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⠀⠀⢰⣿⠁⢀⠀⠂⠁⠈⠀⠀⠀⠀⣰⡟⣿⠀⠀⠀⠀⠀⠀⠀⠐⣾⠇⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⣼⠇⠀⣿⡆⠀⡁⠀⠂⠈⡐⠀⡀⠀⣰⣿⡃⠀⠀⠀⠀⢈⣿⡁⢀⠃⠀⠀⣿⣿⣷⠄⢈⡑⢠⠠⢄⡀⠲⠀⠀⣂⠈⠀⠔⠀⠀⠄⠰⢈⠐⡀⠈⠀⠀⠀⣿⣿⡀ ⠀⠀⣾⡏⠀⡀⠠⠀⠀⠀⠀⠀⠀⢈⡹⣽⠏⠀⠀⠀⠄⠀⠀⣠⣼⡿⠀⠀⠠⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣿⡇⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⢰⡟⠀⠀⣿⡇⠀⠄⠡⠀⡁⠀⠄⠀⠀⣸⣿⠘⠀⠀⠈⢰⢸⣿⠀⠌⠂⠁⢠⣿⡏⣿⡆⢰⢨⠃⡄⠠⡐⠀⠐⢰⣿⠀⢀⠂⢀⠠⡄⢀⠀⠂⠀⠠⠐⠀⠀⢹⡎⢧ ⠀⠀⣿⠄⠀⡐⠀⠀⠂⠀⠀⠀⠀⢰⢾⡿⠀⠀⠐⠀⠀⠂⠀⣶⣿⠁⠀⠀⡁⠀⠂⠀⠄⠀⠀⠀⢀⠂⠀⠀⠀⢀⣾⣿⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢀⡿⠀⠀⠀⢹⡇⠀⡐⠤⠀⠄⡀⠂⠀⠰⣿⡇⠈⠄⠀⠀⢾⣿⣿⠀⢈⠀⢀⣸⡟⠀⢻⡟⡀⠣⣜⢠⠁⠔⠃⠠⢘⣿⠀⠀⠀⠀⢺⣿⠀⠀⠁⡀⠂⠀⠀⠀⢸⡇⠘ ⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⡀⠈⢀⣰⣾⠇⠀⠐⠈⠀⠀⠂⠘⣼⡇⠀⢈⠀⠄⢈⠀⠄⠂⠈⠀⡁⠄⡀⠀⠀⠀⣼⠿⡿⠀⠀⣼⠋⠀⠀⠀⣀⣀⣀⣀⡀⠀⣿⣀⡾⠃⠀⠀⠀⢸⡇⠀⢀⠂⠡⢀⠀⠀⢁⢰⣿⠁⠐⠂⠀⠐⣻⡏⣿⣬⣴⡶⠶⣾⣿⢶⣿⣷⣠⠑⡼⡌⠥⡈⠆⡀⢺⡯⠀⢈⠀⠀⠸⣿⡆⠀⠀⠀⠄⠠⠀⠀⢸⠃⢠ ⠀⠈⣿⠀⠀⡁⠀⠀⠐⠠⠐⠈⠁⣿⣿⠀⠀⠌⡀⠂⠁⣀⣺⣿⠀⠀⠄⠂⡈⠀⠄⢀⠠⠈⠀⡀⠠⢀⠀⢀⣾⡏⢰⡇⠀⣼⣏⣠⣴⣶⣿⣿⡿⠿⠿⣿⣷⣿⡿⠁⠀⠀⠀⠀⢸⡇⠀⠢⠘⢀⠀⠀⡀⡬⣼⡟⠀⠀⠂⠀⢠⣿⠁⣿⠉⠙⠀⣸⡿⠉⠀⣿⡏⠻⢿⣴⣅⠂⢀⠐⢀⣿⡇⠐⠈⠀⠀⠀⣿⡇⠀⠀⠈⠀⢀⠀⠀⣿⠀⠈ ⠀⠀⣿⠂⠀⠐⠀⠀⠈⠄⡁⠀⠰⣾⡟⠀⠀⠂⠐⠀⡀⢤⣿⡇⠀⠂⢈⠐⠀⡀⠂⠄⠂⢁⠐⠀⠂⠀⢀⣼⡟⠀⢸⣧⣴⣿⡿⠋⠁⠀⠀⢻⣧⠀⠀⠋⢿⣿⣧⡀⠀⠀⠀⠀⢸⡇⠀⡁⠌⢀⠀⠀⠠⣼⣿⠁⠂⠀⠀⢀⣿⠇⠀⣿⠂⠁⣦⣿⠁⠀⠀⣿⡏⡑⢊⠭⢿⣶⡀⠀⢨⣿⠇⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀ ⠀⠀⣿⡁⠀⠄⠀⠠⠑⢈⠐⢠⢾⣿⡇⡀⠡⢈⠀⡀⠀⢴⡿⠀⠠⠐⠀⠀⠡⠀⡁⠐⠠⢀⠂⠁⠂⣠⣾⠟⠀⣤⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⢻⡆⠛⣦⠀⠀⠀⢸⡇⠀⡐⢈⠀⠈⠐⢳⣿⡟⠀⡈⠀⠀⣼⡏⠀⢀⣿⡅⢨⣿⠃⠀⠀⠀⣾⡗⡰⠠⠞⠀⢹⣧⢀⣹⡟⠀⢌⠐⠀⣀⢰⣿⡇⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀ ⠀⠀⣿⡇⠀⠠⠈⡤⢁⠠⠀⣼⣿⣿⡇⠠⠁⢂⠀⠀⣈⣿⡏⠀⠀⡀⠈⠄⠡⠀⠄⠀⡁⠂⠄⣁⣰⣿⠏⣠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠘⠃⠀⠀⢸⡇⠀⠄⠠⠌⠁⣹⣾⣿⡇⠀⠀⠀⣵⡟⠁⠀⢀⣿⣦⣿⣿⣄⠀⠀⠀⣽⡟⠤⡑⠎⠀⠀⠻⢿⣿⡇⠀⠌⠀⠀⢘⣿⢿⡇⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀ ⠀⠁⢾⣇⠀⡁⠰⠀⡀⣔⣩⣿⢛⣿⡇⠀⠀⠂⠄⢠⣱⣿⡇⠀⠀⠠⠀⠂⠄⠡⢈⠔⠠⠈⡤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡆⠀⠀⠀⠀⣽⡇⠀⡊⠄⢀⣴⣿⠋⣿⠃⠀⢀⣼⡟⠀⠀⠀⢸⣿⣿⠿⣿⣿⣷⡄⡀⣿⡏⠄⢀⠢⠄⠀⢀⣼⡿⠀⠀⠂⠀⠀⣼⠋⣹⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⡀⠀⠁⠆⣐⣿⡟⠻⢋⣽⣧⠀⠀⠁⢠⣂⣿⣿⠀⠠⠀⡁⠠⠁⡐⠀⠆⡈⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢀⣶⠀⠀⠀⢰⣾⠇⠀⠀⠀⢀⣾⠀⠀⠱⠀⣺⡿⠃⢠⡿⠀⢀⣾⠋⠀⠀⣀⣾⠟⠛⣿⠀⠀⠹⣻⣷⢳⣿⡃⠈⠄⠂⠀⠠⣤⣿⠃⠀⠀⠀⠀⣼⠏⠀⣼⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⢻⣇⠀⠡⣰⣿⠟⠿⠃⠠⣿⣿⠀⠀⠂⠐⣹⣿⡟⠀⠀⠀⠄⠐⠠⠄⠡⠐⠀⣹⣿⣿⣿⡟⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣸⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡿⠀⠀⣀⣾⡟⠁⠀⣼⡇⣠⡿⠁⠀⣀⣼⠟⠁⠀⠀⠈⠁⠀⠀⠿⣿⣿⣿⠀⢀⠣⠀⠀⣴⣿⡿⠀⠀⠀⢠⣾⠏⠀⠀⣾⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠄⠈⣿⡄⣽⡿⠃⢀⠃⠆⢈⣻⣿⡄⠀⠀⢹⣿⣻⡇⠀⢈⠀⠐⠀⢂⠌⡀⣰⣼⡿⣻⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⢀⣴⡿⠉⠀⠀⢸⣿⣷⠟⠀⠀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡿⠀⠀⠀⢀⣼⣿⣿⠃⠀⠀⣰⡟⠁⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠑⣈⠀⢹⣿⠟⠁⡀⢊⠀⡡⢈⡿⣿⡇⠀⢈⣿⠇⣽⡇⠀⠀⠀⡈⢄⠢⠄⣴⣿⠋⠀⠈⢿⣇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡽⣻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⠟⠃⠀⠀⠀⢰⣿⠏⠁⠀⠀⣴⣿⣿⣿⣿⣆⡀⠀⣴⠀⠀⠀⠀⣿⡏⠗⠀⠀⣤⣾⣿⣽⠇⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⢀⠀⠀⠋⠐⢀⠘⢀⢂⠁⠀⠀⠽⣿⡀⢠⣿⠀⣿⠁⠀⢀⠡⠀⣢⣶⣾⠟⠀⠀⠀⠀⠸⠟⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⡶⣯⢷⣻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⠿⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠸⢯⣿⣿⣿⣿⣿⣯⣿⡟⠀⠀⠀⢀⣿⡛⡷⣰⣾⣿⠟⣾⣟⣠⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠐⡈⡀⢢⠁⠢⢀⠊⠀⠄⠂⠁⠀⠈⢿⣧⣼⡏⣸⣿⠀⠀⠠⠀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣿⣿⣿⣿⣿⣿⠿⣵⢯⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⣿⣿⢿⣿⣿⠧⢠⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠈⠔⠁⠀⢂⠐⠀⠌⠐⢀⠂⠐⠀⠀⢘⣿⣿⣤⣹⣿⠀⠀⣀⣩⡿⢛⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢷⣿⣿⣿⣿⣿⣟⢿⣹⣾⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⢫⣯⣿⡿⣡⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⠉⠂⡁⠠⠐⠌⠂⡐⢈⠀⠄⢀⠀⠀⠐⣿⠯⠄⡷⣿⠀⣠⡾⠋⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⢸⣿⢯⣿⣿⣿⣿⡿⣽⣾⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣾⢃⣸⣿⣿⡽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢎⠂⡁⠄⠃⢈⠠⢁⠐⢠⠈⠄⠀⡀⠂⠀⠀⠀⠀⣹⣿⡾⠋⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⢸⣿⢧⣟⡿⣿⢿⡽⣳⣟⣿⣷⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠋⠁⡟⠀⠀⠀⠘⠃⣼⡿⡛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣊⠐⢠⠈⡐⠈⡐⢠⠈⠄⠂⢀⠐⠠⠀⠁⠠⠀⠀⠀⣿⡄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠘⣿⣿⡾⣽⠾⣭⣟⣳⢮⣷⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⢿⣶⣶⣾⡇⠀⠀⠀⠀⣼⡟⠁⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡔⢨⠀⠂⠄⠁⠄⡡⠈⡐⠤⡀⠀⠠⢀⠠⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠄⠀⠀⠀⠀⠹⣷⡀⠀⠀⢿⣿⣿⣯⣿⣷⣻⣿⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣟⣾⣿⡿⠀⠀⠀⠀⣼⡟⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠜⠠⠡⢉⠀⠌⡐⠠⠁⠐⠂⢁⠂⠀⠀⠄⠀⠈⠠⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠁⠀⠀⠀⢰⣿⠃⠀⠀⠀⠺⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢊⠁⠂⠠⠈⠐⢈⠡⠌⠐⠀⠂⠤⡁⠀⠠⠈⠀⠄⠀⠁⠀⡐⠀⠀⠀⠈⠀⠀⠀⠁⠀⠄⠀⠀⠀⣘⣿⣶⠷⣦⡀⠀⠀⠀⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⡛⠛⢻⡀⠀⠀⠸⣿⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢆⡁⠂⠁⠂⠌⢀⠂⠄⡡⠈⢀⠁⡀⠂⠁⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⣠⣶⠿⠛⠉⠛⣦⠈⠻⣦⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣾⣄⠘⣿⡀⠀⠀⣙⠃⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠁⠌⢀⠀⢂⠈⡐⠠⠀⠀⠆⠠⠁⡀⠈⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠋⠀⠀⡀⠀⠀⠈⠳⣆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠋⠀⢸⣷⣾⡟⠿⢻⢷⣤⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠙⢧⡀⠀⢸⡇⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠙⢿⣤⡀⠀⠀⠀⠈⠻⣦⡈⠙⢷⣤⡀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠹⣧⠀⠸⣇⠀⣿⠈⣷⡀⠀⣿⣷⣅⡀⠀⣿⠉⢾⠏⠉⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣉⣴⡤⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢧⣽⣇⠀⠀⠀⢀⣼⠿⣦⡀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⡽⣿⣦⡀⠉⠻⢶⣄⠀⠀⠘⣧⠀⣠⣴⣾⡿⠷⣶⣶⣶⣦⣤⣴⣶⣶⢶⣶⡶⠶⠶⢾⡿⣯⠉⠀⠙⢻⡆⠀⢿⡀⢿⡀⠸⣧⠀⠸⣧⠈⠙⠷⢿⣦⣼⣷⠿⠋⣨⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠉⡍⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⠿⠁⣠⠾⠛⠁⠀⠈⠻⣆⡀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀⠀⣷⠀⠛⢦⡄⠀⠙⠿⣦⣀⣽⣿⠉⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠹⣦⠀⠀⢸⣷⠀⠸⣧⣸⡇⠀⢻⡄⠀⢻⡿⢦⣤⣤⣤⣤⣤⡶⠾⢯⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠈⠛⢦⣼⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣼⣇⠀⠀⠻⣆⠀⠀⠀⣹⠿⣿⣧⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠀⠀⠀⠘⣧⠀⠀⢸⡆⠀⢻⣯⣿⠀⠈⣷⡀⠈⣷⡀⠀⠀⠀⠈⠙⠷⢤⣄⣈⠉⠛⢻⣷⠆⠀⠀⢰⡟⠛⠻⢦⣤⣠⡶⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⠻⠛⠛⠷⠶⣦⣤⣄⡀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠀⠀⠀⢹⣇⠀⣼⠋⠀⢸⣿⠆⠀⠀⠀⠀⢈⣿⠂⠀⠈⠀⢀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠈⣿⡀⠀⢿⣽⡆⠀⠸⣇⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠃⢀⣠⣤⡼⠗⢀⣀⣀⡉⠉⠀⠀⠈⢷⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣼⠟⠙⡙⢂⠇⡀⠤⡀⢠⡙⠻⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠛⠛⠶⠶⠾⠿⠶⣤⣤⣀⣀⣼⠇⠀⣠⣴⠶⠛⠉⠀⠀⠀⠉⠉⠙⠛⠶⣤⣀⠀⠀⠘⣧⠀⠘⣿⣇⠀⠀⢿⡀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠉⠁⢀⣴⠟⠉⠉⠉⠛⠳⢦⡀⠀⠀⢨⣽⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⡟⢃⠙⠓⣤⡂⠄⠘⣄⠡⡠⠁⠐⡀⢈⠉⠛⠻⢶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⢶⣦⣤⣤⣤⣀⣀⠀⠀⠈⠉⠉⣹⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣀⣹⣷⣀⣸⣿⣄⣀⠘⣷⡄⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⢠⡾⠁⢀⡤⠶⠶⢤⡀⠈⢳⣄⠀⢿⣾⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⢋⡐⢈⡡⠓⢠⠡⢦⠰⠈⠄⡠⢘⣀⣠⣬⣧⠀⢂⢠⠈⠛⠻⢶⣦⣄⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠈⠉⠉⢛⣛⠾⢶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡛⣉⣏⠉⢉⣿⠛⡛⠛⢷⣾⣿⣶⣦⣤⣤⣤⡀⠀⠀⠀⠀⠀⣨⡿⢸⠃⠀⡏⠀⣤⠄⠀⢳⡀⠀⢿⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀ ⢠⠈⠒⢧⢨⠙⠨⣁⢂⣼⣥⡶⠿⠛⠋⠋⠉⠛⣿⣆⡠⠘⠀⠃⡄⣈⣉⠉⡉⠉⠉⠛⠻⣿⣿⡶⣾⡿⠛⠉⠉⠛⠛⠛⠛⠛⠛⠛⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢿⣿⠿⠷⣶⠷⣿⣮⣭⣥⣤⣿⣼⣋⣛⣿⠀⠀⠀⠀⣾⠋⠀⢸⡅⠘⣇⠀⠹⣦⣠⡾⠃⢀⣿⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀ ⠂⢡⠘⣠⣤⣦⡷⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⢷⣥⣈⠩⡘⠠⣀⠛⠀⢠⣁⠢⠠⠈⣽⣷⡼⢿⣦⣦⣤⣤⣤⣤⣤⣦⣤⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⣀⠀⠀⠀⠀⠀⢀⣿⡇⢠⣟⠀⠀⣿⠀⢿⡇⠀⢹⣿⣍⣉⣩⣭⣿⠀⠀⠀⠀⠿⣦⣄⣸⣇⠀⠙⢧⣀⣈⣁⣀⣠⡾⠃⠀⠀⣴⡾⠟⠁⠀⠀⠀⠀⠀ ⣼⡶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢯⡛⢷⣄⡁⠄⠚⢧⠀⡀⢤⡐⢀⠠⢹⣷⡀⠀⠙⢳⣤⣤⣄⣀⣀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣶⡶⣤⣴⣿⣿⡁⢰⡇⠀⠀⣿⠀⣻⡅⠀⢸⡏⠉⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⢻⣏⠻⢤⣀⣉⢉⣉⣉⣥⡶⠆⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢀⠙⢿⣦⢈⠈⢃⡌⠐⢠⠁⡆⠐⠻⣷⠀⣠⡾⣿⡟⣿⢻⣟⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⣠⣿⣿⠀⢸⡇⠀⠀⣿⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢉⣭⡛⠉⠉⠁⣠⣶⣦⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡰⠀⠙⢷⣎⡀⠼⢏⡢⢌⠰⢡⠀⣹⣿⣟⢿⣻⡿⣎⢯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠾⠋⢸⡟⠀⢸⠇⠀⠀⣿⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠞⠋⠉⠳⣦⠀⣰⠟⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣦⣰⣿⠋⠥⣛⠻⡒⠦⣙⣾⣿⢟⡻⣞⣻⣿⢻⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠃⠀⠀⢸⡇⠀⣾⠁⠀⠀⣯⠀⣿⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⢘⢢⢩⣗⣉⠲⠡⢿⣿⣾⣵⢯⢿⣏⣿⡿⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⠀⠀⢸⡇⠀⣿⠀⠀⠀⣟⠀⣿⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⢎⡐⠦⣠⢉⡥⢃⠀⠛⢿⡿⣿⡟⣼⣿⣻⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠁⠀⠀⢹⡇⠀⣿⠀⠀⢰⡯⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⣷⠘⡄⢢⡴⠨⠆⠐⠸⢿⣿⣿⣿⢻⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠛⡛⠛⢿⡇⠀⣿⠀⠀⠸⣗⠀⣿⠀⠀⢾⡷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣤⣾⡟⠛⠛⢶⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠦⢈⡥⡀⠇⠌⠠⠁⢸⣿⣿⣿⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⠶⠒⢿⡇⠀⣿⠀⠀⢀⡿⠀⣿⠀⠀⢸⡄⠀⠀⠠⠀⠤⠠⠤⠤⠤⠤⢤⣄⣀⣀⣀⣀⣀⣀⣀⣉⣉⠉⠉⢉⣙⣛⣛⠛⠷⢶⡄⠀⢹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷⣆⠒⢉⠡⠀⡁⣤⣼⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⣠⡼⠓⠶⣶⣶⣦⣾⣷⣴⣿⣤⣤⣬⣿⣤⣿⣥⣤⣼⣇⣤⣄⣠⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣬⣭⡽⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⣿⣀⡾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣶⣿⣿⠿⠟⡉⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠟⣉⠛⠛⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣠⣿⠋⠁⠀⠀