⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⢠⢭⡿⢷⣄⠀⠀⠀⡆⠀⠀⠀⢠⠆⣤⡤⡤⡄⣤⣤⣀ ⠀⢦⡆⠀⠀⡜⢺⠀⠀⠀⠀⠀⠀⠠⠍⠂⠀⠸⢸⠀⠀⢁⣇⠀⠀⢀⡃⣻⠉⠉⠁⠉⠁⠉⠉ ⠀⢽⠇⠀⠀⡂⢺⠀⠀⠀⠀⠀⠀⡂⠉⠀⠀⠌⣘⠀⠀⠀⡝⡄⠀⡪⣀⣗⡀⣀⣀⠀⠀⠀⠀ ⠀⣹⡃⠀⠀⡂⡩⠀⠀⠀⠀⠀⠠⡃⠁⠀⢀⢁⡂⠀⠀⠀⠢⡇⢰⠃⢙⡺⠍⠁⠀⠀⡀⣀⠀ ⠀⣿⠅⠀⠀⡅⣾⠀⠀⠀⠀⠀⠈⣼⣀⡠⢃⠎⠀⠀⠀⠀⠈⣯⣿⠀⣼⣷⡧⠇⠗⠝⠋⠁⠀ ⠀⣷⠂⠀⠀⠱⡿⣦⣤⣤⠄⠀⠀⠈⠓⠒⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢮⢄⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⢖⠴⠂⣦⣄⠀⠀⢰⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠦⡄⠀⠀⢀⢚⠂⠀⠀⠀⠅⠏⠉⠉⠉⠙⣧⠀⢸⡇⠀⠀⠀⠀⢸⣳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡻⡆⠀⠤⡃⠀⠀⠀⠀⣺⠁⠀⠀⠀⢠⡟⠀⢰⡇⠀⠀⠀⠀⣺⡻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠏⢄⢙⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⡞⠁⠀⠘⣇⠀⠀⠀⢀⣏⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠦⠁⠀⠀⠀⠀⠀⠙⠷⠖⠖⠋⠀⠀⠀⠀⢫⡛⠛⢚⠝⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢐⠍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢚⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣖⣟⣷⣶⣤⠂⡄⠀⠀⠀⠀⠀⢀⢀⡀⡀⡀⡀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⡏⠀⠀⠀⠙⣻⡖⡀⠀⠀⣔⡬⠙⠆⡃⡍⡺⢿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠘⣇⠀⠀⠀⠀⠀⠷⡖⡄⡠⣁⢢⡙⠍⠁⠉⢹⢀⡃⠅⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣪⡂⡀⠀⠀⠀⠀⢻⡔⣍⠞⠁⠀⠀⠀⠀⡊⣊⠒⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢷⡀⠄⠀⠀⠀⠀⠀⠋⠃⠀⠀⠀⢀⢐⢌⠅⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣇⣁⡀⠀⠀⠀⠀⠀⠀⠀⡐⠔⢡⠌⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⡶⣦⡄⠀⠀⡀⡢⢊⡐⠨⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠗⣤⣦⡩⠘⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠛⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣴⣶⣶⣶⣶⣄⠀⣀⣴⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣛⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠻⢿⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⠆⠠⣿⡿⣿⣿⣿⢿⣿⣦⣴⣿⣿⡿⢿⣿⣷⣄⠀⢾⣿⣿⣿⣿⡿⣿⠆⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⣠⣿⡿⠁⠀⣰⣿⣿⡗⠋⠉⠉⠙⠻⣿⣿⣧⠀⠘⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣖⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⢰⣿⡿⠁⠀⡎⣿⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⢰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣴⣿⡟⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⢟⡃⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣻⣇⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⡇⣿⣿⣏⣧⠀⠀⠀⠀⢀⣿⣿⣿⡏⠀⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⡃⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣿⣇⣀⡀⠀⠀⠱⣜⢿⣿⣮⣗⣦⣸⣷⣿⣿⠟⠀⠀⠀⢿⣿⣦⡀⠀⠀⣀⣼⣿⠟⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀