠣⠀⢤⡍⠔⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠉⠫⣫⣗⠈⠱⣁⠨⣙⣯⡍⠹ ⠒⢂⡕⠁⠀⠘⡊⣨⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠧⠋⠀⠁⠃⠁⠉⠁⠀⠃