⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⣀⣀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢞⡯⢽⣟⣿⣽⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⢛⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⣻⣜⣮⡜⣿⣻⡞⣧⣻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠦⣏⡼⡹⢷⡀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠉⠉⠉⠉⠙⠻⣧⣿⣱⣳⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠉⠉⠉⠙⠺⣯⣓⠮⣕⣫⢳⢻⣤⢶⠶⣶⢲⣿⠏⠀⢀⡴⠖⠒⠒⠲⣤⡀⠠⠹⣶⣻⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣷⣭⠶⠿⠟⠛⠚⠓⠚⠳⡏⠀⣰⠏⠀⠀⠀⠀⠀⠀⢳⡇⠀⢹⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠘⢧⡀⠀⠀⠀⠀⠀⣸⠇⢀⣾⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣠⣞⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⣀⡴⠿⠿⢿⣦⡙⠲⣤⣤⣤⡴⠋⠀⣼⡟⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣾⢋⡵⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⠜⠡⠀⠀⠀⠀⠉⢿⣦⠀⠈⠁⢀⣠⣾⡿⣼⣻⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢃⠊⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⢀⠂⠀⠄⠀⠀⠀⠀⠀⠀⢹⣧⠀⠉⠉⠀⢿⣳⢧⡿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⡀⠁⡘⡿⣎⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡝⢠⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⡀⠀⠄⣿⣽⢾⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⢸⡄⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠂⠂⡏⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸⣷⣆⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⡈⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠁⠆⠁⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢇⠸⣿⣿⣿⣤⣿⠁⢠⠒⠒⢢⠀⠀⠀⣆⠀⠸⣿⣷⣄⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠂⠀⢱⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠒⠚⢎⢦⣻⣿⣿⠿⠁⠀⠀⠉⡖⠁⠀⡀⠀⠘⢆⠀⢿⣿⣿⣷⣶⣤⣴⣶⠿⣿⠟⡠⠔⠒⠒⠲⣟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⠼⣧⠀⠁⠀⠀⠀⠀⠂⠙⣭⢫⡽⢃⠀⠀⠈⠳⢌⣿⣿⣿⣿⣿⣿⡿⠖⠁⠀⠳⣄⣀⣁⡠⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⡁⠂⠀⢀⠀⠀⠱⡟⠀⢸⠀⠀⠀⠀⠠⠈⠉⠙⠛⠉⠉⠀⠀⠀⠐⠀⣠⢜⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠁⠐⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣤⠶⠛⠁⠂⠀⠀⠈⠀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣙⡷⢶⠶⢤⣤⣤⣤⣠⣤⣬⣤⣤⣶⢶⡾⠛⠙⠛⠦⣄⡀⠠⠀⠀⠀⠀⠄⠅⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠐⢠⠇⠀⠀⡀⠀⠀⡆⠁⣎⠀⠀⠀⢸⡀⠀⠀⠀⠀⠐⠉⡛⢲⠮⠤⣄⠩⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⡏⢀⠂⠉⠀⠈⠑⢌⠉⠁⠐⠈⠀⠄⢳⡀⠀⠀⠀⠀⠀⠄⠀⠀⣀⡼⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⠀⠀⠀⠀⢸⠃⢸⠀⠀⠀⠀⠀⢸⠀⢈⠀⠂⠁⠠⠀⠙⠦⣄⡀⠀⠐⠀⠀⣾⠉⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⠋⠙⢿⣦⣀⣀⣀⣼⡀⠀⠑⠢⠤⠤⠐⠁⠀⠂⠀⠄⢁⣠⣀⣁⣀⣀⣉⡿⠲⠶⠶⠃⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠚⠁⠠⡀⠀⠂⠠⢳⣌⠉⠁⠀⢳⣤⣁⣀⣠⣀⣠⣈⣠⣤⠗⠚⠉⠀⠀⠀⠈⠉⠻⣄⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⣠⠖⠉⢀⠄⠀⢄⠀⢐⣠⣾⠟⠃⠀⠀⠀⢸⠁⠀⠉⠀⠉⠉⡉⡇⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢀⠀⠀⠀⠂⠀⠀⠀ ⢀⡴⡋⠀⠀⠐⠔⢀⣰⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢀⠀⠀⡇⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢌⡆⠀⠀⠀⠀⠠⠀⠀⠀ ⠙⠲⠤⠤⠤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠤⠤⠤⠴⠒⠋⠀⠀⠀⠘⠳⠦⠤⠤⠤⠤⠴⢖⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀