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└|°ε°|┐

⠀⠀⠀⠀⠀⢀⣼⣿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡿⠛⢻⡆⠀⠀ ⠀⠀⠀⠀⢰⣿⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠸⡇⠀⢀⣾⠇⠀⠀ ⠀⠀⠀⠀⠀⣿⣤⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⡿⣏⠀⠀⠀⠀⠀ ⠀⣴⣿⡿⠋⠀⢻⡉⠀⠀⠀⠀ ⢰⣿⡟⠀⢀⣴⣿⣿⣿⣿⣦⠀ ⢸⡿⠀⠀⣿⠟⠛⣿⠟⠛⣿⣧ ⠘⣿⡀⠀⢿⡀⠀⢻⣤⠖⢻⡿ ⠀⠘⢷⣄⠈⠙⠦⠸⡇⢀⡾⠃ ⠀⠀⠀⠙⠛⠶⠤⠶⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀ ⠀⠀⢀⣴⣾⣿⣆⠀⠈⣧⠀⠀ ⠀⠀⠈⣿⣿⡿⠃⠀⣰⡏⠀⠀ ⠀⠀⠀⠈⣙⠓⠒⠚⠉⠀⠀⠀

⣺⣐⣰⣒⣒⣗⣗⣗⣲⣺⢺⣰⢒⡖⡖⠆⠖⠢⠠⠀⠰⠀⠀⠄⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣰⠸⡦⡧⡇⡷⠯⢼⢹⠼⠼⠁⠧⠅⠏⠍⠩⠈⠀⠨⠀⠁⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢽⠭⠭⡭⡯⡯⣭⢿⢹⢸⢩⠩⠋⠇⡇⡁⠀⢀⠐⠀⢀⠀⡀⠂⠀⠀⠐⢐⢀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣛⡙⣇⣗⡗⣛⣺⣺⣺⢒⠒⡇⡖⡇⠂⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢚⠓⠒⡇⡖⡷⢲⢺⢸⠰⠄⠄⡇⠆⠤⠀⠠⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠆⠆⠅⠥⠬⠬⢨⠨⠀⠤⠀⡇⠅⠁⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠄⠁⡅⢉⢀⢘⢀⠀⡂⡂⡇⠀⢀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⡂⠘⢐⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣾⣶⣦⣤⣶⣶⣶⣖⠖⢶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣎⡽⣺⣝⠖⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣮⣌⣻⢛⠿⣷⣼⣿⣻⣕⠮⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣄⠹⣿⣿⣾⣷⡈⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⢋⣿⣿⣿⣿⣿⡿⢛⠛⠿⠿⣿⡅⠂⠀⠀⠀⠀⢉⠿⢿⣿⣿⣿⣿⣷⣦⡹⣿⣿⣎⣦⡹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣿⣿⣿⣿⣿⠟⠉⠀⠀⠈⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠤⢉⣽⢿⠻⣿⣿⣷⣯⡙⢿⣮⣷⣅⣻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⣵⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢻⣿⣿⣿⣿⣷⣾⣿⣷⢹⡗⢸⣯⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢞⣿⣿⣿⣿⠟⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠨⣾⣿⣿⣿⣿⣿⣮⢿⣧⢻⡄⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⣥⣿⣿⣿⣿⡟⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⣿⣿⣿⣿⣿⣿⣎⣿⣟⣷⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣿⣿⣿⣿⣿⣟⡆⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣔⣤⣤⣤⣀⡠⠰⡹⣜⡿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⡔⠡⢁⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣉⠿⡆⠀⠀⠀⠀⠀ ⠀⠀⠠⠊⣠⣷⣾⠿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣷⠀⠀⠀⠀⠀ ⠀⠐⢁⣴⣿⣻⡏⢈⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣯⠇⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀ ⠀⢠⣿⠋⠀⠉⠉⢰⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠙⡆⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣧⠀⠀⠀⠀ ⠀⣾⠏⠁⠀⠀⠀⣿⡏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⢇⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⡇⠀⠀⠀ ⢼⣟⠒⠀⠀⠀⢀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣼⡀⠀⠀⢈⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣧⠀⠀⠀ ⢸⡯⠌⠀⠀⠀⢰⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣿⣿⡷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣾⣿⠿⠋⣅⠀⠀⠈⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⡆⠀⠀ ⢸⡧⣉⠂⠀⣀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⢲⢶⠿⠿⣿⢟⣿⣿⠿⠛⡈⠡⢍⡜⢦⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⣿⣧⠀⠀ ⠀⡷⣈⡄⡂⢴⣿⡟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⡾⠭⠱⠊⣪⢴⣏⢝⢜⡯⠾⠟⣳⠛⡄⡠⣀⡵⢨⡜⣩⢷⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢹⣿⠀⠀ ⠀⢻⣥⢣⣓⣾⣿⡏⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣃⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢚⣏⣾⢏⢠⠪⠮⡫⠥⣈⡡⠚⡀⣤⣺⡟⡡⢎⡑⢤⡱⣌⢣⡜⣥⢫⣿⣧⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⡄⠀ ⠀⠘⣯⡷⣞⣿⣿⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⣿⣿⣿⣿⣿⢿⣟⣶⣶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣖⣯⣗⡿⣷⣺⠗⠛⡁⢤⣌⡰⠙⡴⣴⡖⠋⢻⣿⣶⣲⠿⢴⡇⢶⡘⢥⡚⢬⢳⡜⣯⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣷⠀ ⠀⠀⢹⣟⣿⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⢻⠟⣿⣿⣻⡷⢾⣿⣽⣟⣛⣻⢿⠷⣶⣶⣶⢶⢿⠽⢋⣞⠥⣫⠖⠓⠟⡛⣲⣥⠲⠙⣉⡞⣍⠬⢀⣠⠞⢓⣓⠬⠛⡛⠻⠯⣜⡣⡽⣩⠖⣭⢻⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣽⣿⠀ ⠀⠀⠀⣿⢾⣿⡿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢱⣿⣿⣿⣿⢳⠟⣶⠛⠿⢋⡽⢉⠖⠚⠔⡫⣿⢽⡞⠣⢞⡛⠯⢐⡨⠩⠍⠁⠀⠀⠀⣀⠴⢛⡽⠛⡁⣟⢱⠼⠎⣠⠞⠋⠀⠀⢀⠡⠀⠂⠤⠱⡑⢧⡛⡴⣛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣒⣿⡆ ⠀⠀⠀⢿⣻⣿⡿⡰⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⣿⣿⠯⠜⣤⠴⣶⠻⡸⢣⢶⢒⡽⢷⣖⠞⡰⠂⠖⡄⠀⠀⠀⠠⠀⠀⠀⡀⠀⢂⢐⡁⡠⢆⣹⣶⠇⢔⠋⣀⢄⡚⢁⠀⣄⠄⣡⢉⠒⣡⢊⡤⡙⣰⠭⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢾⣿

⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣡⣇⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⠟⢻⣿⠤⠖⠒⠚⠉⠉⠉⠉⠉⠉⢩⡟⣹⠋⣿⠉⠉⠛⠒⣺⡤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡟⠀⢠⣿⡇⠀⢀⡄⠀⠀⠀⠀⠀⠀⣏⣼⣃⣠⣽⡤⠤⢴⠯⣭⠧⢼⣎⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⡇⠀⣼⣿⡇⠀⠰⣇⣠⡤⠴⠒⠚⠉⣿⠁⣤⣾⣿⡇⢀⣈⣉⣥⡤⢼⠬⣯⣛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣧⣼⣿⣿⠧⠒⠋⣏⣄⠀⠀⠀⠀⠀⢹⣀⡿⠿⠛⠉⠉⠁⠀⣀⣴⣾⠾⠓⠲⡯⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⣿⣿⡟⠀⠀⠀⣇⡿⠃⣀⡤⠴⠚⢹⡇⠀⠀⣀⡠⠖⠚⠉⢀⣀⠤⠖⠚⣹⣋⣏⡟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⠏⢿⠀⠀⣄⠀⠀ ⠀⠀⣴⣿⣿⣿⡟⠀⠀⠀⢀⡫⠖⠋⠁⠀⠀⣠⣤⣧⠴⠋⠁⠀⣀⡤⠚⠉⠀⠀⠀⣰⠃⡽⠣⣏⡧⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢸⣧⣴⣾⣀⠀⢸⡀⠀ ⢀⣾⣿⣿⡿⢻⣷⢀⡤⠞⠉⠀⠀⠀⠀⢀⣼⣿⡿⠏⠀⣀⡴⠛⠁⠀⠀⠀⠀⢀⡴⠁⡴⠁⡼⢸⣷⢸⠀⠀⠀⠀⠈⣧⠀⠀⠀⣀⡠⠔⠚⠉⠁⠀⠀⠀⠈⡇⠉⠁⠀⠉⣑⣧⢄ ⣼⣿⣿⠟⠀⣨⣿⣿⣿⣷⣦⡀⢀⣠⠖⠋⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⣦⣠⠞⢶⡞⠣⣼⢁⡼⢁⡏⠀⠀⠀⠀⠀⢘⣧⠔⠋⠁⢀⡀⣀⡠⠴⠒⠚⢩⣽⡯⠉⠉⠉⠙⠷⠞⠤ ⣿⣿⡏⠀⣾⣿⣿⣿⡿⢿⣿⣿⣏⠁⠀⠀⢠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⢦⠎⢉⠿⣌⡞⢀⡞⠀⠀⠀⢀⡤⠚⠉⠘⣇⣀⠤⠚⣯⠁⠀⠀⣀⣤⠼⠟⠓⠒⠒⠒⠒⢓⠒⠒ ⣿⣿⡇⠰⣿⣿⠁⢻⣧⠀⠹⣿⣿⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⢯⣷⡏⢰⢿⢇⠞⠀⣀⠴⠚⠁⠀⢀⣠⡶⢻⡇⠀⢀⡸⡶⠚⠉⠀⢸⡓⣦⣠⠤⠤⠒⠒⢺⡂⢉ ⠘⣿⣇⠀⢻⣿⣄⠈⣿⡆⠀⣿⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣮⣸⣋⣰⣋⣤⠾⠒⠉⠀⣠⣆⡠⠖⠋⠹⠤⣞⠴⠚⠁⠀⢻⣀⡤⠖⠊⡏⢸⠇⠀⣀⠤⠔⠺⠟⠈ ⠀⠘⢿⣷⣄⡈⠛⠛⢸⣿⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣠⠇⢠⠋⠀⣀⣠⣾⡟⡏⠀⠀⣀⠴⠊⠁⠀⢀⡠⣶⣿⡇⠀⢀⣴⣾⠼⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠛⠿⠿⠟⢻⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⢉⠏⠉⠉⠁⣻⢋⣤⡧⠴⠋⢷⡀⢀⡤⠚⠉⠀⠿⠿⣃⠴⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⡀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⠒⠠⠤⠔⣿⠛⠛⠁⠀⣀⡬⢿⠁⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣆⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠦⣀⣀⣤⣿⣀⡠⠴⠊⠁⠀⢈⣧⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⠟⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠉⠁⠀⠀⠀⠀⢀⣠⡿⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠦⠶⠒⠚⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣠⣶⣒⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⠿⠿⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⡴⠒⡚⢻⠒⢦⣄⢀⡴⠖⠚⠛⠻⢷⣶⣄⠀⣶⣶⡄ ⢰⡏⠀⣾⡁⢸⡀⣠⣿⣿⣶⣶⣷⡆⠀⠈⣿⣿⡧⢉⣁⡀ ⠸⣷⣄⡙⠻⠿⡿⠟⠋⠈⠉⠉⠉⠀⠀⢠⣿⣿⠇⠙⠛⠃ ⠀⠈⠻⢿⣷⣶⣧⣀⡀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⣟⠿⣷⣆⢀⣠⡶⠿⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣆⡀⢹⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠻⢷⣶⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⠟⠃⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⡀⠀⠀⠘⠻⣧⡀⠀⠀⠀⠀ ⠀⠀⢀⣾⡟⠁⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣦⡀⠀⠘⣷⣄⠀⠀⠀ ⠀⠀⢸⣿⠁⠀⢰⡿⠃⣄⠘⢿⣿⣿⣿⣿⣿⠃⢠⡀⠈⢿⣿⡄⠀⠘⣿⡀⠀⠀ ⠀⠀⢸⣿⡤⢶⣿⠃⣼⣿⣷⣄⠙⣿⣿⣿⠃⢠⣿⣿⣦⡀⠹⣷⠶⠶⣿⣧⡀⠀ ⠀⣴⡟⠁⠀⣸⠃⣸⣿⣿⣿⣿⣧⣄⣀⣀⣀⣾⣿⣿⣿⣿⡆⢻⡄⠀⠀⠙⣿⡄ ⢰⣿⠃⠀⢀⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⣧⠀⠀⠀⢹⡇ ⢸⣿⠀⠀⢨⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡀⠀⠀⠈⡿ ⢸⣿⡀⠀⠸⡇⢸⣿⠋⠉⠹⣿⣿⣿⣿⣿⣿⣿⡿⠉⠈⠹⣿⠇⢸⡇⠀⢀⣼⡏ ⠀⠻⣷⣤⣀⣷⠀⢿⣄⣀⣴⣿⡟⢻⡿⢿⡟⢻⣿⣤⣤⣼⠟⢀⣿⣧⣴⠿⠋⠀ ⠀⠀⠀⠙⠛⢻⣷⠀⠙⢻⣿⣿⣿⣬⣴⣶⣤⣾⣿⣿⡟⠁⢠⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣄⣉⣉⠋⠙⠋⠙⠋⣉⣁⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠂⠉⠉⠉⠀⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⣶⡟⢀⣴⣶⣿⣾⣶⣶⣄⡀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⣫⣼⡿⣴⡟⠛⠉⠉⠛⠛⠿⣿⣿⣷⣦⡀⠙⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⢁⣟⡟⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣆⠈⢣⡀⠀⠀⠀⠀⠀ ⠀⢰⣿⢼⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⢱⠀⠀⠀⠀⠀ ⠀⢸⡵⣾⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⢧⠀⠀⠀⠀ ⠀⠘⣴⣿⢯⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠛⠉⠹⡆⠀⠀⠀ ⢀⣼⣿⣧⠟⠁⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣴⣶⣴⡇⠀⠀⠀ ⢸⣿⣼⣿⣋⣉⠀⠀⠀⠈⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣷⡀⠀⠀ ⢸⠁⠊⣿⠛⢛⢟⣦⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢀⠔⣨⣶⡜⠂⠈⠽⣧⡀⠀ ⠸⣶⣾⡯⠤⢄⡀⠵⢿⣦⡀⠀⠀⠀⡷⡄⠀⡰⢁⣾⣿⣿⣿⠀⠀⠀⣿⡹⡄ ⠀⣿⣡⠦⢄⡀⠈⠳⣬⣹⣿⣆⠀⠀⢉⠻⣴⠇⣾⣿⡟⢻⠁⠀⠀⠀⣿⠁⡇ ⠀⣿⡭⡀⠀⠈⠲⣦⣸⣿⣿⣿⣧⣀⠈⡔⣜⣴⣿⡟⢀⡎⡈⠀⠀⢰⡿⢠⣷ ⠀⢸⣿⣄⣒⡀⡀⣿⣷⡿⣿⢿⣿⣷⡰⡸⣯⣏⣿⡷⢋⣼⣁⡢⢠⠟⠀⣼⣿ ⠀⠀⠻⣷⣈⣁⣮⢻⢸⡇⢨⣿⣿⣿⣷⢶⣿⣏⣩⣶⣿⣿⣿⣿⡯⣤⣴⣿⠃ ⠀⠀⠀⠘⠿⣿⣿⣽⣽⣷⣿⣿⣿⣿⣿⡶⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⠿⢿⣿⣿⣿⣿⠟⠁⠀⠘⠿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣠⢤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⢤⣀⠀⠀⠀⠀⣾⠿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣀⣀⣀⡠⠤⠿⢧⡧⠓⠀⠀⣀⣤⠤⠤⢄⣀⣰⠷⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠒⠦⢤⣏⣰⡇⠀⠀⠀⠀⠀⠀⢀⡾⠿⣯⣽⣻⡏⠀⠀⠀⠀⣠⣀⣀⡤⠤⠴⠒⠒⠀⡏⣻⣇⡤⠤⠖⠒⢲⣚⡩⠭⠭⠽⣛⣟⣛⣛⣻⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀ ⠀⠉⠒⠤⣀⠀⠀⣠⣿⠟⠉⠙⠒⠒⢒⣶⡄⡞⠀⠐⠒⢒⡟⠒⠚⠉⠉⠁⡿⣦⣀⣠⠤⠤⠒⢾⡿⣁⣯⠤⠔⣒⣫⣭⠤⠐⣒⡫⠭⣤⡞⠒⠚⠉⠉⠉⠙⠚⠛⠿⢿⣿⣦⣷⡀ ⠀⣀⠀⠀⠀⣽⡿⠿⡧⠤⢀⣀⣀⣀⣿⣿⣿⣁⣠⣶⣶⣼⠡⠤⠤⠖⢒⢺⠉⡹⢁⣀⡠⠤⣶⡆⢉⣁⠤⠖⢂⣏⠭⢿⠂⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠇ ⠀⠀⠉⠒⣼⣏⣠⣴⣷⣦⡄⠀⠀⠀⠀⠀⡀⠀⠈⠛⠛⠁⠀⠀⣀⣠⠿⠟⠒⠋⠉⢀⣠⢼⠟⠛⢉⡠⠔⠚⣩⡇⢰⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠠⢄⡀⢸⡇⢿⠉⣿⠛⣿⠲⠤⠤⠤⢴⣧⠴⠒⠒⠒⠈⠉⠉⡄⠀⣀⡀⠤⠒⠊⠉⣀⣸⠖⠊⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠓⠻⢤⣕⣿⡴⠋⠀⠀⠀⠀⣾⡟⣧⢀⣀⣠⠤⢄⡞⠛⠉⠁⠀⣠⠤⠒⠋⣥⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠦⢀⡀⣠⣤⡀⢹⠈⠉⠉⠉⠉⠉⡏⢻⣿⠁⠀⠀⢀⣜⣹⡧⠖⠊⠉⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⢿⣛⣣⡾⢤⣀⣀⣀⣤⣴⣅⣴⠧⠄⠒⠚⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠘⠛⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⠿⠿⠛⠛⠛⠻⠿⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠉⠉⠙⠛⠿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⢀⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⡄⠀⢀⣴⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀ ⠀⢀⣾⣿⣿⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣤⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⠶⠶⠶⠶⠶⠶⢦⣤⣄⣈⢳⡀⠀ ⠀⡼⣿⣿⠏⠀⠀⠀⠀⠀⠀⢻⣿⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⠁⠀⠀⣀⣠⣤⠶⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⡃⠀ ⠀⣿⣷⣭⣀⠀⠀⠀⠀⠀⠀⢸⡟⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣣⣤⠶⠞⠛⠉⠁⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⠀ ⢸⣿⣿⡃⠉⠛⠳⠶⣤⣤⣠⣼⣿⣿⡏⠀⠀⣀⣀⣀⣀⣤⣤⡶⠶⠟⣿⣍⠁⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣷⣶⣶⣖⣚⠛⠛⠛⠛⠛⠛⠒⠲⠦⣼⣧⡀⠀ ⢸⣿⣿⠙⠳⢶⣤⣀⣴⣿⣿⣿⡟⠙⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⢀⡇⣿⣦⣠⡤⠶⠖⠛⠋⠉⣿⠀⠈⠉⠉⠛⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠈⠙⠁ ⠀⣿⡟⠶⣤⣀⣠⣿⣿⣿⣿⣿⣷⣶⣦⣴⠤⠤⠤⠴⠶⠶⠶⠒⠛⢻⡇⠉⠉⠉⠁⠀⠀⣀⣀⣠⣿⢠⠴⠶⠶⠒⢺⡇⠛⠛⠛⣛⣒⣲⡶⢦⡿⣄⡀⠀⠀ ⠀⢹⣿⣀⠀⠉⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣀⣀⣀⣸⣧⡤⠶⠶⠖⠛⠋⣉⣉⡀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠻⣿⣿⣿⣿⠃⠈⠙⠃⠀ ⠀⠈⣿⡍⠛⠷⣿⣿⣇⣿⠁⠹⡇⠉⢹⣿⣿⠋⠉⠉⠉⢉⣩⣭⣥⣾⡇⠀⠀⠀⣀⣰⣿⣿⣿⣿⡿⠶⠒⠒⣛⡛⢻⡟⠛⠛⠓⠒⠶⠯⢭⣁⡀⠀⠀⠀⠀ ⠀⠀⠈⠛⠶⣤⣻⣿⣧⠹⢾⠻⡇⢶⣾⣿⢧⣤⣤⣤⣤⣿⢿⣿⣿⠿⠳⠚⠛⠉⠉⠉⠀⠉⠉⠁⠀⠀⢾⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢛⣻⣷⣦⣤⣷⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⡤⠶⠶⠶⠶⠶⠿⠿⢭⣥⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⢹⡇⠛⠛⠛⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣏⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣤⣀⡀⠀⠀⢀⣠⣴⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣾⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⠟⠿⢿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⠿⠿⠻⠛⠛⠙⠛⠙⢉⡉⣈⣁⣠⣀⣠⣤⣶⣿⣷⣾⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣛⣵⣤⣶⣤⣶⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⢿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠐⠀⢸⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣤⣴⣴⣴⣼⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⢀⣠⣴⣶⣶⣶⣾⣶⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀ ⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠛⠋⠉⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣭⣿⣿⣆⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡼⢋⣾⠟⢙⣿⠿⠛⠉⠉⠉⠀⠀⠀⠈⠉⠉⠙⠓⠲⢦⣄⡀⢀⣴⣖⣞⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⢋⣴⣿⣷⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡿⣿⣎⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠟⣥⣿⣯⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⢦⡀⠹⡷⣌⣿⣎⢿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⢾⣥⣼⣻⡿⠃⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠙⣄⢼⠋⡙⣿⣯⢿⣦⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⣿⡿⠁⠀⠀⠀⡞⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠘⣎⣷⡱⡘⢿⣧⢻⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⢸⠃⠀⣴⠏⣷⠀⠀⠀⠀⢸⣧⡀⠀⢀⠀⠘⣆⠀⠀⠀⠀⠀⠸⣼⣷⣧⠈⣿⣷⣿⡧⠀⠀ ⠀⠀⠀⠀⣸⣯⡆⠀⠀⠀⣿⠀⡼⠣⠤⢽⡄⡆⠀⠀⢸⠋⣷⡄⠸⣷⣄⠻⡆⠀⠀⠀⠀⠀⢿⣇⠿⣴⣿⣿⡟⠁⠀⠀ ⠀⠀⠀⠀⣿⣿⠇⠀⠀⢀⣿⣼⣁⣀⠀⠀⢷⣹⡀⠀⢸⠀⠘⠻⣟⣿⠛⣦⣹⡀⠀⠀⠀⠀⢸⣿⣾⣿⣿⢻⡆⠀⠀⠀ ⠀⠀⠀⢸⠇⢸⢰⠀⠀⢸⣿⠟⣿⣿⣿⣦⡺⣷⣧⠀⢸⡄⢀⡀⢈⣻⣆⣈⢿⡇⠀⠀⢠⠀⠈⣿⣿⢿⠁⠀⣇⠀⠀⠀ ⠀⠀⠀⣼⠀⢸⠸⡇⠀⣾⡿⠰⡟⢻⣿⣍⡷⠈⢿⣧⡘⡇⢩⣾⣿⣿⣿⡿⣷⣇⠀⠀⢸⡄⠀⣿⡇⠘⡄⠀⢻⠀⠀⠀ ⠀⠀⠀⡏⠀⣿⣰⣷⠀⢹⡟⠀⠻⣅⣈⡿⠁⠀⠀⠙⢷⣿⠈⣏⡹⢿⣤⡇⢸⡿⠀⠀⣸⣇⠀⢻⣷⠀⡇⠀⢸⡆⠀⠀ ⠀⠀⢸⠇⠀⡟⢱⡟⣇⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠹⢤⣠⠟⠁⢉⡇⠀⢠⣿⣿⠳⢾⣾⠀⢇⠀⠘⡇⠀⠀ ⠀⠀⣼⠀⢰⠃⢸⠁⠘⣦⣿⣿⣦⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣠⣿⣹⠇⠀⠀⢸⡀⢸⠀⠀⣧⠀⠀ ⠀⢀⡇⢰⠸⠀⣼⠀⠀⠈⠳⠙⣿⣯⣷⡶⢤⣄⣉⣛⣉⣀⣀⣀⣀⣤⠴⢚⣏⡴⠛⠛⠃⠀⠀⠀⢸⡇⢸⠀⠀⢻⠀⠀ ⠀⢸⠃⢸⠀⠀⣿⠀⠀⠀⠀⠀⠈⠛⠛⢣⣾⣷⣨⡿⣏⣩⡿⠛⢦⠀⠠⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⢸⡀⠀ ⠀⡿⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠀⢸⢶⣏⣉⣧⡰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⢸⡇⠀ ⢰⡇⠀⢸⡀⠀⡇⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⣸⠀⡇⠰⠘⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⡇⠀ ⢸⠁⠀⠘⡇⠀⡇⠀⠀⠀⢀⣴⣿⣿⣿⣟⣧⠀⣯⡄⡇⢰⠀⢸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⣿⠀ ⣾⡆⠀⠀⢻⠀⡇⠀⠀⠀⡼⢿⣿⣿⣿⠞⡜⢰⡏⢁⡇⠸⡄⠀⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⢸⠀ ⢻⢳⠀⠀⠘⣇⣧⠀⠀⠀⠓⠒⠛⢉⣾⣦⡀⣰⣿⣿⣆⢀⣵⣶⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⡀⠀⠸⡇ ⢸⡌⢇⠀⠀⢹⣿⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⡼⠀⠀⠀⠀⠀⠀⢸⡟⠀⢰⡇⠀⠀⡇ ⠀⢻⡈⣧⡀⠀⢿⡆⠀⠀⠀⠀⠀⠈⠙⠻⡭⣭⣿⣟⣿⣯⠭⠽⢷⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢀⢏⡇⠀⢰⠇ ⠀⠀⠹⣾⣿⡢⣄⢳⡄⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣿⡏⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢠⠎⣼⠀⢠⡟⠀ ⠀⠀⠀⠈⠙⠿⣾⣥⣙⣆⠀⠀⠀⠀⠀⠀⢻⣿⣹⣻⡇⣷⣿⠶⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⡴⠃⣰⢇⣴⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⣾⣿⣿⠃⢹⣽⣸⣿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣽⡥⠴⠾⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠀⢸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣶⠛⠉⠉⠉⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣦⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣯⡿⣞⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠛⠛⠁⠀⠀⠀⠸⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠶⠛⠉⠉⠻⣯⠉⠻⣶⣄⠀⠀⠀⣠⡴⠛⠉⠉⠈⠉⠙⢻⡿⣿⣶⣄⠀⠀⢀⣴⣶⣦⠀ ⠀⠀⢠⡞⠁⠀⢀⡼⠂⠀⣿⠀⠀⠈⣿⣧⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣯⣟⣷⡀⠘⢿⣿⠿⠀ ⠀⣠⡿⠀⠀⢀⣿⠀⠀⠀⣿⠀⠀⠀⢸⣿⣾⣿⣶⣶⢿⣷⣦⡀⠀⠀⠀⠀⢿⣳⣯⣟⣇⠀⠀⠀⠀⠀ ⠀⣽⡇⠀⠀⢸⣿⡄⠀⠀⢿⠀⠀⣠⣿⡷⣿⣞⣷⢯⣿⢾⣽⡇⠀⠀⠀⠀⢸⣟⣷⢯⣿⠀⠀⣀⣀⡀ ⠀⣿⣷⡀⠀⠀⢿⣿⣶⣤⣽⣦⣾⢿⣯⡿⠀⠙⠯⠿⠽⠿⠚⠀⠀⠀⠀⠀⢺⣿⢾⣻⡟⠀⢺⣿⣿⣷ ⠀⢹⣿⢷⡀⠀⠀⠙⠿⣾⣽⣳⣯⠿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⢿⣻⠃⠀⠀⠙⠛⠁ ⠀⠀⢻⡿⣿⣦⣄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣾⣻⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢷⣯⣟⡿⣦⣄⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⣷⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠯⣿⢯⡿⣽⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣳⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣟⣾⡽⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢷⣟⣿⣆⠀⠀⠀⠀⣠⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠘⠻⣿⣇⠀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⠀⠀⠀⠘⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣦⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣻⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⡆⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡠⠄⠤⠤⢄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠉⠁⡜⠆⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠀⠀⣀⣀⡄⠀⠘⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢺⡉⠁⠀⠀⢳⡀⢸ ⠀⠀⠀⠀⠀⡖⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠇⠀⣇⠀⠀⡔⠋⠉⢸ ⠀⠀⠀⠀⠀⢱⠸⡾⢽⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⡶⠬⠟⠒⠛⠛⠛⠛⠒⠷⠴⣆⡤⢀⠀⢀⠸⣶⠻⣤⠀⠀⠀⠸⣅⡠⠴⠊⠁⠀⠸⠴⠒⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⠁⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠉⠓⢧⣪⡋⠵⡽⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠋⠀⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡵⠋⣀⣴⢾⣟⣿⡭⠷⠟⠒⠚⠒⠚⠲⠮⢭⣝⣲⣤⡀⠉⠻⡮⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢃⠇ ⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⣠⢾⡿⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⠷⣄⠙⣿⡒⠯⢥⣶⣂⣀⣤⣤⣤⣄⣀⣶⣦⣼⡁⠈⢡⣎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡼⣿⢃⡾⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢋⣽⣦⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠁⠈⢻⡶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠞⢉⣴⣧⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⢰⡇⣺⠁⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣪⠞⠁⡴⣾⠁⣾⠇⠀⠀⠀⣦⣀⠀⠀⡜⠀⠂⠀⠀⠀⠀⠀⠘⢦⣤⠔⠁⠀⠀⠀⢸⡅⣿⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿ ⠀⠀⠀⢀⠀⣤⣀⡦⠗⠋⠁⠀⣸⢱⡏⣰⡟⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢻⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠍ ⢀⣴⡼⠟⠋⠉⠀⠀⠀⠀⠀⠀⢿⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⡶⠦⠴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡙⣧⣠⣾⢳⣶⢤⣤⣄⢂⠀⣀⣀⣤⣤⠶⡟⠙⠀⠀ ⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⣧⢉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⢷⣾⡻⠃⠀⠂⠈⠁⠖⠉⠋⡝⠒⠈⠉⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣼⡷⣤⣀⡀⠀⠀⠀⠀⠀⡾⢻⣟⣿⣶⣆⣼⠛⠶⣤⡤⣴⢶⠻⠏⠃⠁⠀⠀⠀⠀⠀⠁⠀⠀⠑⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠯⠁⠈⠁⠛⠉⠿⢟⡿⣟⢛⡏⣇⠻⣎⡷⡏⢻⡄⠀⠈⠁⠸⣷⠿⠯⢥⣆⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢛⢶⣄⡀⠅⠑⠀⠀⣀⣠⡴⡻⣏⢧⠁⠀⠀⠠⣰⣆⣮⠏⠀⠈⠻⣷⢌⡓⢦⣟⡇⠈⠁⠀⠀⠀⠀⢹⡆⠀⠀⠈⢷⣠⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠹⡧⠓⣿⠿⢟⡋⠁⠰⣞⠃⠀⠀⠰⡿⠁⠹⠋⠀⠐⠶⢶⡟⣎⡱⢭⣯⠃⠀⠀⠀⠀⠀⠀⠸⡇⠙⢦⠀⠸⣷⠣⣎⣞⡶⠀⠀⠀⠀⠀⣠⢶⡐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⡜⡄⣶⡄⠑⠀⣮⠛⠀⠀⠀⣶⡇⠀⠀⠀⠀⠀⠀⠈⣿⠒⢳⣾⡟⠀⠀⠀⠀⢠⣴⣦⠀⣧⣤⡟⠀⢰⣿⢰⡝⡞⣷⠀⠀⠀⣤⢲⢣⡌⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢷⣰⣕⠋⣵⠀⣿⠂⠀⠀⠀⠿⣇⢐⣆⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⠸⣧⡏⠉⠀⢀⣼⡙⠣⠝⠚⠂⠀⠀⡞⢰⡚⢠⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⠄⠀⡰⠂⠉⠄⢟⡶⠀⠀⠀⠈⠛⠛⠫⢳⢦⣤⣴⣏⣀⣀⣀⡀⠀⠀⠀⢸⠇⠀⠀⢸⣿⣥⡤⢶⠻⠁⠀⠀⠀⠀⠀⠀⠀⢣⡘⠂⠊⡡⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠰⠂⠈⢝⢕⡄⡀⠀⠀⠀⢀⡠⣼⠟⠉⠀⠙⠛⠛⠉⠛⠛⠻⠛⣷⡤⡤⢟⠏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠷⠒⠛⠓⠲⠝⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣾⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⢻⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⣀⣿⣿⣿⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⡿⠛⠁⠀⠀ ⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿ ⠀⢀⣿⣿⢳⣿⣿⣿⣿⣿⡜⣿⣿⡄⢠⣿⣿⠃⣿⣿⣿⣿⣿⣿⠀⣿⣿ ⠀⣸⣿⡏⣿⣿⣿⣿⣿⣿⣷⠹⣿⣷⣾⣿⠏⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿ ⢠⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿ ⠈⠛⢋⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠛⠛⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⣿⡿ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⠀⠀⠀ ⠀⠀⠛⠛⢻⣿⣿⢻⣿⣿⠛⠛⠛⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣼⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠙⠋⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠈⠛⠋⠀⠀⠀