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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⢰⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⡆⠀⠀⣿⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⢰⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢸⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢸⡄⠸⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⡅⠀⣿⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣥⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⡿⣿⣿⡿⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠉⡙⢔⠛⣟⢋⠦⢵⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⠀⠀⠁⣿⣯⡥⠃⠀⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⠐⠠⠊⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀ ⠀⠀⠀⡜⣭⠤⢍⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢛⢭⣗⠀ ⠀⠀⠀⠁⠈⠀⠀⣀⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠰⡅ ⠀⠀⠀⢀⠀⠀⡀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⠠⡕⠀ ⠀⠀⠀⠀⣿⣷⣶⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⢆⠀⠀⠀⠀ ⠀⢀⠤⠀⠀⢤⣤⣽⣿⣿⣦⣀⢀⡠⢤⡤⠄⠀⠒⠀⠁⠀⠀⠀⢘⠔⠀⠀⠀⠀ ⠀⠀⠀⡐⠈⠁⠈⠛⣛⠿⠟⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠑⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⠄⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠹⡀⢠⠙⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠇⠈⡇⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣸⢰⢰⣀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⢻⣼⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠉⢣⡀⢱⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠂⢸⢿⣞⠿⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠌⡇⠀⠿⢇⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⡠⠊⠀⡐⠀⠀⠀⠀⠀⠩⡢⡀⠀⠀ ⠀⠀⢎⣀⢔⠝⠀⠀⠀⠀⠀⠀⠀⢡⣈⣄⠀ ⠀⢸⡿⠙⡫⠀⠀⠀⠀⠀⠀⠀⠀⢥⢍⣿⠂ ⠀⠈⡤⣲⠣⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀ ⠀⠀⠰⡀⢆⠀⠀⠀⠀⠀⠀⠀⢀⣌⠀⠀⠀ ⠀⣀⡠⡬⠦⠢⢀⡀⠤⠤⠄⠒⠉⠱⠃⠀⠀ ⠘⠥⡊⠩⠑⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠛⠛⠛⠛⠶⠶⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠟⣉⣩⡽⠿⢷⡥⠄⠀⣀⠀⠴⠟⠛⣻⣷⣦⣤⣀⠀⠀ ⠀⢀⣴⢋⣴⡾⢟⣥⠖⠛⠒⠿⣍⠉⠁⠈⠀⣠⠞⠋⢩⣽⡿⣿⠁⠀ ⠀⣸⠃⠉⠉⠀⣸⢁⣀⣀⠀⠀⢹⡄⠀⠀⢰⡇⠀⠀⠀⠉⢁⣿⠀⠀ ⠀⡟⠀⠀⡠⠶⣿⣼⠿⠛⠀⢀⣼⠁⠀⠀⠈⠷⢤⣤⡤⠴⣿⣽⡆⠀ ⢸⡇⠀⠀⠀⠘⠁⠉⠛⠒⠖⠛⢁⣀⣀⣀⣀⣠⡾⢋⡴⠶⣤⡙⢷⡀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡤⠴⠞⢁⡾⢁⡟⣿⣶⣾⣧⢸⡇ ⠸⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠬⠭⠥⠼⡇⢸⡏⠉⠉⠉⣿⢸⠃ ⠀⣷⠘⡄⣆⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⢰⢇⡏⠀ ⠀⠸⡆⠹⣾⡀⠙⢄⠀⠀⠠⢀⣀⠀⠀⠀⠀⣿⢸⠇⠀⠀⣿⠘⣇⠀ ⠀⠀⢻⡀⠹⣧⠀⢸⡀⠀⠀⠩⢝⡻⢦⡀⢠⡏⣼⠤⢤⡀⢹⡀⢻⠀ ⠀⠀⠈⢷⠀⢻⣇⠀⠣⡀⠀⠦⠤⣈⠳⣅⣼⠀⣧⣀⣀⣨⣾⡇⢸⠀ ⠀⠀⠀⠈⢷⡀⠻⡗⢤⡉⠢⡀⠀⠀⠑⢦⣿⠀⣷⡾⠾⣽⡾⠀⡞⠀ ⠀⠀⠀⠀⠈⠻⣦⡈⠓⠮⢷⣬⣁⣀⡀⠀⠻⣄⠈⠛⠶⠚⢁⣼⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣈⠉⠛⠚⠭⠯⠙⠓⢶⣶⠶⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢦⣤⡤⠾⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⢸⣩⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢹⣇⠀⠀⡎⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⢻⡄⠀⠇⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠸⡇⢸⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⠀⣧⠈⡆⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣆⣽⠀⣧⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⢿⣤⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢺⣟⠃⠛⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⣧⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠴⠒⠲⣿⡿⣤⡿⣩⣷⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⢻⣿⣿⠿⠉⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣿⠀⠀⠐⠿⠻⠂⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⢀⡏⠀⠀⠀⠑⠒⠊⠀⠘⡗⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠉⠀⠀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠑⣄⠀⠀⠀ ⠀⠀⠀⡰⠋⠀⢀⠔⢫⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⢢⡀⠀ ⠀⠀⢰⣥⣤⣴⣇⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣶⣶⣷⡀ ⠀⠀⣸⣿⡿⠉⢛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢭⡄⠘⡿⡇ ⠀⠀⢣⠈⠀⣀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣴⣿⡿⠁ ⠀⠀⠀⢷⠦⢽⡮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠁⠀⠀ ⠀⠀⠀⠘⡄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢆⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠶⡄⠀⠀⠀ ⠀⠀⣀⣀⣀⣀⡵⢄⡑⢤⣀⣀⣀⣀⣤⣤⣤⠒⠊⠉⠀⢈⡷⠃⠀⠀⠀ ⢠⡾⠋⣹⠼⠟⠤⣄⣤⣤⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⠲⠧⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡄⠀⡀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣴⣶⠀⠀⠀⣿⠈⣧⢸⣿⠂⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣹⡇⠀⠈⣿⣦⣀⣸⡏⠀⢸⣿⣿⣦⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⡷⣶⣿⣿⡿⠟⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠸⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡁⣀⣤⠶⠟⠛⠉⠁⠸⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣆⢻⣧⠀⠀⠀⠀⠈⣿⣿⣿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⣀⣀⣀⣀⣠⣤⣀⣀⣀⣴⡾⠟⠻⣿⡼⣿⡆⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀ ⣿⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠛⠿⣿⣿⣀⠀⠀⣀⣿⡿⠋⠀⠀⠀⠀⠀⠀⣀⡀⠀⣼⠇⠀⠀⠀⠀ ⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣼⠇⠙⣾⠋⠀⠀⠀⠀⠀ ⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣏⠀⠀⠘⣧⣀⣀⣤⣤⣀ ⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⣿⠉⠁⠀⠉⠁ ⠀⠀⠈⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣾⠏⠙⠛⠷⣦⡀ ⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣦⣶⠟⠉⠀⠀⣠⠄⠀⠀⢰⡇⠀⠀⠀⠀⢀⣰⡟⠛⢻⣷⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡿⠋⠙⠷⣦⣤⣾⡁⠀⠀⠀⠈⠿⣶⣤⣶⣶⣿⣯⡶⠞⠋⠁⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠉⠛⠛⠛⠛⠛⠛⠛⠻⣾⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢲⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠟⠒⠦⣤⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣠⢺⣿⡀⣾⡆⣇⣀⣀⣀⣀⣀⣀⣀⣀⣠⠞⠋⠈⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⠁⠀⠀⣀⣀⡀⢉⡟⠀⠀⠀⣀⣤⡴⠶⣾⡿⠛⠻⠟⠛⢿⠟⠻⢶⣤⣄⠀⠁⣠⠟⠁⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀ ⠀⠀⠀⣴⠋⠀⣴⣾⡅⠀⠀⣰⣏⣁⡦⣶⠞⠛⢿⠀⠀⠀⡇⠀⠀⡄⠀⠈⡇⠀⠀⡇⠈⢻⣦⣬⠷⣮⣉⠉⢹⣶⣤⡀⠙⢦⡀⠀ ⠀⢠⡾⠁⠀⡞⠻⠿⠃⢀⣿⣿⠏⠀⠀⣧⠀⢀⣾⣧⣄⣴⣧⣤⣴⣷⣴⣶⣷⣤⣴⣇⢀⡆⠀⡟⠙⣮⣻⣄⠄⠙⠛⠑⡄⠀⠹⡄ ⠀⣿⡀⠀⢰⠁⠀⠀⢠⣾⡟⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣴⢱⠉⣿⣷⣄⠀⠀⢷⠀⠀⣿ ⠀⠉⠳⣤⣸⠀⢼⣃⡾⣶⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣏⠳⣄⣸⣠⡾⠁ ⠀⠀⠀⠈⢿⣷⢤⡿⣵⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⡟⢻⠀⠀ ⠀⠀⠀⠀⠸⡟⡄⠀⣸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⢀⡏⠀⠀ ⠀⠀⠀⠀⠀⢻⡘⢶⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⡇⢰⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣼⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⣶⡚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠰⣟⣡⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣄⣻⢆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡧⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠉⠻⣿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣠⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠛⣿⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠚⢿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠟⣷⡄⢹⣿⡿⠿⣿⡏⠈⠛⣿⠟⠻⣿⠉⠙⣿⡿⢿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢀⡼⠀⣽⣿⣶⢿⣇⠀⢸⡇⠀⠀⡇⠀⢀⠇⠀⢀⠇⠀⢸⠉⣟⣷⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣶⣿⡆⠀⣇⠀⢠⡇⠀⣸⠀⠀⡞⠀⡠⠃⣼⡿⠷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣀⣤⠀⠀⠈⠙⠈⢿⣽⣶⣿⣶⣾⣷⣴⣿⣤⣾⣧⣶⣧⣾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠐⠛⢧⣿⣿⣻⣛⡟⠛⣯⢿⣍⣥⢿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⡤⠴⠚⠓⠀⠀⠀⠀⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠿⡿⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠢⠤⣄⡀⠀⠀⠀ ⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠹⡕⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣦⣄⡀⠙⢆⠈⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣏⠛⠯⣕⡚⠷⣄⡀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠉⠑⠲⠬⣑⠒⠤⣀⠀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡢⣄⡀⠀⠀⠉⠒⠬⣙⠲⣄⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⢷⣦⣤⣀⣀⠈⠑⢮⡙⣶⣮⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⣿⣿⣮⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠢⢄⣠⠏⠀⠘⣿⠟⢿⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣉⠶⠴⣟⠦⣄⡀⢿⠀⠘⣦⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠑⠢⠤⣙⠪⣿⣿⣷⠀⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⠀⠀⠀⠐⣾⣿⣿⣟⣿⣴⣷⣼⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣙⣄⡀⢀⡞⢹⣿⣿⣿⣿⣿⠛⢿⣯⣶⣁⠀⠀⣀⡀⠤⠤⠤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣖⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⡇⢸⠀⠈⣹⣿⣿⡟⠁⣀⠟⠛⢛⡟⠉⢿⣀⠤⠔⠀⠀⠈⢳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠹⣿⡷⠤⠔⠒⠲⠤⠤⠤⢄⣀⣀⠹⡘⠦⠴⣟⣋⣁⣈⣀⣀⣤⣴⡾⠃⠀⠞⢻⣀⠠⠖⠀⠀⢿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣭⡁⠀⠀⠀⠈⠛⠣⡀⠙⢦⡀⠣⣄⣱⡀⠀⢠⠞⡸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⣦⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠘⢆⠀⠱⣄⣀⣯⣯⣉⣡⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡁⠀⡠⠀⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣄⠀⠀⠈⢇⠀⠹⡀⠈⡻⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣤⣾⡡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⡄⠀⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠾⠿⠭⣍⣹⡒⢦⡀⠀⠀⢀⡏⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠉⠻⠳⡘⢦⠔⠚⠛⠉⠀⠀⠀⠀⡷⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⢳⠈⠇⠀⠀⠀⠀⠀⠀⠀⣧⠤⠛⠉⠁⠈⢳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠊⠉⢹⣄⠀⠀⠘⢯⡘⠦⣀⠀⠘⡄⠀⠀⠀⠀⠀⠴⠖⠋⠁⠀⠀⡠⠂⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣀⠀⠀⢀⣀⠴⠊⡡⢲⡦⠀⡠⣻⠟⢦⠀⠀⠀⠉⠒⢦⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⡼⠅⠤⠤⡀⠀⠀ ⢀⡴⠊⠉⠁⣴⣿⡿⠙⠻⠂⠀⠘⠛⠉⠀⣠⠞⠁⠀⠀⠳⡀⠀⠀⠀⠈⣣⡀⠀⠳⣄⠀⠀⠀⠀⢀⡤⠚⠀⠀⣠⠞⢳⡀⠀⠀⠉⠠⠀ ⣏⡤⠊⠁⠀⠀⠀⠀⡴⣶⣶⠇⠀⢀⡤⢚⡽⠦⣄⠀⠀⠀⠙⠒⠒⠒⠉⠀⠉⠲⣤⣬⡩⠷⢿⡿⠋⠀⠀⠀⠘⠁⠀⢀⡇⠀⠀⠀⠀⠈ ⢽⠀⠀⢀⠔⠊⠁⠀⠉⠁⠀⠀⢰⣯⠞⠉⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⣀⠤⠖⠊⠉⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⢰ ⠈⠳⠤⡏⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠉⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⣀⣠⠤⣒⡯⠵⠦⠤⣀⣀⡀⠀⠌ ⠀⠀⠀⠙⠢⠤⣀⣀⣀⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢍⡱⠭⠝⠓⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⢀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡄⢇⠱⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣌⢄⠑⣸⠿⠛⠉⠉⠉⠉⢹⠃⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣦⡢⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠠⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠟⢻⣿⣿⠇⢠⠤⣤⣤⣤⣄⣀⡤⢤⣤⣤⡔⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡇⠸⡿⠿⠟⢛⠏⠹⡷⠿⠛⢻⢓⠄⠀⠘⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣄⠑⠒⠒⢉⠐⣂⣩⠒⠒⢹⢇⡔⠉⣀⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠿⠋⠉⠁⠜⠁⠑⠲⢤⣆⣠⣤⣤⣶⡶⠋⠢⡻⠼⠂⠀⢏⠉⠛⢿⣿⣿ ⣿⡿⠁⠀⠀⠀⠀⠐⠢⠄⢀⡈⠢⡀⠀⡠⠋⠀⠀⢀⡸⠁⠀⠀⠀⢃⠀⠀⠹⣿ ⣿⡇⠀⠀⠰⠁⠀⠀⠀⠈⠂⠠⣱⠠⠂⠉⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⢂⠀⠀⣿ ⣿⣧⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢗⢰⣿ ⣿⡇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⣿ ⣿⣷⠀⠀⠀⢱⠄⣀⣀⠀⠀⢀⠿⡀⠀⠀⢀⠤⠊⢀⠔⢇⠀⠀⠀⠀⠀⢀⣿⣿ ⣿⣿⣆⠀⠀⠈⢄⠀⠠⠀⠀⠀⢂⠈⠉⠀⠠⢈⣉⠁⠠⠔⢳⣤⣄⠀⢠⣿⣿⣿ ⣿⣿⣿⣷⣶⣶⣤⣦⣤⣤⣤⣤⣬⣦⣄⣀⣀⣀⣀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣇⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠌⢹⡆⠀⣸⠿⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡾⢃⣀⣿⣴⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡗⢽⣿⠛⣵⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣯⠿⣯⣷⡿⣞⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⢴⣿⠀⠈⠻⠅⠠⡤⡀⠀⠀⠀ ⠀⣠⢮⣥⢴⠕⠁⠀⠀⠀⠀⠀⠈⢂⠑⡄⠀ ⣸⣿⢿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⢼⡀ ⠱⣀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢝⠤⠆ ⠀⠐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀ ⠀⢀⣈⠢⠕⠠⢤⡤⠤⣤⣤⡀⢊⣘⡥⠀⠀ ⠀⠧⣑⣉⡉⠍⠋⠀⠀⠀⠠⠰⠤⠄⠔⠀⠀
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⠀⠀⠀⣠⠖⢛⡟⠛⠛⠓⣶⣤⣀⠀⠀⠀ ⠀⣠⣯⡴⣺⠟⠚⢍⠀⠈⢠⠖⢹⡿⡗⠀ ⠀⡇⠀⣠⡇⡶⠀⢈⠀⠀⢫⣀⣀⣰⣇⠀ ⢸⠀⠀⠘⠉⠒⠒⠃⣀⣀⢠⢞⣵⣮⡹⡄ ⢸⢀⠀⠀⠀⠀⠀⠍⠒⠂⠞⢸⠛⠛⣇⡇ ⠈⡇⢦⠰⡀⠀⠀⠀⠀⠀⢸⡿⠀⢰⢹⠀ ⠀⠸⡘⣇⠈⡀⠀⠰⣦⡀⡘⡇⠠⢸⢸⠀ ⠀⠀⢡⠱⣦⡀⢀⠁⠪⡓⡇⣷⣲⣾⢹⠀ ⠀⠀⠀⠱⢌⡈⠆⠅⣀⡈⢧⣑⠒⣃⠜⠀ ⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡰⠖⠋⠁⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡏⣿⠀⠀⠀⣾⡇⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡇⣿⠀⠀⠀⣿⡇⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢧⣴⢶⣶⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⡟⠻⣎⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣶⣽⣟⠳⣄⣼⣟⣻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠛⠉⢩⣿⣿⣟⠿⢍⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣿⡗⠂⠀⠻⣿⡏⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠖⠊⢁⣰⢿⡿⠃⠀⠀⠈⠉⠀⠀⠀⠀⠹⣍⠲⣄⠀⠀⠀ ⠀⠀⢠⣶⠋⢠⣤⠶⣻⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⡌⠳⡄⠀ ⠀⣰⢷⣿⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⢹⡄ ⠐⣿⠿⠏⠙⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⡛⠛⢿ ⠀⠘⣄⣀⣢⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣶⠞ ⠀⠀⠘⣏⠉⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀ ⠀⠀⠀⠘⣆⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⡁⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⣤⣈⡲⠤⣄⣀⣀⣀⣀⣀⣀⣀⡀⠤⠔⠊⠙⠒⢬⣱⠀⠀ ⠀⠀⣴⡺⠟⡻⠧⠤⠭⠥⢤⡾⠟⠁⠀⠈⠑⠒⠒⠒⢒⠒⠒⠒⠉⡀⠀⠀ ⠀⠀⠘⠣⠮⣀⣀⡀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠮⠤⠛⠷⠛⠀⠰⠇⠀⠀
⠀⠀⠀⠀⡀⠰⣄⠀⠀⠀⠀⡠⠐⣀⠄ ⠀⠀⠀⠀⠡⢀⣽⠃⠐⠲⢞⠂⠁⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⠠⣤⣄⢯⠃⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⡟⠟⠹⣿⣿⡔⠀⠀⠀ ⠀⢀⡴⡺⠁⢙⣿⢤⣤⣾⢹⠹⣄⡀⠀ ⠰⡋⣐⣴⣲⡟⠈⠉⣿⡳⠹⣳⢮⡻⣷ ⠴⢺⣿⣻⡯⠃⠀⠀⢹⡇⠀⢴⣷⢏⡇ ⠀⣸⣿⠛⠁⠀⠀⡠⣾⣏⣆⣸⣻⠞⠁ ⠀⢸⣿⣄⠀⠀⠀⣹⣪⡿⠛⠁⠀⠀⠀ ⠀⣿⠉⠹⡍⣿⡏⢹⡎⠀⠀⠀⠀⠀⠀ ⠀⢻⠀⢰⠃⢿⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⢸⡆⢸⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣧⣾⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⡸⠉⠇⠀⠀⠹⡎⢃⠀⠀⠀⠀⠀⠀ ⠀⡇⢀⠀⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀ ⠀⢸⣸⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡄⠀⠀⠀⠀⣷⡇⠀⠀⠀⠀⠀ ⠀⠀⢿⢇⠀⠀⠀⠀⢳⡇⠀⠀⠀⠀⠀ ⠀⠀⢸⣛⡄⠀⠀⠀⢭⡥⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡡⡲⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣘⠔⣡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠇⠁⠺⠥⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⡱⠋⠉⠑⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣠⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡇⠀⠀⡏⠀⣱⠀⠀⠀⠀⠈⠑⠂⢹⠁⠀⠀⠀⣀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢧⠴⡀⠈⠉⠀⡀⠀⠠⠤⣄⠀⠀⣸⠀⠀⠀⠘⣄⡠ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢎⣣⡦⠀⠘⠤⢍⡄⠀⠀⠈⢁⢎⠀⢹⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⢀⠔⠙⣿⣿⣷⣦⣦⣦⣤⣠⣤⣶⠃⠇⣴⠥⠒⠉⣷⡀⠀ ⠀⠀⠀⠀⢀⢧⠀⢠⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⡟⠛⠛⢄⠘⠁⠎⣜⠠⠆⢱⠀ ⠀⠀⠀⠀⢸⠀⠃⢈⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⠀⠠⡤⠞⡰⠋⠉⣣⠀⠀⣸⠀ ⠀⠀⣠⢤⣈⣧⡀⣸⠀⠀⠀⠀⠀⡶⠀⠀⠈⡻⠓⠤⣑⠒⠋⢂⡞⠡⠀⢠⠇⠀ ⠀⢀⡇⠈⡆⠈⠙⢿⣧⣀⠀⠀⢰⡇⠀⠀⡔⠁⠀⠀⠀⠀⠀⠈⡄⠀⣷⠋⠀⠀ ⢺⢉⢵⣴⠻⠀⠀⠈⣿⣈⠁⡀⠉⣙⠄⣀⡇⠀⠀⠀⠀⠀⡰⢀⠇⢠⠏⠀⠀⠀ ⠀⠣⡰⠉⠆⣠⠖⠚⠻⠿⢦⡐⠄⠠⡁⠂⠘⢄⡀⠀⠠⠀⢀⣮⡶⠋⠀⠀⠀⠀ ⠀⠀⠙⠒⠈⠁⠀⠀⠀⠀⠀⠙⠠⠀⠈⠄⠀⠀⠈⠑⠤⠒⠻⢿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⡴⢺⠇⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢀⠎⣠⠋⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣮⡔⠁⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⠀⠉⢠⣾⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠉⠉⠛⠲⢦⣄⣀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠟⠁⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⢰⠋⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠉⡇⠀⠀⠀⠈⠳⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣼⠓⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⢿⡶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣤⣄⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢹⡀⣀⠔ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠠⡈⢷⣊⣡⠄⠀⠀⢰⡀⠙⠟⠀⠀⠀⠀⠀⠀⠹⠇⠀⡴⠋⠉⠻⣦⠀⠀⠀⠀⠀⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢱⣠⣿⣿⡉⠀⠀⠀⠉⠙⠢⠴⠃⠀⠀⠀⠀⠀⢀⡞⣡⠖⡇⢀⡿⠳⢶⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡠⠚⠹⣿⣿⣿⣿⣿⣶⣧⣦⣴⣄⣀⣤⣠⣀⣀⣰⣤⡞⠀⠁⢀⣴⣋⡤⠖⠚⠉⣿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢠⠎⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⡾⠋⣁⠴⠒⡄⠀⢸⠹⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠉⠙⠲⡄⠈⠀⠀⠣⢤⣪⡥⠴⠛⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢧⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣰⣇⣀⡴⠒⠛⠛⣇⠀⠀⠀⠀⣾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠉⢩⡏⠁⠀⣏⠀⠀⠀⣀⡼⠀⠀⠀⢀⣿⠀⠀ ⠀⠀⠀⠀⣀⣠⣄⠀⢻⣆⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢠⣶⠂⠀⠀⠀⠈⠛⣿⠟⠢⣄⡈⠓⠒⠒⠉⠓⠴⣾⠏⠰⡄⠀⠀⣼⠏⠀⠀ ⠀⠀⠀⣾⠋⠉⢿⠛⡟⠻⣿⣶⣿⣷⡀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠉⠑⠂⠀⠀⠒⢺⠁⠀⠀⢣⢀⣼⠏⠀⠀⠀ ⠀⠀⣀⣿⠀⠀⠸⡆⠀⠀⠈⠙⢿⣿⡷⣤⡀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⣼⣾⠃⠀⠀⠀⠀ ⢰⡟⠋⠛⣇⣀⣠⢿⡆⠀⠀⠀⠀⣿⣇⠈⠙⠒⠒⠒⠒⠉⠹⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡟⠀⣀⣻⡟⠀⠀⠀⠀⠀ ⠈⢧⣠⠚⠛⣿⣗⠊⠁⠀⠀⠀⢀⣿⣿⣷⣄⠀⠠⠂⠀⠀⡤⣌⠓⠦⠤⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡼⠁⢀⣼⠟⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣄⡸⠁⢈⡇⠀⣰⡿⠛⠛⠻⠿⠿⢿⣦⡀⠱⢄⠀⢳⡀⠉⠂⠀⠈⢧⣀⠀⠀⠀⢀⣠⠔⠁⠀⣼⣥⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣧⣤⣄⣤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⠀⠠⠀⠙⢦⠀⠀⠀⠀⠉⠓⠦⣤⠀⠀⢀⣠⣶⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣀⠈⠳⠄⠀⠀⠀⠀⠀⠈⠙⠛⠉⠉⠻⠿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠤⣄⠀⠀⠀⢀⡴⠊⠉⠉⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡴⠒⢄⠑⠄⠜⠁⡔⠲⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⠜⠁⠀⣞⣁⡄⢀⣤⢧⠀⢠⠀⠀⡸⠀⣀⣆⡀⢀⣀⣀⣄⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢾⡀⣏⣻⣏⣳⣬⠗⠚⠷⣌⡁⠀⠛⠛⠉⢨⢿⡉⠉⡍⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠙⢾⣯⣽⡝⠁⠀⠀⠀⠀⠈⠲⣄⠀⠀⠈⠉⠁⠀⠻⢿⣿⡆⠺⠿⠿⠾⠿⠿⡿⠼⠿⠄ ⠀⠀⠀⠀⠀⠀⡴⠋⠀⢀⡴⠊⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠒⠢⣄⠀⠱⣄⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠺⠏⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠀⠀⠀⡎⢀⠤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⢳⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠀⠀⠀⣸⢰⠃⠀⠀⠀⢀⡄⠀⠀⢠⡀⠀⠀⠀⢀⢡⠘⡄⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠃⠀⠀⣰⠃⢘⠏⠁⠀⠉⠁⠀⠀⠀⠀⠈⠉⠁⠈⠉⠘⢆⠘⣄⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⣠⠞⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠘⣦⡀⢳⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣯⣀⣗⣶⠃⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣡⢄⠻⣯⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠷⣧⡍⠀⠻⠛⡄⢀⣻⠀⠀⠀⠀⠀⠀⠰⢶⠶⠀⠀⠀⠀⠀⠀⠀⢸⡆⠸⡏⠀⠑⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⠷⠂⠀⢀⣹⠑⠒⠂⠀⠒⠒⢻⡁⠀⠀⠲⠾⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡫⠇⢀⡠⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⣀⡈⢹⡒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣒⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⠄⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⢀⣠⠖⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠙⢮⣷⢄⠤⣤⣤⢤⣀⣰⢎⣁⡤⠴⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢀⣴⣶⠛⠁⠀⠀⠈⠙⠻⣟⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣿⣽⣿⠀⠀⠀⠀⠀⠀⠙⡎⢾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣸⣿⣧⠄⢰⣤⣾⣴⣤⠀⢻⣄⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢧⣿⣟⣷⣐⣾⣿⠿⣿⣷⣼⢻⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣿⣿⠿⣿⡟⠟⠀⣿⣿⣿⣯⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠻⢟⣿⡆⠉⠀⠀⠀⠛⢻⣿⣿⣿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣾⡿⢛⡅⠀⢹⣿⢟⣿⣦⡀⠀⣠⣿⣾⣿⢻⡇⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣶⣿⠴⠚⠉⠀⠀⠀⣰⡞⢿⣄⠹⣯⢽⣿⢿⡏⣄⣽⡄⠈⠻⣟⡦⣤⡀⠀⠀⠀⠀ ⠀⣠⣾⠛⠁⠀⡄⢰⣆⣤⡴⣿⡟⠁⠈⠛⠙⠻⣿⡟⣿⡄⠈⣷⢼⣷⣤⡈⠛⢿⡻⣷⡀⠀⠀ ⠀⠙⢧⣄⣀⣤⣴⢿⣻⣦⣾⠿⠃⠀⠀⠀⠀⢀⣿⡆⣿⠃⠀⠘⢾⣽⡞⠻⣷⣄⢿⣿⠃⠀⠀ ⠀⣀⣠⣿⣛⣿⢷⣾⣟⣿⠇⡅⠀⠀⠀⠀⠒⠋⠙⣷⣿⠀⠀⠀⠘⢣⡿⣞⢮⡙⢷⣿⠀⠀⠀ ⢸⠏⠉⢹⣿⣿⣿⣡⣿⡟⠚⠁⠀⠀⠀⠑⠀⠀⢀⣿⣿⠀⠀⠀⢺⣟⢷⣻⡀⣷⣘⡿⠀⠀⠀ ⠀⠀⠀⠈⣻⣿⣿⡿⣿⡷⠇⠀⠀⠀⠀⠀⠀⢀⣿⢿⣿⠳⡄⠀⠈⢿⣿⣿⣇⣿⡟⠁⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⡴⢿⣿⣿⣿⣠⣟⡀⢀⡾⣋⣹⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣷⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⣀⣹⢿⣿⣿⣿⢿⡟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣉⣾⣿⣿⠟⠊⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⡿⠿⢿⣷⢤⣤⣴⣄⣤⣶⣿⡿⣿⠹⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠊⠁⠀⠘⢿⡄⠈⣹⣿⣿⠏⠈⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⢿⣿⠻⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡄⠀⠀⠀⣾⡇⠀⢸⣿⠀⡅⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣏⠀⠀⠈⣿⠀⠀⢸⣿⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⢸⡟⠀⠀⠀⢻⡆⠀⠀⢘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⡆⠀⢸⡇⠀⠀⠀⢸⣧⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣷⠀⣼⡇⠀⠀⠀⠈⣿⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⡀⣹⡇⠀⠀⠀⠀⢻⣧⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⠹⣿⡿⠀⠀⠀⠀⠀⠘⣿⣆⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠘⣿⠃⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠘⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣇⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⣭⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣧⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠜⠿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⡛⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠨⣵⣤⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⠁⣸⣧⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠒⠶⣦⡀⠀⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢹⡜⣇⢻⣿⣆⠀⡇⠈⠆⠀⠀⠀⠀⠀⠀⠠⠀⠉⠀⠀⣹⡿⡿⠦⣤⣀⣤⣴⣾⡿⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⣀⣤⠤⢤⣄⠀⠀⡇⠘⣦⣿⠿⠶⠛⠶⠦⣤⡶⠶⣄⡀⠀⡁⠀⠀⠀⠀⠀⠀⠁⢀⡠⠏⣿⣾⣏⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⢀⡾⢳⢠⠠⣆⣹⠆⠀⢻⡾⠋⠀⠀⢀⣀⡀⠀⠈⢛⣦⡀⢻⡆⡀⠀⠀⠀⢀⡤⠴⠚⠉⠀⠀⣩⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⣠⠏⠀⠸⣿⠿⠛⠁⠀⠀⢸⠁⠀⠀⠀⠸⢵⠟⢀⡀⣿⢻⡱⠼⠃⠁⣠⡤⠞⠋⠀⠀⠀⣠⣰⠟⠁⠀⣶⣤⣤⣦⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡀⢰⠏⠀⠀⢀⡇⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠒⠚⠞⠀⣸⣡⡴⢲⡞⠁⠀⠀⢀⡴⠂⣾⡟⠁⠀⢀⡞⠀⠘⠛⡉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠏⠀⠀⣠⠾⠓⢶⡖⠒⠒⠶⣄⠉⣷⣏⣲⣶⣤⣤⣤⣶⣾⠋⠁⠀⠘⠀⠀⣠⡴⠋⢰⡏⠇⠀⠀⢀⡾⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠠⣄⠀⠀⠀⢸⡻⣆⠀⠉⣇⠀⠀⠈⢻⣢⠀⠤⠾⠋⠉⠙⠿⣿⣿⡿⠟⠁⠀⠀⠙⢂⣤⠖⠛⠁⠀⣠⠏⠀⠀⠀⢠⡞⠧⠄⠀⡆⠀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠉⣳⣄⠀⠀⠉⠻⠷⣄⠘⠦⠤⣤⠀⠻⣧⠀⠀⠀⠀⠀⠀⡬⠃⠀⠀⠀⠀⠀⣀⣾⡋⠅⢀⣠⠼⠁⠀⠀⠀⢀⡾⠁⠀⠀⠀⠷⠀⠀⡶⡖⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣶⡄⠀⠀⠀⠙⡳⣤⣀⠈⣵⣶⣼⣄⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢀⣾⢿⣿⠟⢰⣿⠇⠀⠀⠀⠀⠀⣜⠛⡆⠀⠀⠀⠀⠀⢀⡧⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⣴⠃⠀⠈⠛⣷⡚⢿⣝⠲⣤⣤⣤⣤⠱⣤⡴⠖⠚⠋⣴⣿⠇⢠⠿⡏⠀⠀⣠⡆⠀⡼⢋⡟⢹⡀⠀⠀⠀⣠⠞⢱⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢙⣂⣠⠿⠒⠊⠉⠉⠈⣻⣮⣻⡷⢦⠖⠋⡏⠀⠀⠉⠲⢶⠊⢿⣁⣰⠋⠞⠀⠠⢞⣹⠤⠴⢟⣋⠰⠿⢳⡀⢀⡞⣁⣤⣳⣆⣀⠀⠀ ⠀⠀⠀⠀⠁⠀⣠⠞⠁⠀⣀⣀⠀⠀⣰⠞⠛⠉⣧⣿⡄⢠⡒⠤⢼⡄⠀⠀⠀⠀⠣⠀⣸⠁⣠⢖⣫⠭⠤⣬⣉⠙⠚⠉⠉⣉⠉⠉⠛⢾⡁⡀⣿⠁⠀⣇⠀ ⠀⠀⣠⡤⠒⠚⠃⠀⠀⡞⠁⢹⣀⡼⠣⣜⣆⠀⠘⣿⣧⠀⢸⠦⣌⡇⠀⠀⠀⠀⡠⠞⣿⢦⡼⠋⠠⠔⣻⣟⣁⡼⠛⠛⠋⠉⠙⢦⠀⠈⡗⠶⠛⢀⡜⠁⠀ ⠀⣾⠋⢀⡀⠀⠰⣿⡴⠃⠢⡌⠉⠀⠀⠈⢛⣦⠞⠻⣟⠶⣼⣆⠀⡇⠀⠀⣆⣾⣥⣶⡿⢦⣄⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⠰⢯⣤⠀⢁⡞⠙⢦⣬⣱⠀ ⠀⠻⡦⠏⠙⠦⣤⣾⡐⠦⡀⠘⢆⠀⣠⡞⠋⠀⠀⠁⠘⢷⡀⠈⠉⠉⠉⠉⢉⡵⡞⠁⠀⠀⠈⢧⡀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠈⠒⣋⣀⣤⡼⠿⠋⠀ ⠀⠰⢤⣀⠀⠀⠈⠁⠙⣧⣘⠂⢀⣾⠋⠈⣏⠀⠀⠀⠀⠀⠹⣦⡀⠀⢀⣴⠋⠀⠉⠳⣄⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢽⣷⣄⡀⠀⠀⠀ ⠀⠀⠀⣀⠤⠴⠚⢋⣿⡀⢈⣽⣿⣟⠀⠸⠛⠳⠤⣄⣀⣀⣠⣿⣿⡛⠿⢿⡐⠀⠀⠀⠀⠀⠠⡀⠀⠷⢦⡴⠚⢋⡴⠖⣛⡛⠗⠦⣌⠋⠁⠀⢀⡈⢳⠀⠀ ⠀⣠⠊⠁⢀⡀⣴⠛⠈⠓⠻⢄⠙⢻⡷⠀⠀⠀⠀⢘⡟⢯⡉⠻⡟⡇⢰⠏⠩⠳⠦⣄⣀⣀⢀⡙⠢⠀⠀⠱⡖⠀⢐⡯⠛⠀⠀⣀⣞⣀⣀⠀⠘⠹⢯⣤⠀ ⠀⡏⣰⠾⠛⠚⠃⠀⠀⠈⠳⠌⠛⢮⣳⠀⠀⠀⠠⣾⠃⠀⠹⣆⣙⠓⠘⣷⠴⠄⠀⢀⣉⣹⡟⠙⠒⠛⠁⠀⢳⣠⠈⠀⢀⡴⠞⠋⠀⠀⣙⡆⠀⠀⠀⣿⠀ ⢸⡃⣧⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢧⠀⠀⠀⠹⣆⠀⠀⠃⣈⣙⣿⣠⣿⡀⠀⠀⠀⠀⠙⠲⠶⣄⡀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠰⠞⢋⣀⣀⠄⠀⠈⡇ ⠀⠃⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣲⠾⠇⠀⣀⣀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⢀⡼⣷⠄⢀⠈⢳⡆⠀⠀⠀⠀⠹⣏⢻⡧⢴⣀⠴⠃ ⠀⢀⡠⠛⠒⠬⠃⢀⣀⣠⣤⣤⣿⣿⡷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣤⣾⣶⣾⣧⣶⡶⢤⣀⡀⢸⠀⠹⠉⣁⡀⠀ ⠀⠛⠓⠀⣢⣴⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠷⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⣿⣷⣤⣾⠀⠛⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⢀⠐ ⠀⠀⠀⠀⠀⠀⢰⡀⠀⠻⣝⣄⢀⡀⣀⡀⠀⡠⠞⣁⣠⠔⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⢧⠀⣠⣬⡟⠉⠉⠙⠻⢿⡛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣷⣯⣿⡃⠀⢀⠀⠈⢳⡻⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣇⢓⣾⣿⣷⣘⣷⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⣿⣿⠏⣽⣿⣿⣿⣸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣾⡟⣻⣻⣷⠉⠀⠀⣙⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⢟⡫⠗⠀⠚⣛⣿⡳⣤⣴⣾⣿⠇⢿⠘⢿⣦⣀⠀⠀⠀ ⢀⣴⠞⠋⡁⢤⣀⣠⣶⡟⠘⠗⠺⣿⡿⣿⠘⣿⣷⣄⡙⠿⣿⣦⡀ ⠉⠣⣤⣤⡶⣿⣷⣾⡟⠉⠀⠀⢀⣿⡇⡟⠀⠘⢾⣿⠛⣷⣜⣿⡇ ⣴⠶⣿⣿⣿⢟⣿⣯⠇⠀⠀⢀⠉⠀⣿⣇⠀⠀⣨⣾⣻⣳⡝⣿⠄ ⠁⠀⠻⣿⣿⣾⣿⡄⠀⠀⠀⠀⠀⣰⣿⣿⢄⠀⠸⣯⣿⣇⣿⠟⠀ ⠀⢀⣾⣿⡟⠃⠁⠀⠀⠀⠀⢠⡶⣿⣾⣧⣼⣀⣠⣟⣻⡿⠋⠀⠀ ⠀⠈⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⣷⠼⣻⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣷⣄⣀⣠⣀⣠⣴⣿⡶⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠉⠀⠹⣧⠉⣿⣿⡟⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠀⠀⢀⣿⠀⣿⡏⠇⠀⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⠀⠀⢸⡏⠀⢹⡇⠁⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⢸⡇⠀⠘⣷⠀⠀⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣷⠀⣾⠃⠀⠀⢿⡄⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡆⣿⠀⠀⠀⢸⣧⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠻⢷⡏⠀⠀⠀⠈⢿⣄⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡟⡀⣸⠃⠀⠀⠀⠀⠈⣿⡁⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⣸⠀⠀⠀⠀⠀⠀⢿⡅⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣧⠀⣿⠀⠀⠀⠀⠀⠀⠘⣷⡄⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⡔⣿⠀⠀⠀⠀⠀⠀⠀⢹⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⣧⠀⠀⠀⠀⠀⠀⠀⢻⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⣼⡄⠀⠀⠀⠀⠀⠀⢾⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣍⣷⠀⠀⠀⠀⠀⠀⢻⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢻⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⣼⠛⢿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠿⣦⡀⠀⠀⠀⠀⠀⣀⣀⣾⠏⢀⣼⠋⠀⠀⠙⢿⣿⣿⡿⠟⠋⠀⠉⠣⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⣿⡿⠋⠓⢦⣀⠈⢻⣦⣀⣤⣾⣿⣿⣿⡿⢠⣾⢓⣢⣄⠀⠀⠀⠙⠿⣅⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣟⣉⠀⠀⠀⠀⠈⠛⢾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠷⡄⡀⠀⠀⠀⠉⠓⠢⠤⣀⣀⣹⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣿⡿⢛⢻⣿⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⣿⢿⢯⣿⢻⣿⣿⡿⢀⣶⣿⡟⣰⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢟⡃⢠⠈⠉⠙⠓⢦⡀⠀⣼⣿⣿⣿⣷⣿⣧⣶⣾⣿⣿⣿⣟⢇⣳⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢦⣀⣀⠀⢀⣀⠽⣴⣿⣿⢹⡿⣿⣼⡿⢿⣿⡟⢯⢀⣠⣶⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⣟⡤⠊⠉⠙⣿⣿⣴⣿⠏⣧⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢘⣿⣆⠀⠀⠀⠈⢿⣿⣿⠒⢻⢿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣆⠀⠀⠀⠘⣿⣿⣶⣶⣿⠋⠉⠉⠉⠹⣿⠿⣿⣿⣿⣿⣿⣿⣿⣧⡾⠛⠉⢣⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡆⠀⠀⠀⠙⣿⣅⠻⠇⠀⠀⠀⠀⠀⢀⡾⣿⣿⣿⠿⣿⣿⡟⢁⡞⠛⠯⣍⣵⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⣧⠀⠀⠀⠀⢯⣝⡿⡉⠁⣀⠀⢀⡠⠀⢀⣿⣿⣽⡀⣿⣽⣄⡞⠁⡠⠌⠀⠙⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣸⡇⠀⠀⠀⠘⣿⡇⠘⢦⣀⠈⠁⣀⡴⡟⢹⡏⠠⡇⣿⣿⣏⡴⣋⣤⣤⠤⠀⠙⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢱⡀⠀⠀⠀⠘⢧⠀⠈⠻⣿⣟⣽⣿⣿⣻⣷⣇⣡⣿⠿⠿⠛⠋⠉⠉⠀⠒⠲⣜⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠀⠇⠀⠀⠀⡀⠘⣇⠀⠀⢸⠀⢨⠏⠀⠀⠈⣹⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠾⠯⠿⠛⢿⣯⡀⠀⠀⠀⠀⢀⣼⣿⣷⠦⠬⠂⣾⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠗⠤⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⠤⠤⠴⠛⠉⠉⠉⠀⠀⠘⠿⠯⠭⠭⠀⠙⠙⠋⠉⠐⠒⠒⠒⠒⠒⠒⠒⠋⠉⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⣰⡿⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⣷⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣿⠏⠀⣰⡿⠁⠀⠀⠀⠙⢿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⢦⣀⠀⠈⠻⣷⣄⠀⣠⣴⣾⡿⣿⣿⣿⡿⢀⣴⡟⠒⢤⡀⠀⠀⠀⠀⠙⠻⣯⣁⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠙⠻⢦⣔⣾⣿⣿⣿⣿⣿⣽⣿⣿⣿⣧⣾⣿⣶⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠉⠳⠦⣄⡀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣯⣤⡄⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⠟⢙⣦⢤⠀⢀⡀⠀⠀⠀⠀⠉⠛⠓⠶⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⠛⣋⢫⡿⡄⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠿⡿⢿⡟⣾⣿⢻⣿⡿⣿⡟⢀⣾⣾⣿⡞⢠⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢯⡻⡋⢠⡀⠉⠉⠛⠟⠦⣄⠀⠀⠀⣾⣿⣿⣿⣿⣧⣾⣿⣴⣴⣾⣿⣿⣿⣿⣿⢿⡘⢧⣾⣿⣿⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢧⣇⠁⠀⠀⠀⠀⠀⠈⠳⡀⣸⣿⣿⠟⣿⣿⡟⢻⣿⣿⡟⣿⣿⣿⡿⠉⠉⢃⣉⣾⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⠓⠦⠤⠤⣄⣤⠖⢋⣽⠾⣿⣿⣰⡿⢩⣿⣿⣿⠛⣹⣽⣯⣈⣯⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣡⠖⠉⠀⠀⠙⣿⣿⣡⣾⣿⡏⢹⣧⣻⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⡄⠀⠀⠀⠀⠈⢿⣿⣿⣿⠒⠺⡿⣿⣿⣯⡻⣦⣟⢛⣿⣿⣿⣿⡿⣿⢿⣿⣿⣷⣿⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡄⠀⠀⠀⠀⠈⣿⣿⣿⣀⣀⣓⣿⣿⠟⠛⠶⠿⠟⣿⣿⣿⣿⣇⣿⢸⣿⣿⣿⣿⣿⣿⢙⣿⣟⡛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡷⢹⡀⠀⠀⠀⠀⠸⣿⣷⡟⢿⣿⡿⠀⠀⠀⠀⠀⠀⠻⠟⢈⣿⣿⣿⡞⣿⣿⣿⣿⣟⣹⠿⣭⣀⣀⣀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⣷⠀⠀⠀⠀⠀⢹⣿⣧⡨⠷⠇⠀⠀⠀⠀⠀⠀⠀⣘⡿⢻⣿⣿⣿⠛⣿⣿⣿⡟⠁⡼⡋⠉⠛⢦⣤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣿⡆⠀⠀⠀⠀⠘⣯⡙⠻⣟⠉⠁⠀⠀⠀⠀⢀⡤⠁⠀⣿⣿⡟⣹⠀⢹⡇⣿⡀⣸⠟⠁⢀⡨⠁⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⡊⢷⠀⠀⠀⠀⠀⠸⣮⣗⠈⢳⡄⠈⠒⠲⠖⠉⠀⣠⣾⢹⣿⠃⠉⡇⢸⣷⣿⡿⠃⣤⠖⠉⠀⠀⠀⠀⠲⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⡾⡄⠀⠀⠀⠀⠀⢿⢿⠀⠀⠹⣶⣤⣀⣀⣤⣾⣹⣧⣸⣿⢠⠈⡇⢸⣿⣿⢇⡞⣡⣶⣿⣟⣛⠓⠀⠀⠹⣿⡄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⡇⡇⢻⡀⠀⠀⠀⠀⠈⠫⣇⠀⠀⠘⢿⣷⣏⣰⣿⣿⣿⣛⣿⣼⣆⣸⣾⡿⠿⠞⠛⠉⠁⠀⠀⠈⠉⠉⠛⢷⡙⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⣧⣷⡇⠸⡇⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢻⠀⠀⡽⠃⠀⠀⠉⠉⢩⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣤⡾⢾⣿⣾⢿⣿⠇⠀⠅⠀⠀⠀⠀⠡⠀⣼⣿⣦⣀⡀⢸⡄⢠⣇⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠘⢿⣿⣄⠀⠀⠀⠀⠀⣠⣾⣿⣽⣷⡈⠉⠉⢃⣼⣿⡧⢴⣶⡶⡀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⣟⣁⣈⣉⣓⣂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠤⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠓⠒⠒⠒⠒⠒⠚⠃⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⡀⠀⢠⠊⠁⠀⠁⠢⣴⠎⠛⣒⡮⠉⣢⠀⠀⠀⠀ ⠀⠀⠀⣠⠐⠁⢀⣸⠆⠠⣰⡇⢸⢿⣶⣿⡖⠋⡹⠠⠊⡸⠀⠀⠀⠀ ⠀⠀⠔⠉⡗⠈⠉⠉⠀⣰⣻⣏⠚⣿⡿⢿⡀⡰⢁⠄⠊⡇⠀⠀⠀⠀ ⣠⠊⡠⠚⡇⠤⢀⠀⠸⡀⠈⢉⠋⡁⠠⠚⡿⠋⠀⠀⢠⠃⠀⠀⠀⠀ ⠇⠘⠀⡎⠀⠀⠀⠣⠄⠱⡠⡤⠤⢴⠁⢀⠞⢀⣠⠚⠁⠀⠀⠀⠀⠀ ⣆⠸⡴⠷⢤⣤⠤⡎⢀⣢⠞⢁⠔⢻⣷⠃⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠳⣖⠣⣬⡵⠫⠁⣀⣔⣁⣀⠠⢿⣄⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢫⡇⠠⢼⣿⡷⠂⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠠⡤⣀⠀ ⠀⠀⠀⠀⠼⡫⠗⢤⣤⠛⣳⣤⣤⣔⣮⠟⠀⠀⠀⠀⠀⠀⣀⢷⢽⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠐⠀⡾⠟⠁⠀⠀⠀⠀⠀⢠⠖⣷⣿⣼⡗ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠤⣳⡨⠗⢆⢢⠀⠀⠀⠸⣶⠸⠿⠥⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠌⠉⠉⠉⠀⠀⠀⠀⣁⠀⠀⠀⠠⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠋⠢⣐⣤⣀⠤⠒⠈⠁⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠸⠀⠀⠀⢹⠁⠀⡀⠀⠀⠆⢘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠀⠀⣀⠤⠄⣺⡆⠀⠈⠢⡘⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠇⠀⡎⠀⠀⣰⣿⠻⡄⠀⠀⢱⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠔⢦⣀⣴⠟⠁⠀⠙⠦⣤⢼⠐⢽⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⣿⡿⠷⣄⠀⠀⣀⣀⡼⢁⡜⠁⠙⢿⣿⠟⠋⠑⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⠟⠁⠈⠒⢼⣷⣾⣿⣿⣧⣾⣶⣶⡀⠀⠉⠒⠠⢀⡀⡆⠀⠀⠀ ⠸⣿⠟⠏⣧⡀⠀⢠⣾⣿⣿⣿⣻⣿⣿⣻⣳⣾⣳⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢢⡀⠀⣈⠢⣾⣿⢿⣿⠿⣿⠏⣉⣵⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣅⠀⠈⢿⣾⠇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⢂⠀⠈⣿⡶⣾⠋⠉⠙⢟⣿⣿⣿⣿⡻⣞⡉⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡀⠀⠸⣓⡟⠂⠀⡀⠊⣹⣿⢹⣻⡰⠃⠈⠛⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⢻⡄⠲⣌⢠⣾⣽⡇⢸⣿⣵⠵⠒⢀⣙⡇⠀⠀ ⠀⠀⠀⢀⡰⣿⣿⠣⠀⠀⠀⣰⡀⢉⢨⠋⠀⠹⠟⠁⠀⠀⠀⠀⠀⠸⡀⠀ ⠀⠀⠀⠈⠉⠁⠙⠢⢀⡀⠴⠛⠃⠉⠾⠗⠒⠀⠄⠀⠀⠀⠤⠤⠄⠚⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⣤⠀⢰⠀⠀⠀⠢⠀⢤⣀⠀⠀⣀⠀⠀⠀ ⠀⠀⢀⠀⠀⢢⣄⡠⡀⢏⠞⠓⠒⠰⡂⠄⠀⠀⢈⡡⠜⢿⠿⠃⠀⠀ ⠀⠀⠈⠆⡰⠁⠛⠋⠀⢊⠀⠘⠣⠔⢋⡂⠄⠊⡁⣠⠖⢡⠲⠖⠀⠀ ⠀⡀⠀⢸⡁⢔⠉⢯⡉⠦⠳⢷⡶⠚⠁⢈⠤⠊⡜⠀⢠⠇⠀⠀⠀⠀ ⠀⠈⠢⡄⠉⠢⢁⣢⣧⠀⠀⠀⠀⢀⢴⡗⣴⠊⠀⢠⣣⠀⠈⢀⡏⠀ ⠀⠀⠀⡐⠤⠓⢂⡹⣿⠮⠛⡏⠙⠠⠋⠔⣃⠰⠧⣲⠵⠆⣐⠥⡥⡄ ⢠⠔⠚⣀⢎⠦⠚⢆⡹⣇⡄⠅⢀⢠⣺⡚⠉⠺⠥⠒⠀⢰⡈⠒⣁⡂ ⢐⡊⠒⠣⡢⢁⡔⡅⠀⠑⢌⠉⣩⠙⢅⠈⢢⠀⠀⠀⠀⠀⠁⣥⡚⠁ ⠠⢒⢈⠝⠴⡻⡧⠉⠐⡶⡺⡏⡝⠤⣀⣀⡦⠑⠬⢂⠝⢁⣎⡀⠬⡂ ⠶⡉⠁⠀⠈⠈⠛⡀⠘⣄⣑⣢⣭⣁⠐⠙⠤⢀⠘⢄⠈⠁⢠⣃⠀⢰ ⢠⠓⢐⣠⣤⣼⣾⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣾⣧⣦⣧⣤⣄⡎⡛⡅ ⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀
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