⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠐⠒⠋⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠑⠒⠒⠤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠈⠉⠉⣀⣀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⣀⠀⠈⠉⠒⠢⠄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡠⠒⠈⠁⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠉⠉⠙⠛⠛⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠉⠒⠤⣀⠀⠀ ⠀⠀⠏⠀⣠⣶⣿⣿⣿⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⡄⣠⣄⢠⣄⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⢿⣿⣿⣿⣿⣶⣤⡀⠀⡇⠀ ⠀⢰⠀⢀⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⢹⡇⢛⡞⣸⣚⢸⣿⠆⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡇⠀⣗⠀ ⠀⢸⠀⢸⣿⣿⠀⠀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⠀⢀⣀⡀⠀⢀⣀⠀⢀⣀⡀⠀⣀⣀⠀⠀⣿⣿⣧⠀⢾⠀ ⠀⠂⠀⢸⣿⣿⠀⠀⢸⢸⠀⡰⢃⠎⠀⡗⢠⠤⢤⠀⡇⠸⠧⠤⢤⡄⣸⠀⢸⠀⡤⡄⢸⠀⢸⣶⢱⡀⢸⠀⠀⢸⢀⡇⠀⡇⢹⠀⠀⢸⣿⣿⠀⠸⠀ ⠀⠇⠀⣿⣿⡇⠀⠀⢨⠘⠒⢡⡎⠀⠀⡇⢸⠀⢸⠀⡇⠀⠀⣠⠎⡴⠁⠀⡘⢸⠀⢳⢸⠀⢸⠈⣧⢱⣸⠀⠀⢸⠈⠓⠒⠃⢸⠀⠀⢸⣿⣿⠀⠀⠀ ⠀⠀⠀⣿⣿⡇⠀⠀⣸⢸⠉⢆⢳⡀⠀⡇⢸⠀⢸⠀⡇⢀⡴⢡⠞⠀⠀⠀⡇⢈⣉⣩⠀⡇⢸⠀⡇⢧⠙⠀⠀⢸⠀⡏⠉⡇⢸⠀⠀⠀⣿⣿⡄⠀⠀ ⠀⠀⢠⣿⣿⠀⠀⠀⠿⠼⠀⠘⠆⠳⠀⠧⠤⠭⠍⠤⠇⠸⠄⠌⠭⠬⠿⠀⠇⠾⠀⠸⠆⠇⠸⠄⠇⠈⠧⠠⠄⠸⠤⠇⠀⠇⠼⠀⠀⠀⣿⣿⡇⠀⠀ ⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀ ⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀ ⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⣉⣉⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠐ ⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⢭⠭⣭⢭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀ ⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⡈⣀⢸⢸⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀ ⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠉⡟⢹⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀ ⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠛⠛⠛⠛⠛⠒⠃⠚⠚⠛⠛⠟⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀ ⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣻⣛⣛⣛⡛⠛⠛⠛⠛⣋⣉⣉⣍⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀ ⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⢀⠔⠁⡤⠄⠤⡀⠳⡄⢸⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀ ⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡿⠎⠀⢸⡀⠧⠄⣹⠀⠸⢼⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀ ⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣇⣔⣮⣔⢕⠒⢺⢗⣭⡶⡄⣿⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀ ⡀⠀⢿⣿⡇⠀⠀⠀⢀⣀⣠⣷⣀⣀⠀⠀⠀⠀⠀⠀⢸⢸⣇⣉⡇⣏⣉⣀⣈⣹⠀⣏⣁⣿⢸⠀⠀⠀⠀⠀⣀⢀⡼⡄⠀⡀⠀⠀⠀⠀⢠⣿⣿⠀⠀ ⠅⠀⢸⣿⣷⠀⠀⠀⠀⠙⡆⣀⡖⠉⠀⠀⠀⠀⠀⢀⠸⠬⠭⠭⠒⠚⠉⠉⠉⠙⠲⠯⠭⠭⠼⠀⠀⠀⠀⠀⠉⢻⢅⣸⠋⠁⠀⠀⠀⠀⢸⣿⡿⠀⠰ ⢰⠀⠸⣿⣿⠀⠀⠀⠀⠘⠋⠈⠙⠀⠀⠀⠀⠀⠀⠈⢫⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⠉⠀⠀⠀⠀⠀⠟⠁⠙⠇⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀ ⠘⡀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⡀ ⠀⣇⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⢴⣒⣲⢄⠀⣠⣴⣒⣲⢄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⣸⠁ ⠀⠸⡄⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢵⠏⠁⠙⡷⠷⢽⠏⠁⠙⡧⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⡟⠀ ⠀⠀⢳⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⡇⠀⢸⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⢰⠁⠀ ⠀⠀⠈⡆⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠤⠤⠤⠇⠀⠸⠤⠤⠤⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⢠⠇⠀⠀ ⠀⠀⠀⠘⣆⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣄⣀⣀⣤⣀⣀⣀⣤⣀⣀⣀⢤⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⣰⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⡆⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁⢠⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢦⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⣰⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠣⡀⠈⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢘⣺⣓⣒⣒⣚⣒⣒⣒⣛⣒⣒⣒⣛⣚⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠋⢀⡴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠙⢿⣿⣷⣄⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠉⠻⣿⣿⣦⣄⡀⢸⣠⣄⣀⣀⡠⣀⣀⣀⣠⣀⣀⣀⢤⣸⠀⣀⣴⣿⣿⡿⠋⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠈⠙⠿⣿⣿⣶⣮⣁⠈⠈⠉⠙⠓⠚⠉⠉⠉⣉⣩⣾⣿⣿⡿⠛⠁⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠤⣀⠀⠙⠻⢿⣿⣿⣶⣦⣄⣀⣠⣴⣶⣿⣿⡿⠟⠋⠁⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠉⠛⠿⢿⣿⡿⠿⠛⠋⠁⣀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⡀⣀⣤⡤⡖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀