⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡩⢉⢉⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣵⣶⣿⣿⣷⣶⣤⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣿⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⣿⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠁⠀⠈⠉⠉⠉⠉⠟⣿⣿⣿⣿⣿⣫⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣼⣿⣿⣿⠍⡀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣟⣖⣴⣶⣷⣶⣒⣠⣤⣤⣤⡀⠙⢿⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⡷⣄⠀⢩⡿⠋⣿⠛⠽⠿⣻⠤⢼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠛⢻⡟⠀⠀⠨⡷⣤⣤⠞⠀⢸⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⢰⣷⣽⡷⢾⣛⣙⡄⠀⠀⢀⡟⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢈⠉⢝⣛⡾⠛⠻⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣼⣿⠻⣷⣾⣀⠈⠙⠉⠀⠂⢀⣠⢎⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢸⣄⣥⢺⣿⣿⡀⢙⠻⣿⣿⣶⣦⣶⡼⠿⢻⣆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠂⠀⠀⠀⠀⡠⢤⣦⡮⠛⢹⢉⣿⢸⣿⣿⣷⠀⠀⠀⠀⠉⠉⠁⠀⠀⣸⣿⣷⣤⡈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢀⠴⣲⢗⢨⠇⢸⣿⣿⠀⠠⡄⠹⣩⡏⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⡵⢨⣯⣂⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢄⢪⢫⡏⡼⠘⣸⠈⣿⣿⡄⠀⠃⠀⢁⡿⠸⣿⡘⠄⠀⠀⠀⠀⠀⠀⣰⢿⠿⡟⠇⠏⠃⡿⢻⠪⢪⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⢫⠃⣰⣶⢡⡇⠇⡀⣿⣿⣇⠀⢸⠀⢸⠁⡇⠿⡸⣎⠄⠀⠀⠀⢀⣾⠕⠙⠀⡇⠀⢀⡇⡇⢸⠀⠈⠉⣼⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣮⡃⢠⣿⡿⢯⢴⣰⠇⢹⣿⣿⠀⠀⡀⠈⣰⡇⢰⡧⣿⣿⠄⠀⢠⣿⡇⠀⡇⠀⡇⢠⢸⡇⡇⢸⠀⢀⠀⢩⡿⣇⠀⠀⠀⠀⠀⠀⠀ ⢠⡙⢁⣿⣿⠅⣾⢫⣿⢠⢸⣿⣿⠀⠀⡇⠄⡟⢠⢸⡇⢸⣿⡏⣤⢳⣿⠀⠀⡇⠀⡇⣸⢸⠇⠇⠘⡄⠘⡀⢸⢠⣹⢔⠀⠄⠀⠁⠀⠀ ⠌⠃⢸⣿⡿⢠⢿⢹⡃⣸⠈⣿⣿⡆⠀⠁⠈⢠⡏⡌⣤⢸⣿⣿⡟⣼⣿⠀⢀⠇⢠⢳⡟⡜⠇⡼⢶⠇⠀⡇⢘⣿⡁⠀⠉⠀⠀⠀⠀⠀ ⠘⠀⣸⣿⠃⡎⡇⡆⠇⠏⡆⣿⣿⡇⠀⢠⠀⢸⠁⡇⡇⠈⣿⣿⢳⣸⡿⠀⢸⢰⣼⡄⡇⡇⢠⣷⣶⣄⣀⠃⣬⣿⢤⠀⠀⠐⠈⠀⠀⠀ ⠀⢀⣿⣿⢀⢻⢠⠻⡼⢸⢧⢹⣿⡇⠀⢸⠀⢸⠀⡇⡇⡆⣿⣿⣦⣿⡇⠀⢸⠀⠘⡄⡇⣷⢸⣿⠁⣿⣷⡞⣷⣿⢹⠀⠐⠠⠀⠀⠀⠀ ⠀⢸⣿⡿⢸⡌⢸⣾⣿⣣⢹⣧⣿⡇⠀⢸⠀⢸⠀⡇⡇⠁⣿⣿⡇⣿⠃⠀⡎⠀⡇⢣⢀⢸⢸⡿⣸⠏⣎⡟⢼⣿⢰⡄⠂⠀⢄⠀⠀⠀ ⠀⢸⣿⡿⢸⠳⢳⣿⣿⢳⣧⣿⣿⡇⠀⢸⡄⢸⠂⡇⡿⠀⣿⡁⣽⣿⠀⠀⡇⠀⢳⢸⢸⠈⣾⢇⣷⢺⢹⢓⢸⣿⠀⢻⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡇⡎⣧⣶⡿⢫⢺⡟⢿⣿⣧⠀⢽⠒⢾⠀⡇⡇⠀⣿⡇⢸⣿⠀⠀⠁⢠⢸⡀⢸⣿⢿⡺⣧⡏⡌⣾⡸⣿⣷⢪⠀⠀⠀⠀⠀⠀ ⠀⠩⣿⣭⣧⢮⣿⣇⢣⣿⢇⢸⣿⣿⠀⡘⠀⡎⢧⠃⢹⠸⣿⢹⣼⡏⠀⠘⠀⠸⡆⠇⣦⣹⡜⠮⣿⢏⡇⡇⡀⣿⣿⡀⡖⠀⠀⠀⠀⠀