Purple Guy Dot Art

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠠⠤⠤⠄⠒⠀⠉⠉⠐⠢⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠊⠉⠀⣀⣀⢤⡤⠤⠀⠒⠂⠤⢄⡀⠀⠀⠈⠑⣄⠀⠀⠀ ⠀⠀⢀⠔⠁⢀⠤⠂⠉⡞⠁⠀⠈⠒⠄⠀⠀⠀⠀⠀⠉⠒⠤⣀⠈⢢⠀⠀ ⠀⢀⠎⠀⡠⠊⠀⠀⠸⡀⠀⠀⠀⠀⡜⠒⠒⠒⠀⠠⠤⢀⡀⠀⠑⣤⠀⠀ ⠀⡜⠀⡰⠁⠀⡠⠔⢋⣈⠲⠤⠴⠮⠄⠤⠤⠤⠤⠤⠤⠄⢈⣒⣄⠘⠀⠀ ⠀⠹⣠⠁⣠⡮⠔⠈⠁⠀⠀⠀⣀⠠⠤⠤⠀⠐⠒⠒⠒⠀⠈⠉⠉⠙⢇⠀ ⠀⠀⢹⡾⠉⠀⠀⣀⠤⠒⢉⡁⠀⠀⠀⢀⠏⠉⠉⠀⠀⠉⠉⠁⠢⡀⠸⠀ ⠀⡠⠋⣀⠤⢒⠩⠒⠈⠁⠀⠘⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡆ ⡴⠕⢻⠀⠞⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⡇ ⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠑⠠⠄⠠⠄⠂⠁⠀⠀⠀⢠ ⠀⠀⠀⠸⡑⠤⠤⠀⢀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⡎ ⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢊⠕⠁⡰⠁ ⠀⠀⠀⠀⠘⡆⣤⠀⣀⣀⣀⣀⣀⣀⡀⠠⠤⠄⠒⠊⢁⡠⠜⠁⠀⡰⠁⠀ ⠀⠀⠀⠀⠀⢱⠀⠉⠒⠂⠬⠦⠀⠀⠀⠀⠤⠼⠒⠊⠉⠀⠀⢀⡜⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⢒⠈⡏⠁⠀⠀⠀⢹⣱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠢⣧⣀⠀⠀⠀⡼⡉⣆⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⠴⡀⠀⠀⠀⠀⠀⠀⠑⠤⢀⡀⠀⠀⠀⠀ ⡀⠀⡠⠔⠈⠀⠀⢡⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠁⠂⢄⠀ ⡇⢇⠀⠀⠀⠀⠀⡸⡀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢀⡎⠀ ⢇⠀⠳⣤⣀⣤⠶⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⣾⠋⠀⠀ ⠘⡀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣚⠃⠀⠀⠀ ⠀⠱⡀⠀⠀⠑⢌⡶⢤⣠⢤⣒⠒⠶⠛⣾⠝⠁⠀⠀⢀⡀ ⠀⠀⠈⠐⠠⢀⠀⠈⠀⠓⠀⠐⠒⠂⠉⠀⠀⢀⠠⠂⠁⠀ ⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⣀⣀⣀⣀⠤⢲⡊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠤⢀⣠⡄⠒⠉⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠔⠘⡟⠑⠤⢀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⢹⣋⣀⣠⡀⠀⠈⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⢀⡟⢉⣉⢹⣆⣀⣀⣀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⣀⣴⣟⣻⣦⣧⣿⣋⣉⣙⣛⡿⣶⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣟⠉⣉⣉⣙⣿⣿⣿⣿⣿⠿⠛⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠟⠛⠛⠻⢿⡿⢿⡟⠉⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⢸⡇⠸⣷⣀⣠⣴⣾⣿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣄⣀⣴⣿⠁⠀⠙⠉⢉⡽⠛⣅⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡛⠉⠁⣀⣠⠤⢶⠋⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⢻⠋⠉⢹⡀⢀⣀⣧⣴⣿⡿⠋⠀⠀⠀⠀⠀⢀⣠⣤⡤⡀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠛⠛⠉⠉⣉⣨⡿⣿⣶⣾⡷⠶⠶⠒⠛⠋⣿⣿⠻⣗⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⠟⠛⠛⢻⡟⢯⣁⣠⣿⢻⣿⣇⠀⠀⠀⠀⠀⠁⠀⠀⠹⣦⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⡟⠈⠀⠀⠀⠘⣧⠘⣿⣿⣧⣾⠇⠉⠀⠀⠀⠀⣴⣶⠀⠀⠀⠘⣧ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢠⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⣿⣿⠏⢀⣤⠤⠶⢚⣋⣿⡇⠀⠀⠀⠀⠸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠈⠀⠹⣆⠀⠀⠀⠀⠀⠀⠈⣿⠉⠀⠈⣷⠂⠛⠉⠁⢸⣇⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠘⡇⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠻⢦⣀⣰⠏⢻⡄⠀⢀⣠⠾ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣳⣶⣆⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢿⠀⠀⠀⡛⠻⠶⣽⣁⡀⢸⣷⠺⡏⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣍⠉⠻⣟⠀⠀⢹⡇⠀⠀⠀⠀⢸⡇⡀⠾⢥⣤⡤⠄⠈⣿⠀⣿⠀⢻⠀⢀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣿⣿⣧⣤⡿⠤⣄⠀⣿⢦⡄⠀⠀⢸⡿⢧⣤⠀⠀⠀⠀⠀⢹⣷⣿⣀⣼⣿⣟

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⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⠤⠐⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⢀⣞⢉⣫⣀⣀⡀⢙⡆⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣴⠛⢚⣿⣷⣶⡶⠿⣿⡇⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠙⣟⣿⠁⢀⣠⡾⡇⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⣴⠏⠈⢋⡩⢫⣼⠇⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡱⠄⠲⠊⣙⣠⣾⠟⠀⠀⠀⢀⣀⡀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣝⡯⠭⣭⡥⠟⡷⣾⠒⠂⠉⠹⠏⢷⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠇⠁⠀⠹⡸⣿⣷⠏⠃⠀⣀⣴⠀⠈⢣ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠃⢦⠀⠀⠀⠈⢻⠋⠰⡍⠍⠒⣿⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢧⠀⠀⠀⣿⠀⠀⢡⡀⢠⢿⠀⠀⢀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣄⡀⠘⡆⠀⠀⢸⠀⢀⠒⠭⢍⡈⡖⡎⠁ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣷⣈⡇⡀⢳⣀⠀⠈⣷⣉⠈⠉⠀⣧⡇⣸⣴

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢐⡶⠟⠁⣆⠀⡆⠈⠉⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠋⠀⢀⣴⣾⣾⣤⣤⣀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠆⣰⠿⠋⠁⠀⠀⡈⠙⠳⠦⡇⠀⠀⠀⠀⠀⠀⠀ ⡠⢲⣏⠐⡀⠈⡅⣠⠖⢂⠀⡈⠈⠢⣀⠀⡅⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠿⠀⣇⠀⢋⣡⢤⠾⠀⠹⣤⣠⠄⠁⡇⠀⠀⠀⠀⠀⠀⠀ ⠢⣀⠀⠀⠀⠀⠸⡀⢀⣀⠀⣀⠤⡖⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⢄⠐⠠⠔⠋⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⠈⢩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⣴⡉⣘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣤⡶⠾⢛⣿⠋⠉⠙⠛⠿⠷⠶⢶⡶⠂⠀⠀ ⠀⠀⠀⠀⡾⠟⠋⠁⡀⠀⢸⣷⠀⠀⠀⠀⠠⠀⠀⠀⢣⠀⠀⠀ ⠀⠀⠀⢠⠳⢆⡆⠀⠀⠀⢸⣿⠀⢨⠭⠭⠶⠆⠀⠃⠸⡀⠀⠀ ⠀⠀⠀⡈⠀⠀⡇⠀⠈⠀⢸⣿⡄⢌⠀⠀⢠⠀⢸⠀⠃⣧⠀⠀ ⠀⠀⢠⠁⠆⠀⡇⠀⠀⠀⢸⣿⡇⠈⠢⠠⠚⠀⡈⢠⢰⢸⡀⠀ ⠀⠀⡆⠸⠀⠀⡇⠀⠀⠀⣾⣿⡇⢸⠀⠀⠀⠸⣷⠀⠆⠄⣧⠀ ⠀⢸⠃⠄⡐⣼⢹⠀⡄⠀⣿⣿⡇⠸⠀⠀⠀⢰⠈⡄⠸⣸⢇⠀ ⢀⠏⠀⠈⢰⠇⠘⡀⠀⠰⣿⡿⠁⢰⠀⠀⢠⠋⡄⡇⠀⠰⢸⠀ ⣾⠀⠀⠀⣍⠀⡰⠁⢂⢂⢨⠇⢠⠉⠄⠠⠁⡐⢉⢏⠠⠀⠘⡄ ⠙⢗⠀⠀⠁⠡⣘⣬⣤⡥⠤⢴⣦⣴⣶⣷⣶⠗⠁⠀⢀⠠⠘⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠖⠒⠚⠉⠙⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠖⠒⠒⠒⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠴⠖⠒⠒⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⣀⡤⠴⢚⡷⠋⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⢤⣀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡞⠁⠀⠀⢀⡴⠋⠁⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⢻⡄⠀⠀⠀ ⠀⠀⠀⣰⠏⠀⠀⠀⡴⠋⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠤⠤⠤⢤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠳⣄⠀⡇⠀⠀⠀ ⠀⠀⢠⠏⠀⠀⢀⡞⠁⠀⠀⠀⠀⢀⣸⣷⡀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⢤⡀⠀⠀⠈⢿⡇⠀⠀⠀ ⠀⠀⡟⠀⠀⢠⡟⠀⠀⠀⢀⣤⠞⠋⠁⠀⣉⣳⣦⠤⠴⠾⠯⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣀⣀⣀⡉⠳⣄⠀⠈⡇⠀⠀⠀ ⠀⠀⢿⡀⠀⡞⠀⠀⢀⡴⠋⣀⡤⠖⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡤⠤⠬⠽⠿⠿⠷⢶⣷⠀⠀⠀ ⠀⠀⠈⢧⣸⠁⢀⣴⣿⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⠒⠚⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀ ⠀⠀⠀⠈⢿⣶⡿⠋⠁⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⢰⠖⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠲⢤⡀⠀⠀⢷⠀⠀ ⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⣀⡴⠞⠋⣁⣠⠤⠴⠶⡄⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢸⡄⠀ ⠀⠀⣠⠞⠁⠀⣀⡤⠖⢋⣡⠴⠚⠉⠁⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠈⡇⠀ ⠀⡴⢋⣠⣶⠛⠁⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣷⠀ ⡼⠟⠉⠀⢹⡀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢿⠀ ⠀⠀⠀⠀⠈⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⢸⡀ ⠀⠀⠀⠀⠀⢹⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇ ⠀⠀⠀⠀⠀⠀⢷⠙⠶⢤⣀⣀⣀⣀⣀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⣻⠀ ⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣫⠟⠁⢠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⣏⣠⠞⠁⠀⢀⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠖⠚⠉⠀⢀⡴⠟⠁⠀⠀⢀⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⠛⢿⣓⠒⠒⠶⠦⢤⡤⠤⠤⠤⠶⠒⠒⠚⠉⠉⠉⣇⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠈⠉⠓⠲⠤⢤⣹⣄⣀⣀⣀⣀⣀⣀⣀⣤⠤⠼⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⢤⣀⡀⠀⠀⠀⠀⣀⣀⣠⠤⠖⠋⠉⠀⠀⢸⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡉⠉⢹⡅⠀⠀⠀⠀⠀⠀⠀⠘⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⢛⣷⣤⣀⠀⠀⠀⠀⢀⡼⢻⡀⢸⡄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢾⠉⢲⢶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣲⣾⠟⠋⠁⡏⠀⠈⣧⠀⠈⠉⠉⠛⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠛⠁⠀⠀⢘⣷⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⣦⣶⣄⡀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⢀⣴⣿⣿⠟⠉⠉⠀⠀⠉⠙⠻⠿⣶⣤⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⡾⠟⠋⠀⠀⠀⠀⠀⠀⡰⣄⠀⠀⠀⠉⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⢺⡏⠉⠳⡄⠀⠈⢹⡀⠀⢀⡴⠙⣄⠀⠀⢰⠃⠈⠳⢄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠋⠀⢸⣽⡶⠀⢸⠀⠀⠀⣧⡾⠋⠀⠀⢸⡄⠈⣿⡄⠀⠀⠀⠉⠲⠤⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠿⠃⠀⣺⠀⠀⠀⢳⠀⣦⢤⣶⠟⠁⠀⠈⢿⢦⣤⣴⡶⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣄⠀⠀⠀⠀⠀⠈⠉⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠓⠦⠄⠀⠀⠀⠀⠀⠀⠀⢿⡀⠐⢶⢤⠤⠤⡤⢲⠉⣬⠗⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡄⠈⠛⠤⠥⠥⠚⠋⠀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣤⣀⣠⡤⠶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⢀⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢷⡀⣴⠊⠁⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣿⣿⣿⢀⣠⣾⣷⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡾⠿⠛⢹⣿⡏⠉⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⢿⣯⣿⠶⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⢖⣻⡿⠟⠛⠉⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⡈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⠁⠀⠀⠀⡰⠁⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⢠⠃⢹⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⢢⢆⠀⡆⠠⠚⠀⡄⠀⠀⢸⣿⡇⠀⠘⣏⣩⣉⣙⣲⣲⣾⠀⠀⡸⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⠈⠏⢦⡇⠀⠀⢠⠇⠀⠀⢸⣿⣧⠀⠀⡝⠉⠀⠀⠀⠀⡇⠀⠀⡇⠀⡄⢹⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠈⡇⠀⠀⢸⠀⢸⠀⢸⣿⣿⠀⠰⡇⠀⠀⠀⠀⢸⡇⠀⢀⡇⠀⢣⠀⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⢰⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢸⣿⣿⡀⠀⠙⢦⠀⠀⢀⡼⠃⠀⣸⠀⡄⠸⡀⢹⡆⠀⠀⠀ ⠀⠀⠀⠀⢀⠇⠀⡎⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⣿⣿⣿⡇⠀⡄⠀⠓⠊⠁⠀⠀⣀⣿⠀⢱⠀⣧⠘⣷⠀⠀⠀ ⠀⠀⠀⠀⣼⠀⢠⠃⠀⠀⠀⣳⠀⠀⢸⠀⠀⢠⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⣿⢹⠀⠈⡇⠸⡄⣻⡇⠀⠀ ⠀⠀⠀⢠⡳⠀⣾⠀⢠⠀⣿⢿⠀⠀⠘⠂⠀⢺⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⣹⠀⡇⠀⠸⡀⠁⣿⡇⠀⠀ ⠀⠀⠀⣜⠇⠀⡇⣠⠃⣼⠏⢸⡀⠀⡇⠀⠀⣼⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⢀⡇⠀⢳⠀⠀⢷⣠⠛⡇⠀⠀ ⠀⠀⣰⡏⠀⠀⡰⠁⢰⡹⠀⠀⡇⠀⠘⠀⢠⣿⣿⣿⣿⠃⠀⢠⠃⠀⠀⠀⠀⡎⢣⠀⢸⠀⠀⠀⢹⠀⣇⠀⠀ ⠀⢠⡟⠀⠀⠀⠁⢀⣷⠃⠀⠀⣷⡀⠠⡄⠀⠻⣿⡿⠃⠀⢠⣿⠀⠀⠀⢀⠞⠀⠘⣦⡸⣇⡀⠀⠈⠑⢇⠀⠀ ⠀⣮⠊⠀⠀⠀⠀⢨⠇⠀⠀⣰⠋⠘⢦⡈⢆⠀⣼⡧⠀⠀⡎⠀⡰⠀⢠⠏⠀⣠⠞⠁⢹⡉⠑⢤⡀⠀⢸⡄⠀ ⠀⣽⡶⣄⠀⠀⠀⣿⠑⣄⠀⢣⡀⢦⡀⠱⠈⠃⢸⡇⢀⠈⠀⢠⠃⡰⠋⠀⠸⣽⣠⠞⠁⠉⠀⠀⠉⠠⠖⠃⠀ ⠀⠘⠹⣄⠀⠀⠀⠁⠀⠈⠳⣄⣷⣶⣷⣶⡖⠒⠚⢓⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⢀⣠⠔⠁⠉⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⢉⡀⣤⠤⠭⠥⢉⠲⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡴⠈⢃⣈⡹⠠⢄⣀⡀⠑⣼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣘⢴⣿⣵⣶⣶⢶⣾⣿⣟⣓⠺⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢻⠿⠛⢳⡄⣾⠁⠀⠀⠈⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢠⡇⠙⠦⢤⣤⠶⢿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡻⠶⠖⠋⠀⠀⠀⠀⣀⠔⡵⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠳⡒⠒⠒⠒⠀⢉⡰⠒⡑⠀ ⠀⠀⢀⠄⡄⠀⡔⠁⠀⠀⠀⠀⠀⠑⢌⡉⠀⠀⠉⢁⡠⠊⠀⠀ ⠀⣀⠈⡄⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣲⡀⢹⣣⠀⠀⠀ ⠀⢏⢢⡈⡄⠡⣘⠀⡄⠀⠤⠤⠀⠀⠀⠀⣼⣼⣗⣸⢹⠀⠀⠀ ⡀⢈⠢⢙⡾⠚⠉⠀⢀⠂⠔⠁⠀⡠⠔⣺⣏⠰⣿⣧⠘⢧⠀⠀ ⠁⠂⠠⠉⠀⠀⠀⠀⠀⡬⣀⢔⣪⠴⡱⠊⠀⢀⣹⠀⡄⠈⠳⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠓⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠓⠲⢤⣄⠀⠀⠀⠀ ⠀⣰⠀⢀⣠⠔⠊⠁⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠉⠙⡆⠀ ⠘⣿⠸⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⣿⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢀⡟⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⣀⠀⠀⣀⣴⡟⠁⠀ ⠀⣿⠀⠀⠙⢷⣇⣀⣀⣀⣤⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⠟⠁⠁⠀⠀ ⠀⠈⡇⠀⠀⠀⠉⠍⣍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠃⠀⠀⠀⠀ ⠀⠀⢹⠀⠀⠀⠀⠀⠘⣗⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⣅⡴⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⡀⠀⠀⠀⠀⠈⠣⡈⢳⡦⢄⣀⣀⣀⣀⠤⠤⠤⠶⢶⣲⠿⣥⣏⡽⠋⠁⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠓⢤⣀⠀⠀⠀⠀⠈⠻⢭⣙⡓⢦⠋⠹⠛⠛⠋⠉⢉⣀⡤⠞⠋⠀⠀⠀⠀⠀⢀⣠⠞⠃ ⠀⠀⠀⠀⠀⠀⠀⠓⠦⣄⡀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠓⠛⠉⠉⠀⠀⠀⠀⠀⠀⢀⡠⠴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢲⠢⠤⠤⠤⠤⠤⠤⠖⠊⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠧⣀⡀⠀⠀⣀⣠⠤⠚⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢉⣽⣯⣿⣆⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡴⠊⠁⢘⡏⡋⠈⠓⠦⣄⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢸⡇⠐⠀⠀⠀⠀⠉⠟⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠓⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣀⡀⠀⠀⠀ ⠀⢠⡄⠀⠀⢀⣤⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣶⠀ ⢰⢸⠁⣶⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢸⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢸⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⡀⢀⣼⠃⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣤⣄⣀⣀⣠⣴⡿⣏⠀⠀ ⠀⢹⡆⠀⠀⠙⢿⣾⣄⣀⣀⣀⣠⣤⣴⡿⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⢿⡿⠋⠁⠀⠀⠀ ⠀⠘⣷⠀⠀⠀⠀⠙⠛⡛⣛⠛⠛⠛⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠷⠀⠀⠀⠀⠀ ⠀⠀⠹⡄⠀⠀⠀⠀⠀⠁⠹⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢩⡾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠹⣎⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣞⡯⣷⣴⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠉⣿⡢⠤⣤⣤⣠⣤⣤⠤⢤⠐⠒⠚⠛⢟⣻⡿⠳⣶⣇⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣍⠑⠒⢶⣴⠟⠹⠶⠾⠒⠒⠊⠉⠉⠁⣀⣠⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠧⠤⣀⣀⣠⠤⠤⠤⠶⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣶⠦⠤⠤⢤⣀⣀⣀⣠⠤⠶⠛⠉⢈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠚⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠓⠶⢤⣤⣤⣶⣶⡋⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⡴⢿⣿⣾⡿⣄⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⡴⠋⠉⠀⢘⣷⠁⠀⠀⠙⠲⣤⣀⠀⢻⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⢸⣿⠀⠆⠀⠀⠀⠀⠈⠛⢿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣽⣿⣽⣟⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣷⣿⣻⠿⢿⣻⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣀⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⠿⠿⠿⠿⠿⢷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣀⣀⡀⣀⣀⣀⣨⣿⣿⡿⣶⣶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⢁⣿⣿⣿⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣻⣿⢿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠈⠉⢹⣿⣻⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣿⠀⠀⢸⣿⣟⣿⣽⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⣿⣿⣤⣤⣼⣯⣿⣯⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣿⢿⣾⢿⡿⣟⣯⣷⣿⣻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣿⣿⣿⠀⠀⠀⠀⢀⣶⣶⣾⣿⣿⣿⢿⣻⣿⢯⣿⡿⣿⣻⣽⣟⣿⡇ ⢰⣶⣶⣖⣀⣰⣶⣶⣿⣿⡿⣷⣶⣶⣶⣶⣶⣾⡿⣯⣿⢷⣿⣻⡏⢹⣿⣿⡿⣽⣿⣟⣯⣿ ⠸⠿⠿⣿⣿⣿⡏⠿⠿⠀⣿⣿⣷⣿⣏⣿⣹⣾⣿⣿⣹⣿⠉⠉⠁⢸⣿⣿⣿⡿⣷⣿⡿⣷ ⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⢿⣟⣷⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣯⣿⣟⣯⣷⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣟⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣳⣿⣟⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣷⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣷⡿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣾⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣷⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣯⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣾⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣟⣷⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣿⣿⣻⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠻⠯⠿⠟⠾⠿⠽⠇⠀⠀

➖🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪 ⬜⬛🟪⬜⬛🟪 🟪🟪🟪🟪🟪🟪 🟪⬛⬛⬛⬛🟪🟪🟪 ➖🟪⬛⬛🟪🟪🟪🟪 ➖➖➖➖🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪🟪🟪 ➖➖➖➖🟪🟪🟪🟪 ➖➖🟪🟪🟪🟪🟪🟪 ➖➖➖➖🟪🟪🟪🟪 ➖➖➖➖🟪🟪🟪🟪 ➖➖➖➖🟪➖➖🟪 ➖➖➖➖🟪➖➖🟪 ➖➖➖➖🟪➖➖🟪

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

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⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬜⬜ ⬜⬛🟨🟨🟨⬛⬜⬛⬛⬛⬛⬛⬛⬛⬜⬛🟨🟨🟨⬛⬜ ⬛🟨🏽🏽🏽🟨⬛⬛⬛⬛⬛⬛⬛⬛⬛🟨🏽🏽🏽🟨⬛ ⬛🟨🏽🏽🏽🟨⬛🟨🟨🟨🟨🟨🟨🟨⬛🟨🏽🏽🏽🟨⬛ ⬛🟨🏽🏽🏽⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🏽🏽🏽🟨⬛ ⬜⬛🟨🟨⬛🟨⬛⬛⬛⬛🟨⬛⬛⬛⬛🟨⬛🟨🟨⬛⬜ ⬜⬜⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛⬜⬜ ⬜⬜⬜⬜⬛🟨🟨⬛⬛🟨🟨🟨⬛⬛🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬛🟨🟨⬛⬛⬛⬛🟨⬛⬛⬛⬛🟨🟨⬛⬜⬜⬜ ⬜⬜⬛🟨🟨🟨⬛⬛⬜⬛🟨⬛⬜⬛⬛🟨🟨🟨⬛⬜⬜ ⬜⬜⬛🟨🟨🟨⬛⬛⬛⬛⬛⬛⬛⬛⬛🟨🟨🟨⬛⬜⬜ ⬜⬜⬛🟨🟨⬛🟨🟨🟨⬛⬛⬛🟨🟨🟨⬛🟨🟨⬛⬜⬜ ⬜⬜⬜⬛🟨⬛🟨🟨🟨🟨⬛🟨🟨🟨🟨⬛🟨⬛⬜⬜⬜ ⬜⬜⬜⬜⬛⬛🟨🟨🟨🟨⬛🟨🟨🟨🟨⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟨⬛⬛⬛⬛⬛⬛⬛🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟨🟨⬜⬛⬜⬛⬜🟨🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⣠⣼⣿⣿⣿⠿⠿⢯⡿⠿⢤⡀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡝⠀⠀⠀⠈⠸⠗⠽⣼⣿⣿⣿⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣷⣧⣤⡀⢰⣷⣻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⣿⣿⣿⡝⣴⣿⣿⣿⣯⣍⠀⠈⡌⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠣⣺⣗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣝⢻⡿⠟⣻⡟⠋⠉⢋⡟⣷⠎⣄⢁⠊⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⡀⣿⡧⠀⡴⡾⠰⠁⢙⣦⣭⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⣄⣿⣿⣾⣆⣤⣖⣠⣾⡗⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣠⣶⣝⣿⣿⣿⣿⡛⠑⢩⣿⡿⠓⠛⠉⣁⢎⣮⣰⣿⣏⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡓⣿⣿⣿⠀⠀⣀⣷⢿⣿⣿⣿⠩⢙⣯⣗⣎⣭⣲⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣯⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡶⢻⢿⣿⣿⣿⣿⣩⠀⠄⠰⠍⢢⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠁⠈⠙⢻⣋⣹⠐⠀⣿⣿⣿⣿⣷⣖⠁⡀⠀⠓⢣⠀⠀⠀ ⠀⣠⠾⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⡿⠿⠁⠀⠀⠀⠹⢁⠑⠀⡘⡿⣿⣿⣿⣯⢂⣄⡀⠘⣳⡆⠀⠀ ⣼⣷⣏⣠⣌⣨⣿⣿⣿⣿⡟⠋⢠⣿⣿⣿⣿⣿⣿⣿⣷⣮⠁⠀⠀⠀⠀⢣⣈⠁⢃⡹⣿⣿⣿⣿⣖⠎⠁⠀⠁⡸⡀⠀ ⣿⣿⡿⣿⣯⡿⢵⣿⣿⣿⡶⢆⣾⣿⣿⣿⣿⣿⣿⠛⠛⠋⠀⠀⠀⠀⠀⠀⣗⠑⠈⠁⡹⣿⠻⣿⣿⣷⣵⣦⣤⠊⠁⠀ ⠹⣿⣯⣽⣿⣾⣷⡟⠙⠻⢯⠋⣿⣿⣿⣿⣿⣿⣾⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠨⢔⠅⣿⡀⠈⣻⣿⣿⡇⠑⠫⠑⡄ ⠀⠈⠻⢿⣿⣿⡟⠻⢦⣤⠃⢸⣿⣿⣿⣿⣿⣿⣿⡋⠊⠀⠀⠀⠀⠀⠀⠀⠈⣞⣣⢴⢺⣿⡇⢠⣿⣿⣿⠂⠂⠀⠃⢡ ⠀⠀⠀⢸⣿⡿⢿⣤⣤⡜⠀⠘⣿⣿⣿⣿⣿⣿⡿⡋⡷⡂⢀⠀⠀⠀⡀⠀⠀⣗⣿⣓⣾⣿⠇⢸⣿⣿⣿⣧⠠⠀⢲⣸ ⠀⠀⠀⠈⠻⢿⣦⣖⡺⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣵⠐⡈⠀⠀⠀⠀⠀⠀⣷⣝⣄⣿⣿⠀⢸⣿⣿⣷⠊⠀⠀⣢⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡟⡻⢹⣿⠇⠀⠘⣿⣿⣷⣷⣥⣄⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣫⡟⠊⠁⠀⠀⠀⠀⠀⠀⢀⢗⣽⣾⣯⡄⠀⢀⣾⠿⡟⢿⢟⣋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣧⣤⣤⣄⣠⡤⣴⣿⣿⣿⣿⣿⣷⣿⣟⢁⢸⠁⠤⣣⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣤⢦⠜⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠈⠀⠨⢪⢁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣷⡟⡠⡷⠁⢂⠧⢹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡻⢿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣇⣽⡇⣠⣾⢹⡎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠥⠓⠊⠝⣻⣿⠀⠀⣿⣿⣿⣿⡿⡿⡿⠟⢑⣾⠀⠈⠛⠓⠚⠛⠚⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡊⢀⠀⠀⠐⣿⠀⠀⣿⣿⣿⡿⠉⢠⢁⡀⠼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⢒⡐⣄⣴⡿⠀⠀⢹⣿⣿⣿⢀⠀⠀⢀⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢾⠿⢿⡾⠁⠀⠀⠈⢿⣿⣿⣿⠷⠿⡾⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣇⣠⣴⡎⠀⠀⠀⠀⢸⣿⣿⣿⣾⡅⣌⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢏⠉⠉⢹⢷⠀⠀⠀⠀⢸⣿⣿⣿⡏⠁⠀⠪⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠧⠀⠀⣺⠀⠀⠀⠀⢸⣿⣿⣿⢄⠀⠄⠌⡉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡃⠀⡀⠀⢠⣿⠀⠀⠀⠀⢸⣿⣿⣿⡄⠗⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⢞⡔⠀⠺⡇⠀⠀⠀⠀⢸⣿⣿⣿⣧⡂⢀⠴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠇⠀⢠⣃⠇⠀⠀⠀⠀⠀⣿⣿⣿⡟⣏⢀⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣶⣿⣿⣿⣿⣗⠒⢿⣷⡄⠀⠀⠀⣠⣾⣿⣿⣷⠚⢳⣾⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣥⡾⣿⠟⣫⣾⣿⣿⣄⣤⣿⣿⠀⠀⡼⣾⣿⣩⣿⣿⣷⣹⣿⡿⢮⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣾⣯⣸⣿⣿⡿⢉⣀⢹⣿⣿⣧⣾⣿⣯⣽⣿⣿⣿⠇⠉⣿⣧⣦⣱⡵⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⡺⢼⣿⣿⣗⡊⣘⣹⡛⢋⣿⣿⣟⠪⢻⣿⣿⣿⠂⠧⣽⣿⣧⠁⠀⣟⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠛⠓⠒⠒⠚⠁⠈⠛⠻⠧⠤⠛⠛⠿⠯⠿⠬⠞⠛⠻⠭⠝⠓⠂⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣚⣋⣉⡻⠶⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠞⠁⠀⠀⠛⡆⠹⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠑⡶⠁⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⠁⢠⡀⠀⠀⠀⠀⡸⢸⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠚⠫⢟⣮⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡦⢌⣓⡤⣹⡆⠀⠀⣰⢣⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠛⠛⠲⣄⣸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣡⠔⠒⠒⠮⡹⠚⢯⣉⣵⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠁⢀⡤⠚⠉⠙⡍⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡰⠁⠀⠀⠀⠀⠈⢆⠀⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣤⢀⠀⢹⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣲⠁⠀⠀⠀⠀⢀⣀⣸⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡔⠀⠀⢀⣽⣿⠁⠀⡇⠸⡄⠀⠀⠀⠀⠀⠀⠀⣸⣅⡇⡏⠑⠄⠀⠀⠀⠀⣸⢣⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠸⡿⠛⠀⣾⣉⣶⣃⠀⠀⠀⠀⠀⠀⡿⣿⠿⣆⡼⡄⠀⠀⠀⠀⡴⠁⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⣀⡤⠋⠀⣁⣨⣇⠤⠤⠤⠤⠤⣾⣿⣭⣀⠈⠉⠢⢄⣀⡞⠁⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⢉⣉⣥⣔⠾⠛⠉⠁⠀⠀⠀⠀⠀⠰⣿⣟⡏⠻⣕⠢⢤⣀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠙⢶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⡜⠀⠀⡴⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣠⡼⣤⡤⣞⠀⠀⠀⠀⠀⠘⣆⣀⣀⡇⠀⣸⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢰⣞⡕⠉⠁⠈⠙⢷⡤⠃⠐⢤⣠⠾⠓⠒⠫⣝⢅⠀⡀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢸⡜⢀⡴⠚⠉⠒⢜⣆⡀⠀⢠⢇⡠⠤⠤⣀⠈⢟⡏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡈⠉⢿⣃⣜⠰⣶⣰⠀⡸⠯⠕⠒⠿⡏⠀⡄⠠⠈⣆⢸⡏⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠉⠻⣺⣄⣈⡠⠞⠃⢀⣀⠀⠀⠙⢦⡙⠞⠀⣾⣿⠁⠀⢰⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢠⠆⠀⣡⠂⣀⠴⠊⠁⠀⠉⠙⢲⠠⣍⠑⠚⠊⠉⠉⠀⡏⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⢀⠇⠀⡞⠁⠀⣹⠂⠀⠀⠀⠀⢀⡞⠀⠈⢳⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⢤⢻⠁⠀⡀⡝⠋⠉⠉⠓⠢⡎⠀⢀⠀⠀⠇⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡈⣞⠲⠼⢻⣀⣀⠀⠀⢀⡼⠁⠀⣼⣆⠀⠐⢠⡶⣯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢌⠪⣝⡒⠼⣀⣉⣹⡳⠿⠒⢓⡖⠉⣓⡶⣗⣟⣷⡟⢀⡤⠤⢤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣈⠉⠷⢬⣵⡞⠛⠒⡟⠛⠛⣯⠟⠛⣷⣯⢠⠿⢷⡿⠋⠀⠀⠀⠈⠛⣶⣤⡈⡹⢦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠒⠛⠛⠒⢾⡿⠦⣀⠀⠀⠹⠤⣨⠧⠒⠟⢧⣀⠞⠁⠘⠃⣠⢿⡁⠀⠀⠀⠀⠀⠀⠈⢳⡈⠳⡄⠙⣆⠀⠀ ⠀⠀⠀⠀⣀⣠⣴⡏⠀⢷⡄⠀⠀⠀⠀⣿⠦⠈⠓⡤⢄⣀⣄⣀⣀⣀⣀⣀⣠⠤⠴⡞⠓⠚⣇⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠘⡄⢸⡄⠀ ⠀⢀⡴⢛⡽⠚⡿⢷⣀⡼⠃⢠⡦⠀⠀⡿⠒⠁⠸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠇⢰⠷⡀ ⠀⡾⢡⡏⠀⣠⣷⡀⡞⠀⠀⢯⠉⢦⣴⠁⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠳⣄⡀⠀⠀⠀⢠⠏⣠⠾⢚⡟⠀⢧ ⢸⠁⡏⡇⠀⢧⣈⢻⣇⠀⠀⠀⢷⡽⠁⠀⠀⠀⣠⢧⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠸⡅⠀⠀⠀⣠⣼⠛⠒⠶⣾⠛⠚⣡⡴⠋⠀⠀⢸ ⡾⠀⠣⠽⡦⠒⠁⠀⢈⡷⠦⢤⡞⠀⠀⠀⣀⠔⠁⣸⠀⠀⠀⣠⢴⡏⠳⢄⡀⠀⣀⣠⠗⠀⠠⣶⣾⠍⢠⠒⡆⢹⠎⠉⠁⠀⠀⡇⠀⢸ ⢷⠀⠀⠀⠘⠦⠟⠉⠉⠀⠀⡼⠀⠀⠀⠈⠁⠀⠀⠘⠉⠉⠉⠁⠀⠀⠀⠀⠹⢏⠀⠀⠐⠁⠀⠁⠺⠶⢋⣀⠓⠻⡄⠀⠀⠀⠈⠀⠀⡎ ⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢳⡀⠀⠀⠀⢀⠼⠀

⠀⠀⠀⢀⠠⠀⡀⠀⠀⠀⢠⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡐⢱⠈⡗⡜⡀⠀⢀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠱⣜⠂⢚⣡⠠⣴⣿⡏⠙⠛⣿⡂⠀⡔⡨⡭⡑⠄ ⠀⠀⠀⠀⠉⡝⠁⣤⣿⢦⡁⠀⢘⣛⠻⢢⡄⢆⣈⡿⠸ ⠀⠀⠀⠀⣰⠃⡼⠿⠏⠀⡇⢰⣿⠉⠳⡄⣿⠒⠀⠂⠁ ⠀⠀⠀⣴⠋⣢⣑⣤⣠⣴⣇⣿⡉⠀⢀⡇⡿⠀⠀⠀⠀ ⠀⠀⢸⠹⠶⡟⠁⠀⠀⠉⠒⠛⠙⠻⣍⠔⢺⠀⠀⠀⠀ ⠀⠀⠸⡆⢰⡟⠷⣤⣀⠀⠀⠀⠀⠀⣸⢦⢾⠀⠀⠀⠀ ⢀⢔⢢⠙⢾⣹⣦⣀⣉⠈⡛⠛⠛⢫⠇⢀⡞⠀⠀⠀⠀ ⢸⠁⡠⠥⣆⠈⣹⣿⠿⢿⣿⣷⡿⠷⠖⠋⠀⠀⠀⠀⠀ ⢸⣿⣁⣠⡞⡏⣾⣿⣷⣿⣿⣿⣿⡇⠂⢄⠀⠀⠀⠀⠀ ⠀⠙⠛⣿⠋⢠⠿⠟⠋⡉⡈⠓⠛⡌⡄⠀⢆⠀⠀⠀⠀ ⠀⠀⢸⠁⠀⠏⠀⠀⠘⠿⠟⠀⠀⠸⣸⢀⣀⠀⠀⠀⠀ ⠀⠀⢸⡄⠀⡆⠀⠀⢰⣿⣷⠀⠀⢠⡏⠉⣻⣷⠀⠀⠀ ⠀⠀⠈⢻⣧⡘⠦⣀⣀⠉⣁⣠⠴⣫⢷⡾⠉⢹⠀⠀⠀ ⠀⠀⠀⢰⠉⠛⠷⣶⠼⢭⡥⠖⠋⠀⡌⢧⣠⠏⠀⠀⠀ ⠀⠀⠀⡸⠤⠤⠤⠬⡄⢸⠤⠤⠤⠤⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣅⡀⠀⠀⢀⡷⣇⠀⠀⠀⣀⣸⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣿⣥⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⡤⠤⣤⣤⣀⡀⠀⠀⢿⣍⡛⠶⣤⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣤⠶⢛⣩⡿⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀ ⠀⣴⠟⡩⠤⠔⠦⠤⢄⣈⠙⠳⣤⠈⠻⣬⡛⠲⠽⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠯⠖⣛⣽⠟⠁⣴⠞⠋⣁⡠⠤⠴⠦⠤⢍⠻⣦⠀ ⣸⢇⡎⠀⠀⠀⠀⠀⠀⠈⠱⡆⣹⠀⠀⠀⣹⣷⢦⣤⣀⡉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⢉⣀⣤⡴⣾⣏⠀⠀⠀⡇⢰⠊⠁⠀⠀⠀⠀⠀⠀⢱⡘⣇ ⢻⡘⡆⠀⠀⠀⠀⠀⠀⠀⢰⢁⣿⢷⣤⣾⠟⠁⠀⠈⠉⠙⠛⠳⠶⠶⠶⠶⠤⠤⠤⠴⠶⠶⠶⠶⠚⠛⠋⠉⠁⠀⠈⠻⣷⣤⡾⣿⡘⡆⠀⠀⠀⠀⠀⠀⠀⢰⢃⡟ ⠘⣧⠙⣄⠀⠀⠀⠀⠀⢠⢃⣼⢃⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡘⣧⡘⡄⠀⠀⠀⠀⠀⣠⠋⣼⠃ ⠀⠘⢷⣌⠳⢄⡀⢀⠔⢡⡾⢣⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡜⢷⡌⠢⡀⢀⡠⠞⣡⡾⠃⠀ ⠀⠀⠀⠙⠷⣤⣉⢁⣴⢿⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⡿⣦⡈⣉⣤⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠋⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠈⠙⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⡿⠿⠛⠛⠛⠛⠛⠿⢿⣿⣿⡄⠀⠀⠀⠀⣰⣿⣿⡿⠿⠛⠛⠛⠛⠛⠿⢿⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠀⠀⣤⣶⣾⣿⣿⣷⣦⡈⠙⢿⡄⠀⠀⢰⡿⠋⢡⣴⣾⣿⣿⣿⣶⣄⠀⠀⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠀⠈⠹⣿⡄⠀⠁⠀⠀⠈⠀⢠⣿⠏⠁⠀⠀⠈⢻⣿⡆⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⢿⣿⡗⢲⠒⣶⡒⡖⣿⣧⠀⠀⠀⠀⠀⠀⣾⣿⢲⢒⣖⠒⡖⢺⣿⡇⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣈⠢⠭⢔⣡⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣌⡢⠭⠔⣁⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⠿⠟⠋⢀⣀⣀⣀⣀⣀⣀⡀⠙⠻⠿⢿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠾⠟⠛⢻⣿⡟⠋⠉⠉⣻⣿⣿⣿⣿⣿⣿⡟⠛⠻⠶⢶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠈⠻⠷⣶⣶⣾⣿⣿⣿⣭⣶⠿⠛⠁⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⣀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢹⡻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⠏⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠻⣯⠙⠿⣶⣦⣤⣴⠶⠾⠛⠛⠉⠉⠉⠉⠉⠙⠛⠛⠷⠶⣶⣶⣶⣶⠿⠋⣽⠏⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠈⠳⣤⣻⣰⠒⠒⠲⡄⡠⠖⠒⠲⡄⢠⠖⠒⠲⢄⢠⠖⠒⠒⢆⣏⣠⠞⠁⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠈⠙⠛⠶⣤⣤⣷⣧⣀⣀⣀⣇⣼⢀⣀⣀⣼⣾⣤⣴⠶⠛⠋⠁⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠶⣶⣶⣶⣶⡶⠶⣶⣶⣶⣶⠶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➖➖🟪🟪 🟧🟪🟪🟪🟪 🟨🟨🟨🟨🟨🟨 🟨⬜🔳🟨⬜🔳 🟨🟨🟨🟨🟨🟫🟫 🟨🟨🟨🟨🟨🟨🟨 ➖⬜➖⬜🟫⬜🏻🟦 ➖⬜➖➖🟫🏻🏻🟦🟦 🟨🟨🟨🟨🟨🟨🟨🟦🟦 🟨🟨🟨🟨🟨🟨➖🏻🏻 🟧🟧🟧🟧🟧➖➖🟫🟫 was that the bite of '87???

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠉⠉⠉⠉⠉⠉⠉⠉⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠒⠒⠒⠒⠒⠒⠒⠒⠓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⠀⢠⡤⢄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡠⢤⡄⠀⣀⣀⣀⡀⠀ ⡰⠕⠀⠐⠂⠍⡆⠙⣭⣛⡀⠤⠤⠤⠤⠤⠤⠤⠄⢐⣛⣭⠋⢰⡩⠐⠂⠐⠫⢆ ⢣⢄⠀⠀⢀⢠⢛⠞⠁⠀⠉⠉⠁⠒⠒⠒⠒⠈⠉⠉⠀⠈⠳⡛⡄⡀⠀⠀⡠⡜ ⠈⠳⣕⠀⣰⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣝⣆⠀⣪⠞⠀ ⠀⠀⠀⠉⢠⠇⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠸⡄⠉⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⢠⡾⠿⠿⠿⣿⣄⠀⠀⣠⣿⠿⠿⠿⢷⡀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠈⢀⣶⠛⠛⢦⠙⠀⠐⠋⡶⠛⠛⣷⡀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠃⠀⠀⠸⣷⡈⡃⣸⠇⠀⠀⠸⣇⢹⠁⣾⠇⠀⠀⠘⢇⠀⠀⠀⠀ ⠀⠀⠀⢸⠁⠀⠀⠀⢀⣩⠿⢿⡭⠤⢶⣶⣤⣭⡿⠿⣉⣀⠀⠀⠀⠈⡆⠀⠀⠀ ⠀⠀⠀⠘⢆⡀⢀⡞⠁⠀⠀⠀⠙⠛⠿⠿⠛⠋⠀⠀⠀⠈⢳⡀⠀⡰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡄⢷⣀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⡾⢠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⠈⠫⣹⡒⠚⢉⠉⢉⡉⠉⣉⠓⢒⣏⠝⠁⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⠙⠒⠛⠤⠼⠧⠤⠛⠒⠋⠁⣀⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣤⣀⣠⣄⣀⣠⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⢹⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⢀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⢧⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⢀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⡙⣼⣿⣧⡀⠀⠀⠀⠀⣸⠆⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⢦⣄⣤⣴⣿⣟⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢌⢿⣻⣝⢒⣶⠖⠋⢁⡴⠛⠀⠀⣀⡠⠤⠤⠤⠐⠒⠒⠒⠢⢽⣿⣶⣤⣤⣤⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠈⢻⣮⣋⣀⣠⣴⣿⣇⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢻⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣷⣶⣤⡀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⣴⣿⣿⣿⣿⣿⣷⡄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣾⣿⣿⣿⡿⢿⣿⣿⣷⠀⢠⣿⡋⢹⠛⣿⣶⠈⣉⣿⣇⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢿⡇⠀⣿⣿⡯⠟⠁⢿⣶⣿⢿⣿⣿⣧⠀⠘⠿⠿⠛⠀⢀⣿⣿⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢃⡿⠀⠀⣿⣿⡀⠀⠀⠀⠉⠁⣸⣟⣛⣿⣦⣄⣀⠀⢀⣴⣿⣿⠟⠀⠀⠈⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠛⢿⣿⣦⣄⣠⣴⣾⣿⣿⣿⣿⣿⡿⠻⠿⠿⣍⣁⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢉⡽⠟⠋⠁⠙⠛⠛⣿⠛⠋⠁⠀⠀⠀⠀⠈⠙⣦⠴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⢀⣀⡤⢞⣿⠙⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠞⢻⣿⠘⣷⣤⣤⣀⣀⣠⣤⣖⣫⣥⠾⢿⠿⣿⣿⡿⠶⠞⠋⠀⣷⣟⣠⢤⣤⡤⠤⠤⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⡴⣾⡋⠀⠀⠈⣿⣧⡉⠻⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⡁⠙⣷⣿⣿⡄⠀⠀⠈⢧⡀⠀ ⠀⠀⣀⡼⢠⣿⠀⠀⠀⣰⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣾⣟⣛⡛⠻⣿⣿⣿⣿⡆⠀⠀⠀⢇⠀ ⣠⢞⠿⣷⡘⠁⠀⠀⣰⣿⣿⣿⡿⣿⡿⠿⠷⢶⣶⣶⡶⠿⢿⣿⠟⠛⣉⣿⠿⠛⠋⠉⢹⣿⠛⣯⠻⣿⣿⣿⠀⠀⠀⠈⠆ ⠁⠋⠸⣿⣷⣄⣀⣴⣿⣿⣿⢏⣰⣿⠀⠀⠀⠀⢀⢉⣻⣿⠛⠙⢳⣾⣿⡧⠀⠀⢠⡀⣼⠇⠀⢹⣧⣿⣿⡿⠀⠀⠀⡰⠃ ⠀⠀⠀⢿⣿⣿⣿⣿⠿⣿⢧⡞⠘⢿⣄⢀⠀⠀⢻⣿⣿⣿⣇⣠⣾⠛⠛⠃⠀⠀⢀⣿⡏⠀⠀⠀⠘⣿⣿⡇⣠⠔⠋⠀⠀ ⠀⠀⠀⠈⢻⣿⣿⣿⣶⡟⢸⠁⠀⠀⠙⣿⡶⠀⠀⢉⣼⡟⠉⠉⠹⣷⡆⠀⠀⠀⣸⡿⠀⠀⠀⠀⢀⣿⠿⠋⠁⠀⠀⠀⠀ ⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠈⠉⠀⠀⠛⣏⠛⣛⡿⠋⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠉⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⠉⠉⠉⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⡀⠀⢰⡤⣀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⢴⠆⠀⠀⠀⠀ ⡐⡡⠐⠒⠠⡑⢢⠻⣒⠭⠆⢀⣀⣀⠀⠀⠀⠀⣀⣀⡀⠼⠅⡢⠋⠀⠀⣴⠀⠀ ⠇⡆⠀⠀⢀⠂⠖⡴⠊⠉⠒⠢⠤⠤⠀⠀⠀⠠⠤⠤⠔⠂⠉⠑⣌⣉⡩⢝⠀⠀ ⠈⠬⡢⠄⣡⢊⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠈⢞⣆⠀ ⠀⠀⠈⠉⠉⡏⠀⠡⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠀⠈⢧⣼⣿⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠙⢷⣦⡀⠀⠀⠀⠀⢠⣴⠟⠉⠀⠀⠀⠀⢸⠉⡎⡆ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣤⣤⣬⡷⡄⠀⠀⣰⣟⣥⣤⣄⡀⠀⠀⠀⢸⠀⡵⡘ ⠀⠀⠀⠀⠘⣆⠀⠀⢸⣿⣿⣿⣿⣿⠉⠀⠀⢱⣿⣿⣿⣿⣿⡆⠀⠀⡼⠀⠉⠀ ⠀⠀⠀⢀⡞⢁⣤⣄⣸⣻⣿⣿⣿⡿⠀⠀⠀⠘⣿⣿⣿⣿⡿⠀⠀⠀⠘⢦⠀⠀ ⠀⠀⠀⢸⠀⢹⠶⢚⠿⠛⠛⠋⢿⣟⣉⣹⣿⣿⣿⡯⠙⠛⠣⢤⡀⠀⠀⢸⡆⠀ ⠀⠀⠀⠘⢦⡀⠀⡇⠀⠀⠀⠀⠀⠈⠛⢻⠟⠋⠁⠀⠀⠀⠀⠀⢱⠀⣠⠞⠀⠀ ⠀⠀⠀⠀⠀⢹⠲⣇⠀⠐⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡄⠀⡼⢺⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡆⢸⡦⣀⠀⠀⠀⠀⣀⣸⣀⣀⠀⠀⠀⠉⡠⢾⠁⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⢃⣷⣿⣭⣹⣯⣩⣿⣦⣼⣯⣩⣿⣍⣽⣷⡏⢝⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢆⠣⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡯⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠒⠩⢏⡻⠛⣟⡻⠛⣏⡹⠙⠒⢡⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⣀⣀⣀⣀⣀⢤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢡⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⢆⣀⠜⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⢦⠤⣤⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠩⢋⠩⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡀⠅⡪⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡢⠅⡪⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠛⠚⠛⠚⠛⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀ ⠀⠀⣠⢋⡴⢂⢩⠭⣑⢦⠀⠀⠀⠀⠀⡴⣚⠉⣑⠢⣄⠙⣆⠀⠀ ⠀⡼⢣⡿⢠⠁⣸⣷⠈⣾⠆⠀⠀⠀⢸⢸⢠⣶⡀⠱⡘⣧⡈⢧⠀ ⢰⠃⣿⣧⠸⣄⣉⣉⢜⡞⠀⠀⠀⠀⠈⢾⢌⡛⠋⣠⢃⣿⡇⠸⡆ ⢸⠀⠹⣿⣷⣶⣴⠾⠋⠀⠀⠀⠀⠀⠀⠈⠳⣮⣭⣴⣾⣿⠇⠀⡇ ⠸⡄⠀⠀⠉⢉⣠⡤⣄⡀⠀⠀⠀⠀⢀⣀⡤⢤⣍⡉⠉⠀⠀⣼⠁ ⠀⠉⢳⠖⢚⠉⠀⡇⠀⠉⡗⠒⠒⠚⠹⠀⠀⢸⠀⠉⡟⢲⡏⠁⠀ ⠀⠀⠈⡇⢸⠀⠀⠇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⢸⠀⠀⠀ ⠀⠀⠀⡇⠈⡀⠀⢰⠀⠀⢀⠀⠀⠀⡇⠀⠀⡇⠀⢠⠀⣸⠀⠀⠀ ⠀⠀⠀⢷⠀⡇⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⠇⠀⢸⠀⡇⠀⠀⠀ ⠀⠀⠀⠸⣄⣰⠀⠀⡆⠀⢸⠀⠀⠀⠃⠀⢸⠀⠀⣇⣰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠓⠒⠧⠤⠬⠤⠤⠤⠤⠤⠼⠒⠚⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠛⠛⠟⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠿⠿⠛⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⠀⠀⠀⠀⢀⠀⠐⡄⠀⢀⡄⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⢱⡀⡇⣰⠏⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⢀⣿⣿⠄⢀⣀⣤⣤⣤⣛⣛⣋⣤⣤⣤⣄⠀⢿⣿⡇⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣤⣄⣴⣿⡿⡋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⡻⣿⣦⣀⣠⣤⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠛⠋⢈⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⡈⠻⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣀⠉⠉⠉⠛⢿⣿⣿⣿⡿⠛⠉⠉⠻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⢙⠉⡋⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⣿⣿⣿⣷⣄⡀⠀⠀⢀⣸⡿⠧⠀⠀⠀⣀⣠⣾⣿⣿⣿⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴ ⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣛⣿⣿⣿⣿⣿⣫⣶⣿⡟⠉⠁⠀⠉⠙⢿⣶⣮⡻⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇ ⠀⢻⣿⣦⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣧⣄⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣼⣿⠏⠀ ⠀⠈⢿⣿⣿⣄⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⢿⢿⢿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⡿⠿⠿⠿⠛⠛⠉⠀⠀⢀⣴⣿⣿⡟⠀⠀ ⠀⠀⠈⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠲⢩⡍⣽⠛⠛⣻⠍⣭⠱⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡆⠀⠈⠀⠙⠀⠀⠙⠀⠁⠀⢀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢹⣷⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣼⡟⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⢿⣧⡑⢿⢀⣦⠀⠀⣴⠀⡾⠜⣰⡿⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣦⣀⠀⠀⠈⠻⣿⣶⣦⣬⣤⣤⣥⣶⣶⣿⠟⠁⠀⠀⣀⣴⡿⢛⣽⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⣀⣴⣾⠟⣉⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣝⡻⢿⣶⣄⡀⠀⠀⠀⠀⠀⣀⣴⡾⠟⣉⣴⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠙⠻⣿⣿⣶⣬⣙⠻⢷⣦⣄⣀⠛⠛⠁⣴⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣶⣬⣉⠛⠿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⠀⢤⣴⣾⠿⠛⣁⣠⣍⡛⠻⢿⣿⣶⣦⣬⣉⡛⠻⠿⣿⣶⣶⡦⣀⣴⣿⠟⠀⠀⠀⠀⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⣄⠀⣤⣶⣶⣦⢿⣿⣿⣧⠀⣠⣶⣿⡿⠟⠛⠉⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣶⣶⣤⡄⢾⣿⣿⢃⣾⣿⣿⣿⣿⢨⣿⣿⡄⠀ ⠀⠀⠀⠀⣿⠟⠿⠏⠸⠿⠿⠿⠟⠘⢿⣿⣿⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠃⢸⣿⡟⠀⠛⠛⠛⠋⣁⠹⣿⠟⠀⠀ ⠀⠀⠀⠀⠈⠛⠚⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣿⡿⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠊⣡⠴⢦⣄⠑⣄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⢸⡅⠀⢸⣌⡧⢸⡄⠀⠀⣠⣤⣿⣿⡿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⡈⠳⢤⣤⠟⠁⡼⣀⣠⣤⣿⣿⡛⠛⠻⠿⣿⣿⣷⠀⠀⠀⣠⠖⢉⣉⣉⠓⢄⠀ ⠀⠀⠀⠀⠀⠙⠶⠤⠤⣶⡿⠛⠉⢸⣿⠿⠿⠷⠀⠀⠀⣤⣟⣳⢄⠀⢰⠃⡴⠉⠙⣽⣷⡈⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢠⣴⣿⡿⣿⣦⡀⠀⠀⠀⣉⣙⡛⠿⠳⣽⡄⠻⣄⡀⣸⡿⠁⡿ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢠⣿⣿⣷⡿⠀⢩⣧⠀⢠⡾⣿⠿⠿⣦⡀⢹⣿⠦⣈⣉⣉⡤⠞⠁ ⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⣿⠙⠛⠋⠀⠀⢸⡟⢀⣿⣿⡿⠀⠀⠈⣷⢸⣿⠀⠈⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡟⠋⠙⣆⠙⢷⣤⣀⣠⣦⣿⡃⢸⣛⠉⠀⠀⠀⢀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣧⠀⣴⣿⠟⠛⠉⠉⠙⠿⣿⣉⣹⣿⣷⣶⣦⣶⣾⠃⢀⣻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠈⠛⠛⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠙⢷⣄⡾⠹⢙⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⡆⠀⢠⣿⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣨⣼⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣄⢸⣿⡆⠈⠛⠿⣗⣶⠤⣤⣀⣀⣀⣀⣀⣠⣴⡟⠙⠛⢫⡇⠀⠀⠀⠀⠀⠀ ⠀⢠⠞⢛⢢⡈⠿⣿⣏⢻⣮⣤⣀⡀⠉⢉⡙⠒⠒⠛⠛⠛⢉⡿⠁⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀ ⢀⣯⠞⠁⠈⢧⢄⠈⠙⠛⢿⣿⣿⣿⣿⣶⣾⣷⣶⣦⣤⣴⣟⣁⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⡀⢠⡶⠛⠻⣧⠀⢀⣴⣾⣿⡟⠛⠛⣿⣿⣿⣿⣿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡏⠀⠀⣀⣿⢻⡏⢾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡗⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣶⣿⣿⣧⠟⠁⣿⣿⢿⣿⡿⣿⣿⢿⣿⡻⢿⡟⢧⡀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⠻⣿⡿⠁⠀⣰⡟⠿⠟⠋⠀⣀⣄⡀⠋⠻⠟⢻⡄⢳⡀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠃⠀⢰⡟⠀⠀⠀⠀⢸⣧⣾⣿⠄⠀⠀⠀⢻⡌⣷⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⠀⠀⠀⡿⠁⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠘⣷⢸⣄⠤⣄⣏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡀⠀⠀⣷⡀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⢀⣿⡏⠉⠉⣿⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣧⡆⡄⠹⣧⡀⠀⠀⠀⠘⢿⡿⠟⠀⠀⠀⢀⣾⢿⠀⢀⣶⠿⢾⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣦⡈⠳⢦⣤⣀⣀⡀⠀⣀⣠⣴⡾⢟⣡⡞⣿⣿⠇⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠛⠿⣿⣷⣦⣬⣉⣹⣛⣛⣉⣭⣥⠾⠛⠉⣇⠘⣧⠀⠀⣼⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠉⠛⢿⡟⠛⠛⣿⠟⠉⠀⠀⠀⠀⢻⠀⠙⠻⠾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣧⣄⣀⣀⣀⣀⣠⣧⠀⠀⣿⣀⣀⣀⣀⣀⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢸⣆⣾⠃⠀⠀⠀⠀⡀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⣄⣀⠀⠀⠀⠀⣀⣸⡿⣿⡀⡀⠀⠀⠐⣘⣤⣀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⠍⠩⡗⢆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡔⠁⠀⠀⢸⢸⠀⠀ ⠀⠀⠀⠀⠀⠤⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣄⣦⣰⠀⠀⣼⠆⠀⠀ ⠀⠀⠀⠀⠀⠠⠞⠉⠑⡤⠷⢄⠀⠀⠀⠀⠀⠀⠀⡰⡡⠂⠐⠻⠙⠬⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡀⠀⠀⣀⡈⠎⡆⠀⠀⠀⠀⠀⣰⣱⠁⠀⠀⢀⡇⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠀⠠⡿⢁⡔⡼⠀⠀⠀⢀⣾⣖⣠⠀⠀⠀⡐⡱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⠄⠠⢜⣁⡭⠇⠐⠒⠒⣿⣧⣄⠑⠠⠌⡔⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠓⡸⠋⠁⠀⠀⠀⠀⠈⠙⠂⠁⠫⡃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⣌⣀⠂⠀⠀⠣⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡘⠀⢰⠟⢉⣉⢳⠂⠐⡴⠛⠛⢛⣄⠀⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣃⠒⣿⡈⢤⡄⡹⠲⠴⡗⠉⠉⢂⡷⠂⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡅⠀⠈⠓⡀⢊⠠⠀⠤⣈⡢⠥⠾⠧⢠⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⣠⢁⡄⠁⣇⣀⣀⢀⠌⠈⢂⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣱⠦⢶⣀⠀⠀⠍⠀⣇⠈⢠⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢫⠪⢎⢜⡢⢼⢽⢭⡯⢼⡾⣿⣿⠔⠒⠒⣖⡂⢤⡀⠀⠀ ⠀⠀⠀⠀⣠⢴⠒⠒⠲⡗⢄⠈⠡⠼⠐⠚⠤⠊⢛⡰⡏⠀⠀⠀⠀⢫⠑⠌⢆⠀ ⠀⡠⡲⢿⢇⣈⠃⡄⠀⡯⠀⢎⠁⠃⠀⠀⠀⠉⢹⠀⠘⡀⠀⠀⠀⠀⡇⢸⢸⠆ ⠸⣱⠁⡜⢦⠁⠈⠌⡶⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⣢⢄⣀⡴⠵⣣⠏⢸ ⡆⠣⢦⢊⣈⡵⠂⡜⠀⢀⠔⢩⣀⣀⠤⠓⠤⣀⠤⠅⠀⡶⠏⠔⣈⡗⠈⠀⠀⢸ ⠣⠀⠀⠉⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠉⠒⠀⢃⠀⠀⢀⠆

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⠁⠀⠈⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⡿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣴⣿⣿⣾⣿⣷⣦⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣽⣿⡀⠀⢠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠉⢻⣿⣿⣿⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣥⣤⣶⣶⣿⣿⣿⣿⣦⣤⣤⣤⣾⣿⣿⣟⣉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⢿⣿⣿⣿⣿⣿⡿⠋⠋⠉⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⡿⠁⣠⣤⠙⢻⡏⠉⠀⠀⢠⡾⠄⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠛⠋⠁⠀⠳⠀⠀⣀⣤⡴⠚⠛⡏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣦⣤⣤⡤⠴⠚⢿⠋⠁⠀⠄⠀⢀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣤⣬⣧⣤⣴⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢛⣻⣋⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠉⠳⢦⣄⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣷⡍ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣾⣿⣿⣿⣿⣿⡿⢁

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟪🟪🟪🟪🟪🟪🟪🟪⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟪🟪🟪🟪🟪🟪🟪🟪⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟪🟪🟪🟪🟪🟪🟪🟪⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟨⬛⬜🟨🟨⬛⬜🟨⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟨⬛⬛🟨🟨⬛⬛🟨⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟨🟨🟨🟨⬛⬛🟨🟨🟨⬜⬜⬜⬜⬜⬜ ⬜🟨🟨🟨🟨🟨⬛⬛⬛⬛⬛⬛🟨🟨🟨🟨🟨⬜⬜ ⬜🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛🟨🟨🟨🟨🟨🟨⬜⬜ ⬜🟨🟨🟨🟨🟨🟪🟪🟨🟨🟪🟪🟨🟨🟨🟨🟨⬜⬜ ⬜🟨🟨🟨🟨🟨🟪🟪🟪🟪🟪🟪🟨🟨🟨🟨🟨⬜⬜ ⬜⬜⬜⬜⬜🟨🟪🟪🟨🟨🟪🟪🟨⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟨🟨🟨🟨⬛🟨🟨🟨⬜⬜⬜⬜⬜⬜ ⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜ ⬜⬜🟨🟨🟨🟨🟨🟨🟨⬛🟨⬜🟨🟨🟨🟨⬜⬜⬜ ⬜⬜🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜🟨🟨🟨🟨⬜⬜⬜ ⬜⬜🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜🟨🟨🟨🟨⬜⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⢀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣹⢮⣿⣶⣾⣿⣿⣿⢿⣻⣽⣦⣵⣘⡖⣥⣾⣽⣿⣿⢛⡁⠀⠀⠀⠀⠀⠀ ⢰⢣⣿⣿⣿⣿⣿⣿⠿⣩⢿⣿⣿⠿⣿⠿⢫⡜⡭⢛⡻⣿⠸⣿⢆⠀⠀⠀⠀⠀ ⢸⣳⢟⣿⣿⣿⣿⡏⢧⢳⡝⠋⠉⠁⠪⢷⡗⣮⢵⡋⠁⠀⡈⠻⣻⡃⠀⠀⠀⠀ ⠀⠙⠿⢿⣿⣿⡟⡼⢣⡉⠀⢀⡜⣧⢀⣢⢹⣵⡏⠀⠰⢦⡕⢇⣣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠟⡼⣱⢫⣅⠀⠀⢧⡻⢿⣵⣠⣿⣇⣀⣻⡹⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⡜⡹⠜⣯⣿⣴⡤⠀⡗⣿⣿⣿⣿⣿⣿⣿⣅⡁⠆⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⢨⠵⣩⢶⡋⣁⢠⡕⢲⠙⡦⢻⣿⣿⣿⣿⡟⠁⠐⠆⠑⠀⠀⠀⠀ ⠀⠀⠀⠀⢇⢣⢚⡱⠎⠶⣐⡩⣆⠳⡀⣲⡂⡹⠽⣏⠩⢠⠁⠢⠰⢆⠂⠀⠀⠀ ⠀⠀⠀⠀⠘⣆⢧⣿⠠⢇⠪⣭⢌⡔⡻⣰⠰⣑⢫⠆⡱⢀⣌⠡⣆⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⢈⣴⣌⡛⠖⠿⣴⢎⣴⠱⡦⠷⠭⠖⡼⢒⠫⢈⢅⣾⣳⢞⣤⡄⠀ ⢒⡮⡛⡽⡹⣟⡿⣿⣷⣼⣠⠌⠢⢄⠣⣀⠓⡊⠔⣐⣢⣵⣾⣿⢯⣝⠮⡽⠠⠀ ⡁⣞⢭⠳⡽⣞⢿⣻⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣛⢮⠳⡌⠃⠀ ⠰⡈⣮⢝⣣⠝⣎⡷⣫⣿⣿⣿⣿⣿⣿⣿⠻⣝⡹⢻⢿⣿⡙⣾⡹⣎⠷⠁⠀⠀ ⠀⠁⠜⡦⢃⡻⣌⣷⡷⣯⣟⡿⢿⣿⠿⣋⠳⢬⡑⢣⢊⠶⣹⣭⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⣹⣿⣭⢿⡷⣿⢛⠴⢍⡋⢄⠣⢆⣍⠣⢎⠸⣷⣿⣳⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⢈⣿⣿⣯⣿⣿⣷⣎⡚⡔⠌⡆⢓⡌⢦⡹⣬⣿⣿⣳⡟⣾⢽⡶⣂⠀ ⠀⠀⠀⠀⣼⣯⡷⣯⣷⣟⣿⣾⣳⡜⡱⡘⢢⠜⣦⣿⣿⢯⣷⡯⣽⢩⠟⡘⠧⣉ ⠀⠀⠀⢰⣯⣷⣿⢿⣷⣿⣻⢷⡿⣽⡆⢑⠢⣝⣾⣿⣯⣿⢽⠝⡡⢃⠎⡱⠃⠄ ⠀⠀⠀⣸⣷⣻⢾⡿⣟⡷⢯⠿⣽⣷⣻⠛⠛⠋⠉⠻⣿⣾⠁⡊⠐⢂⠒⠀⠑⡈ ⠀⠀⠀⢹⡞⢏⢣⠂⡏⠜⡡⠒⠌⠳⠯⠀⠀⠀⠀⠀⠈⠁⠧⣁⠌⣀⠠⠄⠀⠀ ⠀⠀⠀⠈⣗⠈⢂⠐⠠⠊⠄⠃⠌⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠓⠄⢈⡀⠐⢈⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣽⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⣁⣠⣤⣄⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⠀⣴⠏⠁⠀⡏⠹⣆⠈⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⠀⢿⡇⠀⠀⢸⣶⡏⠀⡜⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⣸⣿⣿⣅⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠙⣄⠀⠛⠲⠴⠾⠋⠀⣰⢃⣠⣤⠶⡾⠿⣿⡍⠉⠉⠙⠻⠿⣿⣿⣿⠁⠀⠀⠀⣠⠞⠉⣠⣤⣤⡀⠙⢦⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣤⣤⣴⣻⡟⠋⠁⢸⣿⠿⠿⢿⣿⠂⠀⠀⠀⢠⣼⡛⠷⣤⠀⠀⢰⠋⢠⡞⠉⠙⢏⣛⣧⠀⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⣠⣼⣾⣶⣶⣄⠀⠀⠀⠀⠀⠘⠛⠿⢿⣶⡟⣄⢺⠀⠸⣆⠀⠀⠈⣿⣿⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⢠⣿⣿⡟⣿⠙⠛⣿⣷⠀⠀⠀⢀⣴⣾⣶⣤⡈⠁⠈⢿⣷⡀⠘⠣⣤⣼⠟⠁⢠⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⢠⣿⣻⣿⣿⡿⠀⠀⠀⣿⠀⠀⢰⣟⠻⡟⠛⠛⢿⣦⠀⠈⣿⠛⠲⣤⣄⣠⣤⠖⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⣸⠉⠛⠛⠛⠀⠀⠀⢀⣿⠀⢠⣿⣿⣿⠏⠀⠀⠀⢹⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⠳⣦⡀⠻⣧⡄⠀⠀⠀⢀⣀⣿⡏⠀⡼⠿⠛⠋⠀⠀⠀⠀⢨⡷⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⡃⠀⠀⣨⣇⣠⣬⣽⣿⣦⣼⣿⣿⣿⣤⣤⣿⣶⡄⠀⠀⠀⠀⢀⣾⠇⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⢿⣷⣀⣸⣿⡿⠛⠁⠀⠀⠀⠀⠙⠻⢿⣦⣠⣾⣿⠿⢿⣿⣷⡿⠾⠏⢀⣀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡇⠈⠛⠛⢫⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠙⢷⣦⢰⡟⠹⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠺⣧⠀⠀⠀⣸⣿⣷⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣿⣇⠙⠻⣿⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣷⣾⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠹⣿⣆⣀⡿⣿⡆⠀⠀⠉⠙⠯⣉⣓⣲⡶⠦⠤⢤⣀⣀⣀⣤⣴⣾⡿⠀⠈⠉⢡⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡴⠋⠉⠳⣄⠙⢿⣿⣿⡌⢿⣾⣥⣀⣀⠀⠀⠉⠉⠉⠒⠒⠒⠋⠉⠉⠉⢉⣿⠁⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢃⡴⠊⠀⠻⣀⠀⠈⠙⠿⢾⣝⣿⣿⣷⣷⣶⣶⣭⣑⣦⣆⣀⣀⣀⢀⣴⡿⠃⠀⣀⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡏⠀⠀⠀⣀⣿⣙⣆⠀⠀⠀⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣯⣶⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣧⢀⣰⠟⠁⠀⠉⢻⣄⢀⣴⢾⣿⣿⣿⣏⠉⠉⣉⣉⣹⣻⣿⣿⣯⣉⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⡿⣿⠏⠀⠀⠀⣀⣼⠟⣿⠃⢾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⣿⣷⣴⣴⣾⣿⣟⣴⠟⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⡄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣿⡿⣟⣿⡿⠃⠀⢀⣿⣽⣧⣾⡿⠋⠉⠉⠉⠈⢛⢿⣦⣽⣿⡄⠙⣄⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣩⣿⠛⠀⠀⢀⣼⠏⠙⠛⠁⠀⠀⣠⠴⢶⣤⠀⠀⠉⠉⠀⢹⡄⠘⣆⠀⠀⠐⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⣿⣤⣶⣿⡇⠀⠀⠀⠀⠀⣿⡀⢿⡀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⢹⣧⠈⣇⢀⣀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⣿⢰⠟⠒⠤⣿⢿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⡿⠟⠀⠀⠀⣸⡆⢻⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣦⡇⣆⠀⢻⣧⡀⠀⠀⠀⠀⠀⠹⣿⡿⠟⠁⠀⠀⠀⠀⣠⣿⢽⡀⠀⣠⣾⠿⠛⢾⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣼⣦⡄⠙⢷⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⢡⣾⢛⣿⣿⠅⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣷⣦⣄⡈⠙⠛⠿⠶⣶⣦⣴⡶⠾⠟⠛⣩⣤⡾⠿⡁⠘⣿⠋⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠉⠛⠻⣿⣿⣷⣶⣤⣴⣦⣤⣤⣤⣴⡾⠟⠋⠁⠀⠀⣧⠀⠹⣧⣀⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠙⠀⠀⠀⠀⠀⠉⠻⣿⡏⠉⠉⠙⣿⠟⠁⠀⠀⠀⠀⠀⠀⢹⠀⠀⠉⠻⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠀⠀⠀⠀⠀⠀⢈⣧⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣄⠀⣶⠟⠉⠉⠉⠉⠉⠉⠉⠉⠙⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣴⡟⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⢿⣧⡀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠒⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⣤⠀⠀⠀⠀⠀ ⠀⣸⣿⡄⠀⠀⠀⠎⡆⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⢀⣼⡟⠀⠀⠀⠀⠀ ⠀⠐⠽⡿⡢⣤⠄⢊⠇⠀⣀⠀⠀⠠⠤⠤⣣⣥⣚⣻⡵⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠮⡤⣶⣿⠖⠉⠀⠀⠀⠀⠀⠀⠀⠙⢏⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠁⣤⣴⣶⣦⡄⠀⣴⣾⣿⣿⣷⡄⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⢸⣿⣿⢻⣻⣷⣤⡏⢹⣽⡆⢸⣿⠘⢣⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠳⠁⢸⣏⠀⠈⠉⣹⣿⣷⣄⣀⣠⡾⠟⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢣⠀⠈⠙⡻⠖⠛⠿⢿⠿⠋⠉⠁⠒⢄⣤⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢳⣶⠎⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⢼⢿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠴⢻⡟⣦⣤⣀⣤⣴⡮⠟⠶⠶⠾⠗⠉⣾⣡⢤⡄⠤⢄⠀⠀ ⠀⢀⢺⡇⠀⢸⣿⣦⡉⠉⠉⠀⠀⠀⠀⠀⢀⣠⣾⡷⢮⣿⣿⡄⠀⢱⠀ ⠪⢻⣌⠀⣠⣿⡿⢻⠟⠛⠒⠶⣟⡿⣏⣩⡟⠉⡉⣹⠙⣞⣿⡇⠀⠀⡃ ⠀⠸⣿⣿⡿⣿⡝⠸⣄⡄⠐⣾⣿⣦⣾⠛⠁⠀⣱⠇⠀⠙⣿⣇⠔⠊⠀ ⠐⠠⠼⠿⠿⠧⠇⠀⠈⢏⠬⡴⠋⠀⠈⠳⠤⠤⠏⠠⠤⠔⠋⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠶⠶⠖⠛⠓⠓⠶⠶⠶⢶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀ ⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⣠⡶⢛⣉⣩⣉⣛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢛⣉⣍⣉⡛⢶⣄⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀ ⠀⠀⢠⡿⠀⠀⠀⢀⣤⡾⢫⠔⠉⠀⠀⠀⠈⠑⠮⣙⣓⣦⠀⠀⠀⠀⠀⠀⣴⣞⣋⡵⠊⠁⠀⠀⠀⠉⠢⡙⢷⣤⡀⠀⠀⠀⢻⡆⠀⠀ ⠀⠀⣾⠃⠀⠀⠀⠹⢷⣶⣁⠀⠀⠀⠀⠀⠀⣀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀⠀⠀⠀⠀⠀⠀⣈⣳⡾⠟⠀⠀⠀⠘⣷⠀⠀ ⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⠓⠒⠛⠛⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡛⠛⠓⠒⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⢹⣇⠀ ⢀⣿⠁⠀⣠⠖⠋⠉⠙⢦⡀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⢀⡴⠛⠉⠙⠲⣄⠀⠀⣿⡄ ⢸⡇⠀⡼⠁⠀⠀⠀⠀⠀⣷⠀⠸⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⡇⠀⣼⠁⠀⠀⠀⠀⠈⢣⠀⢸⡇ ⣿⡇⠠⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⠀⠀⢿⠀⠀⠀⠀⠀⠀⢸⡆⠀⣷ ⢸⣇⠀⢧⡀⠀⠀⠀⢀⡼⠃⠀⠀⢷⠀⠀⠀⢸⠀⠀⣀⣠⡤⠤⠤⠤⠤⢤⣄⣀⠀⠀⡏⠀⠀⠀⡼⠀⠀⠘⢧⡀⠀⠀⠀⠀⡸⠁⢸⡇ ⠈⢿⡄⠈⠙⠒⠶⠒⠋⠀⠀⢀⣀⣸⣤⣤⡤⠬⠧⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠼⠧⢤⣤⣤⣇⣀⡀⠀⠀⠙⠓⠲⠖⠋⠁⢠⡿⠁ ⠀⠈⢿⣦⡀⠀⠀⠀⠀⢀⡾⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⢷⡄⠀⠀⠀⠀⢀⣴⡿⠁⠀ ⠀⠀⠀⠙⢿⣦⡀⠀⠀⢸⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢸⡇⠀⠀⠀⣰⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⢿⡀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⣾⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠈⢷⡄⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢀⡾⠃⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠻⣦⡈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢁⣴⠟⠁⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠈⠙⢶⣤⣈⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⢁⣤⡶⠛⠁⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠈⠙⠛⠶⢦⣬⣉⣉⣙⣛⣉⣩⣥⡤⠶⠛⠋⠁⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣀⡤⠤⠭⠭⠭⠭⠥⢤⣀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⡀⠀⠙⢦⣀⠀⠀⠀⠀⣀⡤⠊⠀⢀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣤⣌⣉⣉⣉⣉⣥⣤⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠛⠛⠉⠉⠛⠛⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀ ⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀ ⠀⢠⡇⠀⠀⢀⡴⡫⠭⠭⢓⢤⣀⠀⠀⠀⠀⢀⡤⡚⠭⠭⢝⢦⡀⠀⠀⢸⡄⠀ ⠀⣼⠀⠀⠸⢭⣊⡀⠀⢀⣀⠽⠊⠀⠀⠀⠀⠓⠯⣀⡀⠀⠀⣑⡯⠇⠀⠀⣧⠀ ⢰⠇⢀⡤⠤⢄⠀⢹⠉⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⡏⠀⡠⠤⢤⡀⠘⡆ ⣾⢠⠃⠀⠀⠀⡇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠀⠘⡄⢷ ⢿⠘⡄⠀⠀⡠⠃⠈⡄⠀⢠⠀⣀⠠⠤⠤⠄⣀⠀⡄⠀⢀⠃⠘⢄⠀⠀⢀⠇⡼ ⠘⣦⠈⠉⠉⠀⣠⠔⠓⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠚⠲⣤⠀⠉⠉⠁⣴⠃ ⠀⠈⠳⢦⠀⠀⡏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⠀⠀⡠⠞⠁⠀ ⠀⠀⠀⠈⢳⡄⠱⡜⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢣⠎⢀⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣆⠘⠦⣑⠢⣀⡀⠀⠀⠀⠀⢀⣀⠄⣊⠴⠃⣠⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠉⠒⠮⠭⣤⣦⠭⠵⠒⠋⠁⢀⡼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠪⣉⠉⠉⢉⠕⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⠦⠭⠭⠶⢶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣠⣅⡧⠤⠴⠶⠾⢿⣟⠃⠀⢉⣽⠛⠻⣯⡉⠀⢠⣿⣤⣤⣤⣿⣿⣷⣶⣶⣾⣿⣿⣧⣶⣾⣿⣿⣿⣿⣯⣴⣷⣾⣷⣬⣿⣷⡞⠉⠰⣿⠇ ⠀⠹⣿⣷⠖⢲⣶⣶⢿⣿⢃⣤⣌⣿⣦⡀⢼⣧⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣉⣹⣏⡉⠻⣿⣿⡆⠂⠐⠀ ⠀⠀⣾⣿⢿⡿⢠⡥⠀⠻⠋⠀⠙⢿⠂⢹⣾⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡴⠋⠩⠘⠉⠙⠳⣄⠈⣿⡄⠀⢀ ⢠⣿⣿⠁⢸⣿⡟⠀⠀⠀⠀⠀⠀⢸⡇⣾⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠹⣆⢹⣷⠀⠾ ⠀⠀⠀⠀⠀⢻⡻⣄⠀⠀⠀⠀⢠⡟⣰⣿⣿⣿⠏⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣛⢿⣟⣦⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⡿⠀⠀ ⠀⠁⠀⠀⠀⠀⢳⣍⠳⣤⣞⣰⠏⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣿⣿⣯⡳⣄⣤⠀⠀⢀⡼⠁⣿⣧⡄⢀ ⠀⠀⠲⠀⠀⠀⠀⠙⠿⠿⣽⣥⣾⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢻⣿⣿⣿⣮⡉⠳⣶⣋⣠⣾⣿⣿⡄⣸ ⠀⠀⠈⠁⠀⠀⠰⣶⣶⡾⠋⢡⣿⠟⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠹⠋⠻⢷⣿⣿⠟⣋⠙⣿⣯⣤⠋⣿ ⠈⠀⠊⠀⠀⠀⠀⠹⠋⠀⠀⣸⡏⣐⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠰⢖⡀⢹⣿⣷⡀⢼⣿⠟⣿⠀⠘ ⢀⣀⡀⠀⠀⠀⠀⠀⣰⡆⡀⣿⠙⠛⠋⠉⠙⠻⣿⠇⠀⠀⠀⠀⠀⢾⣿⠿⠛⠛⠛⠻⢿⡶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠺⡏⠀⣉⢠⣀ ⠘⣿⣿⡷⠂⠀⠀⠀⠈⠠⠀⣿⣦⠀⢀⣴⣿⣷⣮⣁⠀⠀⠀⠀⠀⠀⣠⣴⠶⢦⠶⡷⠀⠀⠀⠀⠀⠠⡄⠀⠀⡄⢸⣿⣿⣿⣾⣧⡀⣽⣾⣽ ⠀⠋⠁⠀⠀⢰⣷⣦⡀⠀⠀⣼⣿⢀⣼⣿⣿⠛⢻⣟⢻⡍⠉⢀⣴⣿⣿⣷⠞⢿⣟⢲⣿⣆⠀⠀⠀⠙⠻⣤⣼⣶⣻⣿⣿⣿⢿⣿⣿⠈⢻⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⠗⠀⢹⣧⠚⣿⣿⠻⣆⠈⠛⠿⡇⠀⢸⣿⣿⣿⣿⡄⠈⠛⠟⢋⣿⠀⠀⠀⠀⠀⢿⣿⣟⠻⣿⣿⣿⣾⣟⣿⣷⡄⢿ ⠀⠀⠀⠈⠀⠀⠛⠋⠁⠀⠀⢸⣿⣷⡜⣿⣶⣿⣷⣶⣾⠃⠀⠀⢿⣿⣿⣿⣿⣷⣶⣶⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⣆⣸⣿⣿⣷⡛⢻⣿⡇⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠿⠿⣿⣿⣿⣿⣷⣶⣶⡄⠻⢿⣿⣿⡿⣿⣟⠋⠀⠀⠀⠀⢀⣤⠘⣿⣿⣿⣿⡟⣿⣿⣿⡇⣀⣴⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢸⡿⠉⠀⠀⠀⡿⠿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠠⡼⠃⠀⣿⣿⣿⢿⢤⠸⣿⣛⣇⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢀⠀⠀⠀⠀⣿⣿⣿⡏⣼⣦⢿⠉⣵⣿⣽⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⡷⠀⠀⠀⢀⣴⢿⣿⣿⣷⣿⡟⢸⡟⠻⠟⠸⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢄⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣸⣿⣠⣤⠶⠛⣻⡟⠀⠀⣿⣿⠀⣤⣗⠀⣤⢌⠀ ⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠘⣯⡀⠀⣀⠀⠀⠀⠀⢀⣯⡴⢿⣿⣾⠿⢿⣤⢼⡿⠁⠀⠀⣼⣷⣦⠉⣿⠀⢛⡈⠀ ⠀⠀⠀⠀⠀⠛⠛⡂⠀⠁⠀⠀⠀⣈⣿⡟⠲⣖⠚⠉⣿⣽⣟⡓⠒⠶⣶⡶⠚⣻⣯⣤⣾⣿⡀⣠⡼⠟⠈⠀⠀⠀⣼⣏⣿⡟⠀⣿⠀⣼⡅⠠ ⠀⠀⠀⠀⡄⠀⠀⠈⠀⢠⣠⣶⣿⡟⣿⣷⠒⢹⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⢿⡏⢀⡨⠟⠉⠀⠀⡄⠀⢠⣴⣿⣿⣭⣇⠀⣿⣶⡿⢿⠿ ⠀⠀⠀⠀⠀⠀⠀⠆⠀⣾⣿⠿⣿⠿⣿⣟⣷⣴⡋⠉⠙⣿⣿⡿⠋⠉⢻⣿⣅⣠⣤⠟⠋⠁⠀⠀⠀⢰⡇⣠⣾⠋⠛⢿⣿⣿⣿⠟⠞⠁⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠒⠀⣿⠿⠻⠈⠙⠛⢛⡛⠻⠿⠶⠶⠛⠛⠉⠉⠀⠀⠀⠀⠀⢲⡀⢈⣿⠋⠉⠀⣦⣦⢻⣿⡇⠀⠀⠀⠀⠀ ⢴⠃⠀⠀⠀⠀⠀⠀⣾⡃⠀⠀⠀⣴⣿⣷⣧⡐⠎⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣸⡷⠿⡿⠀⠀⠀⣿⣇⠘⢿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃⣄⣀⣼⣿⣿⣽⠟⠿⢶⣶⣶⣤⣤⣤⠤⣤⣦⣤⣤⣄⣀⣴⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠉⠉⠀⣀⣗⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⠍⠩⡗⢆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡔⠁⠀⠀⢸⢸⠀⠀ ⠀⠀⠀⠀⠀⠤⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣄⣦⣲⠀⠀⣸⠆⠀⠀ ⠀⠀⠀⠀⠀⢠⠞⠉⠑⡤⠷⠄⠀⠀⠀⠀⠀⠀⠀⡰⡡⠂⠐⠻⠛⠤⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡀⠀⠁⣀⡀⠎⡆⠀⠀⠀⠀⠀⣰⣱⠀⠀⠀⢀⡇⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠀⠠⡿⢁⡔⡼⠀⠀⠀⢀⣶⣶⣠⠀⠀⠀⡐⡱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⠄⠠⢜⣁⠥⠇⠐⠒⠒⣿⣧⣄⠑⠠⠌⡔⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠓⡸⠋⠁⠀⠀⠀⠀⠈⠙⠂⠁⠫⡃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⣌⣀⠂⠀⠀⠣⠀⠀⠀⡀⠑⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡘⠀⢰⠟⢉⣉⢳⠂⠐⡴⠛⠛⢛⣄⠀⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣃⠒⣿⡈⢤⡄⡹⠂⠴⡗⠉⠉⢂⡷⠂⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡅⠀⢈⠓⡀⢊⠠⠀⠤⣈⡢⠥⠾⠧⢠⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⣠⢁⡄⠁⣗⣀⣀⢀⠌⠈⢂⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣱⠦⢶⣀⠀⠀⠍⠀⣇⠈⢠⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢫⠪⢎⢜⡢⢼⢽⢭⡯⢬⡾⣿⣿⠔⠒⠒⣖⡂⢤⡀⠀⠀ ⠀⠀⠀⠀⣠⢴⠒⠒⠲⡗⢄⠀⠡⠬⠐⠚⠤⠊⢛⡰⡏⠀⠀⠀⠀⢫⠑⠌⢆⠀ ⠀⡠⡲⢾⢇⣈⠃⡀⠀⡯⠀⢌⠁⠁⠀⠀⠀⠉⢹⠀⠘⡀⠀⠀⠀⠀⡇⢸⢸⠆ ⠸⣱⠁⡜⢦⠁⠈⠌⡶⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⣢⢄⣀⡴⠵⣃⠏⢸ ⡆⠣⢦⢊⣈⡵⠂⡌⠀⢀⠔⢩⣀⣀⠤⠗⠄⣀⠤⠅⠀⡶⠏⠔⣈⡗⠈⠀⠀⢸ ⠣⠀⠀⠉⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⠀⠉⠒⠀⢃⠀⠀⢀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠿⠿⠿⠿⠿⠿⠿⠿⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⣶⣶⣤⡀⠀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣄⠀⢀⣤⣶⣶⣤⣀⠀ ⣸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣇ ⢸⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⢿⣿⣿⡿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠙⠿⢿⠿⣿⣿⣿⣶⣿⣿⣷⣾⣿⣿⣷⣾⣿⣿⣶⣿⣿⣿⠿⡿⠿⠋⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⡟⠋⣭⠙⢿⣿⣿⡿⠋⣭⠙⢻⣿⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⣄⣀⣾⡟⠋⠙⢻⣷⣀⣠⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⡿⠛⠉⠉⠙⠛⢿⡿⠛⠛⠉⠉⠛⠻⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⣷⣤⣤⣤⣤⣤⣾⣷⣤⣄⣀⣀⣤⣴⣿⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣉⣿⡇⣸⣇⢸⣿⣉⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠷⣶⡶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠒⣚⠉⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢉⡤⠖⠊⠉⠈⡇⢸⠀⠀⠀⠀⠀⠀⠀ ⣤⠶⣒⠒⠒⠒⠲⠦⠤⠤⢤⣀⣀⠀⢀⣀⣀⣈⣷⣄⠙⢦⡀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⠴⠊⠁⠀⠀⠀⠀⠀⠇⠘⡇⠀⠀⠀⠀⠀⠀ ⣇⠀⡏⠉⠉⠉⠉⠒⠂⠤⣀⣠⣾⣯⣭⡤⠤⣄⣀⠉⠳⡄⢳⠶⠒⠋⠉⠉⠻⡇⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⢸⠀⠸⡀⠀⠀⠀⠀⠀⠀⠋⠉⠳⡄⢸⠀⠀⣠⡼⠛⣳⡇⠈⠀⠀⠀⠀⠀⠀⢻⡈⢇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠘⡇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⣼⣠⣾⢃⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡈⢆⠀⠀⠀⠀⠀⠀⠀⡜⠀⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡄⠈⡄⠀⠀⠀⠀⠀⠀⠀⠸⢀⡿⠁⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠳⡌⠣⡀⠀⠀⠀⠀⣠⠇⢀⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⡀⠹⡀⠀⠀⠀⠀⠀⢠⠇⡼⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠀⠈⠦⣙⣦⡈⠉⠉⠉⠉⠀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⡀⠱⣄⠀⠤⠤⠔⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠳⣄⣀⣀⣀⡤⠴⠚⡟⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⣆⠀⠀⠀⠀⢠⠞⣀⠤⣴⡶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⢞⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⢀⡀⠈⢇⠀⠀⠀⠏⡴⢁⣔⡥⠒⠉⠉⠉⢳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠋⢀⡾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠀⠀⣧⣼⠉⠉⠙⠪⡀⠀⠀⠀⡇⢸⡎⠀⠀⠀⢾⣧⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠙⢶⣏⠛⠀⠀⠀⠀⠈⢆⠀⠀⢧⠘⡄⠀⠀⠀⠈⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠴⠯⠤⠒⣺⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠹⣄⠀⠀⠀⠀⠀⠈⢧⠀⠈⢧⡹⣄⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⠦⣈⠱⣄⠀⠀⠀⣠⣼⣷⣶⣾⠛⢺⠷⣦⣤⣴⠞⠁⠀⠀⠀⠀⠀⣀⣤⣶⡋⠀⠀⡴⢎⣓⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣁⠈⠑⠲⣾⣿⣿⣿⣿⠏⠀⠀⠀⣸⣿⢧⣄⣀⣠⠤⢴⡖⠻⣿⣿⣿⠛⣦⣼⣧⣾⣡⣴⠒⡗⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡗⠒⠴⣿⣶⣧⣭⣷⣤⡤⣴⢾⣿⣿⠀⡇⠀⠀⠀⠀⢣⠀⢻⠀⠁⣰⢹⢧⣍⢳⣤⡚⣓⡶⠌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠓⠛⠀⠀⠈⢣⣿⣷⡘⣄⢳⣼⣾⡿⠋⠂⡇⠀⠀⠀⠀⢸⠀⣸⠀⠀⣏⢸⣀⡈⠟⢧⣄⠀⠈⢇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⡤⠒⠒⠒⠒⢤⡀⡼⠛⡿⣿⣟⠉⠁⠁⣀⣤⣧⡇⠀⠀⠀⢀⡜⢠⣟⠳⠤⣸⣦⣹⠶⢳⡂⢻⠑⣄⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⣷⣤⠤⠤⢤⣀⠀⣿⠇⢀⣻⡈⢻⡷⣶⣟⣯⣿⣿⡇⠀⠀⢠⣾⣵⢯⠬⢻⣦⣀⠀⠀⠀⢸⠶⠋⠀⠈⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡏⡞⠀⠀⠀⡄⠈⠻⣿⠔⢋⣠⠿⣦⣙⢮⣿⣯⣶⣋⣀⣤⣺⣿⡟⠻⠾⠯⣄⣻⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⡀⠀⠀⡧⠀⠀⢻⣴⣋⣉⡑⠲⡏⠛⣷⠛⠛⠓⠛⠉⠁⣸⠛⢄⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠛⠃⠀⣰⠃⠀⢀⡾⠥⢄⣀⠀⣹⢃⣼⠃⠀⠀⠀⢀⣤⠞⠁⠀⠀⠑⠦⣄⣀⣀⠤⣾⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⢀⣴⣇⣠⠴⠯⣀⣀⠀⠤⠟⠋⢡⡏⠀⠀⢀⣴⣏⡀⠀⠀⠀⠀⠀⣠⠆⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠳⠦⢭⣽⣶⣶⡒⠒⠓⠲⣏⠑⣯⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠷⡶⠒⠒⣲⠖⠦⠤⢄⡀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣜⡀⢀⡜⠁⠀⠀⠀⠀⠈⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣴⡤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣤⠀⠀⠀ ⠀⠀⠀⠀⢿⡄⠀⠀⠙⢷⡀⠀⠀⡀⣄⠄⠀⠀⣴⠋⠀⠀⢀⣿⠀⠀⠀ ⠀⠀⠀⠀⠈⢷⣄⣀⢀⣼⠇⣤⣤⣼⣯⣤⣤⡸⣧⡀⢀⣠⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⠛⠡⣿⣿⣿⣿⣿⣿⣿⣷⣌⠛⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣤⠉⠙⠻⠿⠛⠉⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣄⣀⠴⠶⣀⡠⣼⣿⣧⣤⠀⠀⠀⠀⠀⡠ ⠀⢷⣄⠀⠀⠲⣶⣶⣿⣿⣿⣿⣯⣤⣤⣼⣿⣿⣿⣿⣶⣶⠶⠀⢀⣾⠃ ⠀⠈⢿⣷⣄⠀⠀⠀⠉⠉⡍⠈⠝⡟⢻⠻⠉⢩⠉⠉⠀⠀⢀⣴⣿⠃⠀ ⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⢿⢃⡀⠀⠀⢀⠀⡾⠀⠀⢀⣴⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠈⠛⢿⣿⣦⣀⠈⠷⢥⣧⣼⡬⠾⠁⣀⡴⣻⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⢦⣄⠀⠀⣀⡴⢞⣭⠞⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠲⣆⠀⠈⢙⡿⣮⣝⣒⠦⣬⣉⡀⠀⠀⢠⡶⠂⠀⠀⠀ ⠀⠀⠀⣠⡀⣤⣤⣿⣦⢘⣭⠷⠒⠈⠙⠛⠶⢯⣭⣟⣵⡟⣥⣤⣔⣶⠀ ⠀⠀⠘⠭⠉⠉⠉⠘⢿⣄⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠃⠀⠀⠊⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀ ⠀⣰⡿⢉⡇⠀⠀⠀⣠⣾⠟⢡⠞⠀⠀ ⣰⡿⢀⡼⠁⠀⠀⣰⣟⣡⠖⠁⠀⠀⠀ ⣿⡷⠟⣇⠀⠀⢰⣿⠀⣸⠀⠀⠀⠀⠀ ⢿⡇⠀⢸⢀⣀⡼⠿⠤⡃⠀⠀⠀⠀⠀ ⠘⢿⣄⡾⡟⠁⠀⠀⢀⣨⣦⠀⠀⠀⠀ ⠀⠀⢸⣿⠁⣾⡟⢃⣸⣿⣹⣦⠀⠀⠀ ⠀⠀⢸⡿⣄⠙⡳⠋⠛⠛⠃⠈⠢⠀⠀ ⠀⠀⠈⢿⠦⠭⢇⠀⠀⡀⠤⢤⡇⠀⠀ ⠀⠀⣠⢴⣻⣶⣾⣷⣤⣤⣴⢎⠀⠀⠀ ⠀⣼⠇⠀⢻⣿⣿⠿⠛⠙⠻⣦⣣⠀⠀ ⠀⣇⣆⣀⣸⡇⠀⠀⠀⠀⠀⠸⢃⢃⠀ ⢸⣄⡏⠁⢸⡇⠀⠀⠀⠀⠀⠀⢟⣬⡄ ⠈⠛⠓⠒⠚⠓⠒⠀⠒⠀⠀⠈⠉⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢚⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣄⠀⠀⢀⡴⢺⢷⡞⠁⢀⣟⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢰⢮⠙⢦⡞⠀⣞⡟⠀⠀⡼⡾⠀⣿⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⠚⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢳⣸⡇⠀⣿⠀⠀⢠⡿⠁⢰⣏⠀⠀⠀⠀⣴⠋⠀⡰⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡸⡀⠀⢳⣷⠀⠘⣆⠀⠟⠀⣴⢻⠏⠀⠀⠀⢸⠁⠀⡼⠁⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣳⡀⠀⢣⣙⡦⠆⠀⠀⠒⠒⠓⠒⠒⣦⣄⢸⡀⢸⠁⠀⠀⠀⠀⢠⡏⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⠶⠞⠁⠀⠀⢀⣀⣀⣀⣀⠀⠀⢹⣮⣿⣷⡸⣄⢀⣀⣀⡠⠟⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⢰⢿⡀⠀⣠⠖⠊⠉⣁⡤⠬⠟⠿⢶⣼⣿⣿⣿⠳⣌⡂⠉⠉⠀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⢣⣲⠳⡀⠈⣷⡇⠀⢣⠤⠒⠋⠁⠀⠀⠀⠀⠀⠈⢻⣿⣿⡇⠈⠉⠉⠉⠋⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠶⠒⣲⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠹⡆⠙⢒⣿⡇⠀⢈⡴⠒⠒⢦⣄⠀⠀⠀⠀⠀⠀⢩⣝⣗⣀⣀⣤⠴⢲⠆⠀⠀⢀⣠⠔⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠞⠁⣰⠋⠉⠙⢞⡆⠀⠀⠀⠀⠀⠀⣀⣀⣹⣦⣤⣼⣤⣼⣿⡿⣷⣟⠈⠉⢿⣻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⣠⠴⠒⠉⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡏⠀⢸⠃⠀⠀⠀⠈⡧⠀⢰⡖⠛⠿⣿⣭⢤⣠⡀⠀⠀⠀⠀⠀⠳⢄⢿⣧⣀⠀⣀⣼⡿⣀⣀⠀⠀⠀⢀⣀⣀⣠⠴⠚⠉⠉⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣾⣿⡿⢃⠿⠇⠀⠀⠀⠀⠀⠀⠀⠳⣬⠛⠻⣿⣿⣿⢯⣗⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⢿⡛⠋⠁⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⠏⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣀⡀⠀⠃⠀⠀⢀⣀⣀⡤⣤⣴⣞⣹⣻⠟⠁⠀⠀⠀⠀⠀⠈⣗⣦⡤⣀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡄⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣏⠙⣿⡉⢹⡏⠉⣷⣀⡟⣿⡷⠟⠁⠀⠀⠀⠀⣀⣠⠴⠚⢯⣭⣭⣉⡑⠒⠦⠤⣄⡀⠀⠀⢀⣴⣶⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀ ⠀⢳⡀⠀⠀⠙⠦⠤⠤⣄⠀⠀⠀⠀⠠⡾⢽⣶⣿⣳⣀⣿⡤⠧⠟⠋⠉⠀⢀⣠⣴⠶⠾⣿⣿⣿⣶⣤⣀⣙⣿⣿⣿⣿⣶⣶⣬⣉⣷⡾⠿⢛⣩⠤⢾⣿⡍⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢦⣄⠀⠀⠀⠀⠈⠳⡄⠀⠀⢠⣇⡀⠀⠀⠀⠈⠁⠀⠀⠀⣀⣤⡖⠛⢷⣇⠀⢀⣤⣀⠀⠀⠀⠉⠉⠉⣉⣻⣿⣿⡟⢿⣁⠠⠖⠮⠝⢲⡛⣉⣥⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠓⠲⣤⡀⠀⠹⡆⠀⠺⢮⠤⠔⠢⠤⠤⠤⠖⠒⠋⢁⡞⠀⠀⠀⢻⡀⢸⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⣿⣿⡇⠀⠈⠙⣆⣠⠾⣿⠟⠉⠉⠉⠓⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠀⢻⣀⡠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⢻⡼⡄⠀⠀⠀⠀⠀⣰⠶⣤⣾⣿⡿⡇⠀⠀⠀⣸⣷⠟⠁⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⢺⣃⣨⠏⣀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢿⣀⣀⣤⠤⠖⠋⢘⣷⠀⠀⠀⠀⣼⣿⡆⠘⣿⠟⢀⡇⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡄⠲⠤⠤⠴⠚⠁⠀⢀⣠⠇⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⡼⠉⢧⡀⠀⠀⣷⡙⣿⠸⣿⣀⡼⠁⠀⠀⠀⠘⣿⣤⣀⣠⡤⠤⠴⠒⠛⣏⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣀⡀⠀⢀⣀⣠⠴⢛⡇⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⢰⠃⠀⠈⢳⡀⠀⢸⣿⣿⠀⣽⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⡇⡇⠀⠀⠀⠀⠘⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢯⣉⣁⣀⡤⠊⠳⡄⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣴⠃⣿⠀⠀⠀⠈⢧⡀⠈⢿⣿⡄⣿⠀⠀⠀⠀⠀⢠⣿⣿⠙⠁⡇⢹⡀⠀⠀⠀⠀⠘⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⠉⠀⠀⠀⠙⢦⡀⠀⠀⠀⡿⠀⠀⠀⣰⡟⢠⠇⠀⠀⠀⠀⠈⢧⠀⠀⠀⣧⠇⠀⠀⠀⠀⠀⣿⠛⢹⠀⠀⡇⠘⣧⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠙⠲⣄⣰⠃⠀⠀⢰⣿⠁⡾⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢰⡇⠀⢸⡄⠀⠀⠀⠀⠘⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣾⠃⣼⠃⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⡇⠀⠀⢳⡀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠘⣿⠀⠀⠁⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠸⣧⠀⠀⠘⣷⠀⠀⠀⠀⠈⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠻⡄⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣦⡶⠛⠀⠀⠀⠘⣷⡀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢄⣀⣀⣠⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠳⡀⠀⠀⢀⣠⠴⣚⡯⠵⠻⠿⡄⠀⠀⠀⠀⡟⢿⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⠲⠚⠯⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠑⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇⡈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣮⣷⣄⡈⠑⣄⠀⠀⠀⠀⠀⠀ ⢀⣤⣀⣀⡀⠀⠀⢀⣀⠤⠤⠒⠒⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡻⢿⣦⡈⢳⡄⠀⠀⠀⠀ ⠸⣷⣤⣀⠈⠉⠉⠁⠀⠐⠀⣀⣤⣀⢀⡞⠲⡀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣷⣿⣷⣈⣵⠀⠀⠀⠀ ⠀⠘⠿⣏⣛⢿⣷⠦⠤⠿⠿⣿⣽⣿⡟⢦⠀⠘⡄⠀⠀⠀⠀⠀⠀⣿⠾⠟⠋⠙⢧⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠚⢿⣿⣿⠁⠀⠳⡀⢹⠀⢀⣀⣀⣀⣀⣿⡀⠀⠀⢀⠏⡜⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣄⠀⣠⠗⠊⠉⠀⠀⠀⠀⠀⠉⠙⠲⢶⣋⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣁⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⢤⡀⠹⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠉⠳⣄⠀⠀⠀⢠⡞⠁⠀⠀⠀⠈⠢⠈⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⡤⠤⣄⠘⠆⠀⠰⠋⣠⠖⠒⡖⢦⣀⠀⠀⢸⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡾⣆⡀⢨⣳⡀⠀⠀⢰⣧⠀⠀⣇⣠⣿⣧⠀⢸⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣿⠻⣷⣶⣿⣇⠀⠀⢹⠻⣿⢿⣿⡿⣻⣹⣤⣼⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣛⠂⠽⣮⠟⠋⠉⠑⠚⠷⠌⠷⢶⣾⢿⣋⠉⢹⣿⠒⠒⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⢠⡯⠷⢤⣤⡤⠀⠀⠀⠀⠰⠶⣏⣤⠞⠓⢤⣾⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠬⠷⢯⣙⠢⠄⣀⣤⣤⣤⣤⣤⡤⠔⢊⣁⡤⠞⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣷⣾⣿⣭⣴⣶⣶⡿⠛⢇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣝⣡⣿⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠟⠉⠀⠀⠘⢿⣯⢹⣇⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⣀⡠⠴⠒⢿⠏⠀⠀⠀⠀⠀⣀⡼⠭⠿⣿⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡀⣿⣿⣏⠀⠀⠀⡼⠉⠙⣷⣄⣤⠔⠉⠀⠀⠀⠀⠈⣇⣀⡤⢼⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⢸⣿⣿⣀⠠⠔⣿⡄⠀⠈⢿⣮⣙⠂⠀⠀⠀⢀⣼⣿⡁⢴⣀⣀⣻⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠓⠿⠛⠛⠒⠚⠛⠛⣆⠀⠈⣿⣿⣷⡦⠴⠞⠛⠋⠉⠉⠉⠁⠀⠀⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠔⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣒⢤⣀⡔⢻⡿⠁⢀⣾⢻⡀⠀⠀⠀⠀⢀⠔⠊⡡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢆⢹⠀⢸⠁⠀⣼⠏⢸⠃⠀⠀⢀⠜⠁⡠⠊⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣆⠀⢻⣆⠘⠄⠰⠃⢠⡿⠀⠀⠀⡎⠀⡜⠁⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⢈⡯⠗⠀⠀⠈⠉⠉⠉⢱⣦⣧⢸⠁⠀⠀⠀⡴⠁⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣼⠋⠀⣀⠤⠔⠒⣲⣤⣄⣸⣿⣿⣷⡣⠀⠒⠊⢁⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢳⣠⢦⠀⣿⡆⠘⡥⠔⠊⠉⠀⠀⠈⠉⢿⣿⣇⠙⠒⠐⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡤⠒⣒⣶⡀⠀⠀⠀⠀⠀⠀⠸⡀⠙⡄⠑⣿⣇⢀⡴⣒⣒⣤⡀⠀⠀⠀⠀⠩⢿⡠⠤⠴⢲⠂⠀⣀⠤⢚⠇⠀⠀⠀⠀⠀⠀⠀ ⢠⠎⢠⠎⠀⠈⢿⠄⠀⣀⣀⣠⣤⠤⠿⠒⠚⠒⠻⣟⢿⣅⠈⠻⢟⣷⠀⠀⠀⠀⠀⠀⠀⢀⡴⠧⠔⠊⠁⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⢸⠀⠀⠀⠈⠁⢸⣧⣤⣿⡿⢻⡇⠀⠀⠀⠀⠈⠹⣟⠷⣶⣿⣿⣿⣦⡀⠀⠐⠒⠉⠁⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢾⠀⠀⠀⠀⠀⠀⢿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣾⠟⠁⠀⠉⣁⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠸⡄⠀⠀⠀⠀⠀⠈⠳⣤⣄⣀⣀⣀⡠⣤⠔⣶⣾⣿⠟⠁⠀⠀⠀⠀⢀⡷⠶⣤⣤⡒⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡀⠀⠙⢄⠀⠀⠀⠀⠀⠀⣹⣷⣸⣧⢸⣇⣸⣶⠯⠟⠁⠀⣀⣤⣤⣴⣎⡉⠹⣷⣶⣤⣭⣉⡒⢤⣀⣴⡿⠗⣲⣶⠷⠀⠀⠀⠀⠀ ⠀⠑⢄⡀⠀⠉⠉⠲⡄⠀⠀⡍⠉⠉⠉⠙⠉⠉⠀⣀⣠⠴⢿⡏⠉⣉⡉⠉⠉⠓⠛⢛⣿⣿⡿⢿⡋⠩⠵⠶⣿⢛⣋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠑⠲⢤⡀⠘⡄⠘⠿⠄⠒⠢⠤⠔⠒⠉⢡⠇⠀⠈⢧⢀⠁⠈⠉⠉⠉⠈⠀⢠⣿⡇⠀⠈⠳⣤⣺⠟⠉⠉⠉⠢⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣙⡄⢱⡖⠒⠲⣄⠀⠀⠀⠀⠀⡞⠀⠀⠀⣈⠷⣇⠀⠀⠀⢠⣞⢲⣿⡿⢷⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⣾⠩⣈⣉⡩⠔⠀⠀⣸⠀⠀⠀⠀⠀⢉⣶⡟⠉⠁⢀⠿⡄⠀⠀⡟⢿⠀⣿⢀⡇⠀⠀⠈⣿⡀⠀⣀⣀⡠⠤⡔⠚⠀⠀ ⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⣀⡤⢞⠇⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⡎⠀⠘⡄⠀⢹⣿⡄⢹⠁⠀⠀⠀⢀⣿⣿⢿⢣⠀⠀⠀⠘⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠹⣅⡠⠴⠋⠣⡀⠀⠀⠀⢠⠁⠀⠀⡼⢰⠁⠀⠀⠘⡄⠘⠿⡇⡆⠀⠀⠀⠀⣼⣿⠉⢸⠘⡄⠀⠀⠀⢸⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠙⠦⣀⠀⡎⠀⠀⣸⠇⡞⠀⠀⠀⠀⠹⡄⠀⠹⠁⠀⠀⠀⠘⠋⠸⠀⢸⠀⢣⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠈⠹⡅⠀⢠⡟⣸⠁⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠈⡆⠀⠀⠀⠸⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⣿⠀⠈⡰⠃⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠐⡇⠀⢸⠀⠀⠸⡄⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠘⣄⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠀⠀⠀⢀⣠⣷⣶⡏⠀⠀⠀⢹⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠢⣀⢤⠾⠿⠛⠉⠉⠙⠀⠀⠀⠈⠙⠷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠶⠞⠛⠛⠶⠶⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⠶⠟⠛⠛⠛⠛⠛⠷⢶⣦⣄⡀⠀⠙⣷⡀⠀⠀⠀⠀⢨⡟⠀⠀⠀⢀⣀⣤⣤⡴⠶⠶⠶⢶⣤⣤⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⡘⢿⡄⠀⠀⠀⢸⡇⢀⣤⠾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⡄⠀ ⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣮⣿⡄⠀⠀⣾⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠘⢿⣷⠀⣼⠟⠁⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠘⣷⣄⣀⣀⣀⣤⣴⠶⠾⠛⠛⠋⠉⠉⠉⠉⠛⠛⠷⣦⣄⠈⢿⣴⠏⢀⣠⣴⠾⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠻⠶⢶⣤⣤⣴⠟ ⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣿⣷⣾⣿⣶⣿⣭⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠁⠀⠀⠀⠰⠿⠿⠿⠟⠛⠿⠿⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠿⠿⠛⠛⠿⠿⠿⠷⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀ ⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠈⠙⠛⠃⠀⠀⣀⡀⠀⠛⠛⠉⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀ ⠀⢀⣿⠃⠁⠀⠀⠀⠀⡠⠚⣩⠖⠋⠉⠉⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠉⠉⠓⢯⡙⢦⡀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀ ⠀⣸⡇⠀⠀⠀⠀⢀⠞⠀⡼⠁⠀⢀⣀⣀⣀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⣀⣀⣀⠀⠀⠹⡀⠙⢆⠀⠀⠀⠀⠈⣿⡀⠀⠀ ⢀⣿⠀⠀⠀⠀⠀⢸⠀⢀⡗⣊⣉⣥⣤⣤⣄⣉⣙⣺⡀⠀⠀⠀⠀⠀⠀⠀⣾⣚⣉⣁⣠⣤⣤⣍⣉⡒⡇⠀⢸⠀⠀⠀⠀⠀⢸⣇⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⢸⠀⢸⣿⣿⡟⠋⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⠛⣿⣿⣷⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⢸⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠈⢇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⠏⠀⠀⠀⠀⠀⠀⣿⠆⠀ ⢹⡇⠀⠀⠀⠀⣀⣤⣤⣙⠚⠻⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠛⢚⣡⣤⣀⡀⠀⠀⠀⠀⣿⠀⠀ ⢸⡇⠀⠀⣠⠞⠁⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠉⢦⠀⠀⠀⣿⠀⠀ ⠈⣿⡀⢠⠇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠈⣇⠀⣸⡏⠀⠀ ⠀⠸⣧⢸⡄⠀⠀⠀⠀⠀⢠⠇⣴⣤⣤⣤⣤⣤⡤⠶⠶⠞⠛⠛⠛⠛⠻⠶⠶⣶⣤⣤⣤⣤⣤⣴⡌⣧⠀⠀⠀⠀⠀⠀⡼⢠⡿⠀⠀⠀ ⠀⠀⠻⣧⢳⡀⠀⠀⢀⡠⠋⠀⢿⣿⣿⣿⣏⣿⢹⣷⠒⣶⠖⢶⡶⠶⢶⡖⢲⡟⢹⣏⣿⣿⣿⣿⠁⠈⠧⣀⠀⠀⢀⣼⢣⡿⠁⠀⠀⠀ ⠀⠀⠀⠙⣷⡍⠉⠉⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣶⣿⣦⣼⣷⣤⣾⣿⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠉⠉⠉⣴⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠹⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠁⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄⠀⠀⠀⠀⠀⠈⠳⣿⣏⢹⣿⡏⢻⡟⢹⣿⠉⣿⣟⢹⣿⠷⠋⠀⠀⠀⠀⠀⢀⣤⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⣀⠀⠀⠀⠀⠉⠙⠛⠓⠚⠛⠚⠛⠓⠛⠛⠉⠁⠀⠀⠀⢀⣠⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⠛⠷⢶⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⠾⠟⢛⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡆ ⠀⠀⠀⠀⠀⡟⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⠊⠉⢀⠌⡃ ⠀⠀⠀⠀⢰⠁⡶⡄⠀⠉⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⡴⢻⠀⠁ ⠀⠀⠀⠀⡜⠀⡇⠙⣆⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⡠⠛⠀⠀⠀⠀⠀⡠⠊⠀⢸⠀⡀ ⠀⠀⠀⠀⡇⠀⡇⠀⠈⠢⡀⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⢀⠜⡏⠀⠀⠀⢀⣾⡀⠀⠀⠀⠀⢠⠞⠀⠀⠀⣼⠀⡇ ⠀⠀⠀⠀⡇⠀⠃⠀⠀⠀⢹⣦⡀⠀⠀⠀⠈⢆⠀⠀⣠⠖⠁⣼⠴⠂⠀⠀⠚⠳⠬⣓⠤⣀⣰⢻⠀⠀⠀⢀⡇⢠⠇ ⠀⠀⠀⠀⢹⠀⠸⡄⠀⠀⢸⣿⠘⢆⠀⠀⠀⠈⢧⡾⠃⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠛⠚⣶⡇⠀⡸⠀⢸⠀ ⠀⠀⠀⠀⠸⡄⠀⢣⠀⠀⡞⠘⢆⠘⡆⠀⠀⠀⢸⡗⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⠞⢩⠇⡰⠁⠀⡸⠀ ⠀⠀⠀⠀⠀⢣⠀⠸⣄⣀⣇⠀⠈⣶⡇⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠺⢥⡀⠘⣲⠚⠋⠁⠀⡰⠁⠀ ⠀⠀⠀⠀⠀⠀⠳⡀⠙⢿⣹⡆⠀⠀⠀⠀⢀⣴⠥⣀⡀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣀⡀⠀⠑⣄⣈⠑⣢⠴⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣨⡶⠄⠈⠉⠀⢀⣠⣶⣯⡀⠀⣀⣈⠳⣄⠀⠀⠀⠀⣼⣗⠉⠙⢯⣿⣷⣾⡗⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⣺⠻⣿⢿⠟⢿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢰⣿⣿⠁⠀⠀⢹⠏⢹⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣻⠸⡀⣼⣿⣿⣿⠛⣿⣿⣿⡤⢤⣾⢿⣿⣿⠀⠀⠈⣷⣬⣶⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡿⢃⡤⢷⣿⣿⣿⣿⣾⣿⣿⡟⠀⠀⠻⠬⢤⣇⠀⢀⣼⠟⢿⣍⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠯⢤⣾⡀⠂⢹⠛⠿⠿⣿⡿⠛⠁⠀⠀⠀⠀⠀⢠⣽⣿⣷⣰⣿⠃⢈⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⠻⢷⡟⠀⠀⠀⠙⢷⣤⣄⡀⠀⠀⠀⠀⠈⢻⠟⣿⠟⢁⣠⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠉⠢⣄⣀⣛⣓⣶⣄⣠⣤⣌⡙⠛⠿⢶⣶⣲⣒⣾⣾⢟⡻⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠊⢢⣸⠀⠈⡇⠀⠀⠀⠀⠀⠀⢨⣷⣾⣿⣇⠀⠉⠑⠒⠒⠒⠛⠋⠁⠈⠁⠀⠀⠀⢀⣠⣦⡀⠀⠀⠀ ⢠⡤⢄⡀⢇⠀⣸⣿⡶⠶⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⡾⠶⠒⠛⢿⣿⣿⠀⠀⠀ ⢸⡀⠀⢱⣸⡛⠋⢻⣆⢀⣷⡀⠀⠀⠀⠀⣰⣶⣏⣿⣇⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⢿⣿⣿⣶⣤⡀⠈⠻⣿⣇⠀⠀ ⠀⠙⢾⠛⠙⢷⠤⠼⠛⣛⠵⢷⠀⠀⡴⠉⢹⣿⣿⣿⡟⠀⠀⠀⣰⣿⡿⠏⢻⣆⠀⢸⣿⣿⣁⠙⠻⡄⠀⣿⣿⡄⠀ ⠀⠀⠀⠑⢤⡾⠤⠒⠉⠀⠀⠀⢧⠼⣧⣀⣼⣿⡿⢅⡀⠀⠀⢰⣿⡟⢁⠀⠀⢻⡆⠸⣿⣉⡽⠀⣰⣿⣏⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⢸⣀⡴⠃⠀⠉⠓⠤⣌⣷⣾⣿⣿⣇⣘⣀⣠⣼⠟⠀⠙⣿⣷⠿⠟⠛⣛⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⣀⣼⣅⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣿⣿⣿⣿⡆⣼⣟⣉⣁⠀⠀⢨⣿⡏⣣⣼⣿⣿⠇⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⡉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣿⣿⣿⣿⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣵⣿⣿⣿⣿⣿⣾⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡴⢖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣹⣦⢀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣷⣿⡿⠿⠿⠿⣿⡿⠟⠋⠉⠉⠙⠻⠤⣄⠀⠀⠀⠀⢀⠴⠊⠉⠉⠉⠳⣄⠀⠀⠀ ⠀⠀⠀⣠⠔⠒⠒⠢⢄⠀⠀⠀⠚⣠⠜⠋⠀⢀⣀⣀⡀⠘⣇⠀⠀⣤⣴⣶⣶⣦⣤⣑⣦⣀⣸⠃⢠⠞⠉⠉⢻⣆⠈⢧⠀⠀ ⠀⢀⡾⠁⣤⠖⠒⢦⡀⠙⣦⢀⠞⢁⣴⣾⣿⠿⠿⠿⠇⠀⣿⠀⠀⢻⣟⣛⠉⠉⠛⠻⠋⢻⣽⠀⢸⣄⣀⣦⣾⡏⢀⣼⠀⠀ ⢀⣾⡇⢸⣯⠀⠀⠀⣿⠀⢻⡌⠀⠙⠋⢀⣤⣶⣶⣤⣄⠀⣿⠀⣠⣾⣿⣿⣿⣷⣦⠀⠀⠈⣿⣦⣀⡙⠛⢛⣋⣤⣾⠏⠀⠀ ⠈⠹⣿⣄⠻⠿⣶⠿⠋⢀⣾⠁⠀⠀⣰⣿⡿⠟⠛⠻⣿⣇⣸⡄⣿⠋⠁⠀⠈⠙⢿⣧⠀⠀⢹⣟⠛⣻⡿⠿⠛⠋⠁⠀⠀⠀ ⠀⠀⠈⠻⢷⣶⣶⣶⡾⢿⣿⠀⠀⢠⣿⠃⠀⢀⣀⠀⢀⣿⣿⣿⣷⣄⣀⣶⡄⣀⣼⣿⣀⠀⢘⡟⠃⠀⢲⣶⣀⠀⠀⠠⡄⠀ ⠀⠀⠀⠀⣄⠀⠀⢀⡀⢠⣼⣄⣀⣀⣿⣦⣤⡼⢿⣚⣿⣿⣿⣿⣿⡿⠈⠙⠩⠭⣟⣿⣿⢿⡿⠿⣄⠀⠀⠀⠀⣀⠀⠀⠈⠀ ⠀⠀⠀⠀⢿⣇⠀⢧⠉⢀⣼⣿⡿⢿⣿⡟⣡⠖⠁⠀⠈⠙⠻⣿⡏⠀⠀⠀⠀⠀⠀⠉⣿⣶⡹⣿⢿⣷⡄⠈⢁⡋⡀⠀⠈⠀ ⠀⣀⡀⠁⠐⣄⠉⢩⣀⡝⢡⡴⣷⣶⣿⡴⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣿⣿⡟⢧⢀⡏⠀⠙⣆⠀⠀ ⠀⢠⡁⢠⠀⠈⠓⠀⣸⡡⣟⣠⣼⣿⡏⣿⣄⡀⠀⠀⠀⣀⣤⣿⣷⣤⣤⣤⣴⣾⣿⣿⣿⣿⠙⠿⠟⠁⣸⠤⡟⠢⡤⠬⣁⠀ ⠀⠀⠉⠧⣠⡖⠀⢶⡻⣄⠻⣿⡿⢛⣿⣿⣿⡿⣿⡟⢛⣟⠉⣹⣯⣉⣹⣥⡼⢿⣴⠿⣤⡿⠷⠦⣴⣾⠛⠃⡿⢿⠁⠀⠈⡇ ⠀⠀⠀⠀⠈⠻⣄⠈⠳⡿⣷⣶⠶⠿⢿⠖⠛⠓⣿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣀⣸⣿⣀⣩⣩⠀⡧⠀⢠⣀⡼⠋⠈⠓⠤⢞⡁ ⠀⠀⠀⢀⠀⠀⠛⣆⠸⡁⣩⡷⢀⠠⣀⣤⣤⣴⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣤⡀⢸⡆⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⢸⣦⠀⢀⣠⣄⠀⠹⢂⣼⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⣠⡿⡅⠈⡽⢇⠂⠀⠀⠔ ⠀⠀⠀⠀⠀⢉⠏⣁⡼⣄⢠⠋⢿⣄⣠⣿⣿⡿⢿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣛⣿⣯⡽⠷⠿⠛⠉⢁⣴⣿⠀⠀⣼⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⠝⠟⠀⠜⣯⣧⣀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡏⠥⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠉⠐⢒⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠳⠤⠤⠜⣿⠀⠿⠹⣿⣷⢶⣤⣤⣤⣤⣤⣤⣤⣤⣿⣷⣤⣤⣀⣠⣤⡴⢾⣿⡿⠛⠁⠀⠀⠀⢈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠖⢋⣤⣯⠛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣭⣷⣿⣿⠁⠀⢀⡆⠐⠦⠤⠚⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠚⢿⣿⣿⣿⠿⠛⠋⠉⠟⠉⠟⠻⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠠⠤⠤⠊⠀⠈⠁⠀⠈⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠋⠉⠙⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠚⠋⠉⠉⠉⠙⠒⢦⣄⠳⡄⠀⠀⡾⢀⣠⠴⠒⠚⠛⠛⠒⠲⢤⣄⠀ ⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⢠⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳ ⠀⠸⣄⣀⣀⡤⠤⠖⠒⠒⠒⠒⠲⢤⡈⣧⠎⣀⡤⠖⠚⠛⠛⠛⠒⠒⠦⠤⠤⠼ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠛⠛⠛⠛⠛⠓⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⣰⠋⠀⠀⠴⠶⠶⠶⢶⣤⡀⠀⠀⠀⢀⣤⣶⠶⠶⠶⢦⠄⠀⠙⣆⠀⠀⠀ ⠀⣰⠃⠀⠀⠀⡠⣤⠤⠤⢄⠈⠉⠀⠀⠀⠈⠁⡠⠤⠤⢤⢄⠀⠀⠀⠘⣆⠀⠀ ⢠⡏⠀⠀⠠⠊⣌⡀⠀⠀⢀⣱⠀⠀⠀⠀⠀⣜⡀⠀⠀⢀⣱⠀⠄⠀⠀⠸⡄⠀ ⣸⠀⠀⠀⠇⠀⣷⡶⢻⣿⣶⣾⠀⠀⠀⠀⠀⣷⣶⣾⡟⢶⣶⡄⠀⠀⠀⠀⣧⠀ ⡟⠀⠀⠀⢰⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠁⡆⠀⠀⠀⢸⠀ ⣿⠀⠀⡠⠤⠥⡚⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⢛⡬⠤⢄⠀⠀⣸⠀ ⢸⡀⡜⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢣⢀⡏⠀ ⠀⢳⣣⠀⠀⢀⠌⢾⣶⣶⣲⣯⢍⡉⣉⢉⡭⣽⢶⣶⣶⡷⠱⡀⠀⠀⣜⡾⠀⠀ ⠀⠀⠻⣍⠉⠁⠀⠈⢿⣿⣿⣿⣾⣷⣿⣶⣷⣿⣿⣿⡿⠁⠀⠈⠉⣩⠞⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⡀⠀⠀⠙⢽⣻⣿⢻⣟⣟⣿⣛⡿⠋⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠓⠦⢤⣄⣀⣀⣈⣉⣁⣀⣀⣠⡤⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣲⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣽⣿⣿⣷⣇⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣮⣿⠿⢿⣿⠿⠛⠲⠇⡂⠀⠐⢀⠤⠐⠀⢄⠀⠀ ⠀⢀⠔⣀⣐⠢⡀⢈⠔⣁⣤⣤⡄⢹⠀⢶⣶⠶⢶⡕⡤⠁⡎⢉⣹⠄⡃⠀ ⢠⣿⢸⣀⢈⡇⢰⠃⠚⣩⣵⣦⣄⢸⢠⣼⠿⢶⣦⠀⢸⣦⣙⣛⣫⡴⠃⠀ ⠀⠙⢦⣭⣭⣴⣿⠀⢰⡟⠉⠈⢙⣾⣾⣁⣠⢀⣹⡇⠀⡧⠈⢯⡁⠀⢀⠀ ⠀⠀⢰⡄⢠⠄⣺⣤⣼⡷⢚⠇⠻⢿⡿⠗⠀⠙⠻⢿⡻⣗⣄⠀⢔⠄⠀⠁ ⠀⠀⠀⢍⠨⣰⢫⢷⣾⡗⠁⠀⠀⠀⣏⠀⠀⠀⣠⣾⣿⣷⡿⡇⡎⠐⢄⠀ ⠀⠀⢌⡠⢡⢆⠳⣾⢿⣿⣶⣤⢴⡖⣻⣛⣟⡻⣻⢟⡧⢍⣥⠯⡫⡕⠐⡄ ⠀⠀⠀⠑⡄⠻⢳⡚⠛⠂⢉⣧⣹⣿⣿⣿⣿⣤⣿⣼⣄⣅⠰⢐⠁⠉⠒⢅ ⠀⠀⠷⣀⣬⡬⠈⣸⠞⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣅⣀⠵⡌⠴⡄⠀⠜ ⠀⠀⠀⡼⠶⢑⣞⣈⠒⠛⠛⠛⠛⠛⢻⡟⠛⠚⠛⠉⢁⣤⡾⠃⠤⠃⠀⠀ ⠀⠀⠀⠑⠒⠚⣄⡫⢻⢶⣶⣶⣶⣶⣾⣷⣶⣤⣖⣾⠟⠋⠀⣀⡸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢘⠸⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠛⠉⠀⠨⠀⠘⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⠢⢴⣒⠐⠦⡀⠀⠀ ⠀⠀⠀⢀⡔⠑⠲⢄⡀⠀⠀⠀⡰⣹⡄⠀⠀⠈⠁⠀⠘⢦⠀ ⠀⢀⠴⠋⠉⠀⠀⠀⠙⢆⠀⢠⠳⣿⣿⣦⣤⣀⠀⠀⠀⠈⡇ ⠸⣇⣀⡄⢀⡀⠀⠀⠀⠘⡆⢸⢠⠻⣿⣿⡿⠛⠿⣄⠀⠀⡇ ⠀⠹⣌⣿⣷⣮⣶⡀⠀⠀⢹⡚⠚⠲⢿⣟⠀⠀⠀⠈⢦⣠⠇ ⠀⠀⠈⠙⠻⣿⣿⣿⣷⣦⡜⢃⠀⠀⣠⢿⣷⡄⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⢰⠃⠙⠻⡿⠿⠇⠸⡀⠀⠀⢉⣷⣿⡴⠃⠀⠀⠀ ⠀⠀⠀⠀⣿⢀⠐⣤⣷⠦⣤⣀⠱⣄⠀⣸⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⣧⠈⠙⣿⢀⡤⢿⣿⣧⠈⠢⣹⣷⣿⣩⡗⠦⣀⠀ ⠀⠀⠀⠀⠸⡀⠀⠹⣿⣿⣾⣿⡿⠀⠀⠘⡟⢘⡽⢧⣀⡀⠀ ⠀⠀⠀⠀⠀⠙⢦⣄⣀⣰⠋⡜⠉⠒⣊⣽⣿⠋⠀⠀⠉⠁⠀ ⠀⠀⣠⣄⠀⡰⠁⣾⣿⣿⣿⣿⣿⣿⡿⠛⢻⡆⠀⠀⠀⠀⠀ ⠀⢀⣻⠿⡞⠀⣠⡿⣿⣿⣿⣿⣿⣿⠧⣦⡾⠀⠀⠀⠀⠀⠀ ⠀⢿⠀⠀⢹⣾⣿⠂⠿⠿⣿⣿⢿⣟⡤⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠘⢦⣶⣿⠋⠁⢄⣀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⣿⣿⡇⢀⡠⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣧⣿⣿⣏⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⠀⠀⠀⠹⣤⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠟⠘⢶⣉⣏⠉⣻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣿⡟⣻⣿⣿⣿⣿⣿⣏⡹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢘⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⡵⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⡻⣦⠀⠀⣀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⡀⠉⠉⠀⠀⠀⠈⠁⠀⠀⣠⠴⠒⠒⠒⠲⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⢀⣿⠿⠛⠉⠉⠉⠉⠙⠻⣿⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⣌⠀⠀⠀⢀⡴⠊⠁⣀⣤⣤⣤⣄⠀⠙⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠛⠉⠉⠉⠓⠦⣀⢀⠀⠀⠈⢁⡴⠋⠁⠀⣀⣀⣀⣀⣀⡀⠀⣿⠀⠀⠀⣶⣶⣯⣽⣿⣿⣶⣶⣌⡹⢦⢀⣸⠁⠀⣾⠋⠠⠀⠀⣽⣷⠀⠘⣆⠀⠀⠀ ⠀⠀⠀⣴⠏⢀⣤⡶⠶⠶⣦⡀⠈⠳⣆⠀⡴⠋⢀⣤⣾⣿⣿⣿⣿⣿⣿⠃⠀⢿⡀⠀⠀⠻⣿⣟⡛⠋⠉⠛⠛⠿⠟⠘⣏⣹⠀⠀⣷⡐⣃⣒⣤⣿⡿⠀⣀⣿⠀⠀⠀ ⠀⠀⣴⣿⠀⢸⡟⠀⠀⠀⠈⢿⡄⠐⣧⡜⠁⠰⡿⠟⠋⠉⣁⣤⣤⣀⡀⠀⠀⢸⡇⠀⢀⣴⣿⣿⣿⣾⣶⣤⡀⠀⠀⠀⢹⣿⣆⠀⠙⠿⣿⣿⡿⠟⢁⣤⣿⠟⠀⠀⠀ ⠀⢰⢿⣿⡄⠸⣿⣮⣀⣀⣠⣾⠇⠀⣿⠇⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣦⡀⢸⣧⢸⣾⣿⡿⠟⠛⠻⢿⣿⣷⣄⠀⠀⠈⣿⣿⣷⣶⣤⣤⣤⣶⣾⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠘⣿⣷⣄⠙⠻⠿⠿⠟⠋⢀⣼⣿⠀⠀⠀⠀⣾⣿⠿⠛⠉⠉⠉⠻⢿⣷⢸⣿⢸⣿⠁⠀⠀⠀⠀⠀⠙⣿⣿⡀⠀⠀⢸⢿⠁⠈⠭⠽⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⠿⣿⣶⣶⣶⣶⣾⢿⣿⣿⠀⠀⠀⢸⣿⡏⠀⠀⢀⡀⠀⠀⠀⣿⣿⣿⣿⣷⣀⡀⢰⣧⡄⢠⢀⣸⣿⡇⠀⠀⠈⣿⠛⠃⠀⢻⣰⣆⠀⠀⠀⠀⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⠀⠉⢉⠉⠃⠀⠈⣿⠀⠀⠀⠸⣿⣇⣀⣀⣺⣿⡧⢷⣿⣿⣿⣿⣿⣿⣿⡍⠛⢛⣛⣛⡿⢿⣿⣿⣿⣿⣿⣿⣄⠀⠂⠀⠈⠉⠁⠄⠀⠀⠀⠹⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⣦⠀⢠⡐⢶⠈⠙⣿⣿⣶⣶⣶⣿⣿⡿⠛⢉⡥⠒⠘⢻⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠈⠉⠓⠟⣯⡉⣩⣭⣭⣝⡳⣄⠀⠀⢤⠙⣷⣄⠀⠀⠰⠀⠀ ⠀⡀⠀⠀⣀⠐⠿⠷⣀⠀⣷⠆⢀⣼⡿⠿⠟⠛⢿⣿⡏⢠⡾⠋⠀⠀⠀⠀⠀⠀⢿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣧⡐⣿⡙⣿⡼⡆⠀⠀⣬⡥⢄⠀⠀⠀⠀⠀ ⡀⠈⣀⠀⠉⠀⠐⢆⠈⠉⣁⣀⣨⠏⣠⡶⣿⣶⣶⣿⣱⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣧⣿⣿⣿⡇⢿⠀⢸⠁⢀⡈⢳⡀⠀⠀⠀ ⠀⠀⠉⡉⠀⣀⡀⠘⠻⢦⠀⠙⡏⣠⡟⠀⢘⣿⣿⡏⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⣂⣀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⠹⣿⣿⡿⠁⢸⣄⣹⡷⣄⣀⠀⠙⠦⠀⠀ ⠀⠀⠈⠷⣤⠋⠀⢀⡀⢠⡀⣾⡇⢻⣷⣭⣭⣿⢿⣷⣸⣿⣷⣤⣤⣤⣤⣤⣶⡿⠿⢿⣿⠿⠿⣿⠟⠛⣿⠟⢛⣿⠛⢻⣿⣀⠈⠉⢀⣠⣾⣏⠙⣦⣤⡼⠉⠉⠳⡄⠀ ⠀⠀⠀⠀⠘⠳⢶⣿⠀⠈⢻⡍⢿⣄⠙⠿⠟⢋⣨⣿⠿⠻⣟⠟⢻⣯⣉⣩⣿⣄⣠⣼⣷⣤⣴⣿⣶⠚⠛⣷⣾⡙⢳⣿⡟⠻⡛⣿⣿⠟⠁⢈⡱⣋⢺⡄⠀⠀⠀⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠻⣌⢿⣿⣶⣾⠿⠿⠿⠶⠞⠉⠙⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣧⡲⢸⡀⠲⠀⢳⡀⠀⢦⢄⣰⠟⢁⡀⠙⠶⠶⢚⡁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡀⢰⡛⠈⢟⣧⠀⠀⣀⠉⢀⣀⣀⣀⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣿⣄⠀⠉⠈⣧⠀⠀⠀⠀⠈⠀⠀⠙⡆ ⠀⠀⠀⠀⠀⣧⡀⠀⠀⠈⠳⡀⠑⠠⢟⡉⢐⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠉⠻⣦⠴⠛⠦⢤⡖⢄⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⢿⢳⣄⣀⣲⡶⢲⠖⠂⠉⣡⢾⣿⠋⠈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⡿⢿⣦⣄⣀⣤⠾⠛⣧⠀⠺⠟⠳⡌⠑⠀⠀⠚⠁ ⠀⠀⠀⠀⠀⠀⠀⠈⡽⢦⣅⣼⣤⡀⣸⠃⢿⣥⣄⣠⣽⣿⣿⠟⠿⣿⡷⠿⣿⣿⠛⢻⣿⣿⢟⣻⣿⣛⣿⣿⣭⣿⡷⠾⠛⠛⠉⠀⣠⣴⣟⡆⠀⠀⣴⡷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⠀⣾⣭⣽⣿⠀⣀⠾⡛⣦⡀⠀⡉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⢋⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⠙⠓⠶⠴⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⢀⢏⡞⠙⣞⢿⣦⣵⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠈⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⡿⠋⠀⠀⠂⠀⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠋⠘⣇⠀⠋⣀⡝⢿⣮⣛⡿⢿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⠿⣟⣻⣿⠾⠛⠁⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠛⢋⣤⢼⣧⡉⢻⣷⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣽⣷⣶⣾⣿⣿⣇⠀⠀⠀⣸⠀⠘⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠗⠈⡿⠓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡈⢁⣠⢿⣟⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠘⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⢩⠀⠈⣀⡬⠙⠿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠦⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⢉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠈⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠈⣏⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡀⠀⠀⠸⡄⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⡸⡇⠀⠀⣰⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⡇⠙⠒⠚⠁⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠓⣶⠒⢶⡶⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠟⠛⡻⠟⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⢉⡠⠔⢉⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⣁⠤⠒⣁⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣉⡠⠔⢊⡡⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠠⠔⠚⣉⠤⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠿⠶⠶⠿⠶⠾⠿⢷⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠟⢁⣠⠴⠖⠒⠒⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠶⢤⣀⠀⠉⠻⣦⡀⠀⠀⠀ ⠀⠀⠀⣠⡿⢁⣴⠋⢀⡠⠖⣖⠓⠲⣄⠹⣆⠀⠀⠀⠀⠀⠀⠀⢠⡞⢉⡴⠖⠒⠦⣄⡈⠻⣦⡀⠘⣷⣄⠀⠀ ⠀⠀⣰⠟⣠⣿⠇⢀⡞⠁⠀⣿⣿⣄⠈⡇⣿⠀⠀⠀⠀⠀⠀⠀⣾⢱⡏⢀⣾⣿⠀⠈⠳⡄⠸⣿⣄⠈⢿⣆⠀ ⠀⣴⡏⢠⣿⣿⠀⣾⠀⠰⣿⣿⡿⠃⢠⢇⡟⠀⠀⠀⠀⠀⠀⠀⢻⡼⣇⠘⣿⣿⣷⡶⠀⢻⠀⣿⣿⡆⠈⢿⡄ ⢰⣿⠀⢸⣿⣿⣆⠘⢧⣀⣀⣀⣤⠶⣫⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣝⢦⣀⡉⠉⢀⣠⡟⢀⣿⣿⡧⠀⠸⣧ ⢸⡇⠀⠘⣿⣿⣿⣷⣤⣤⣉⣥⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣬⣉⣉⣉⣁⣴⣾⣿⣿⡇⠀⠀⣿ ⢸⣇⠀⠀⠈⠛⢿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⡿⠋⠀⠀⢠⡿ ⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠉⠁⠀⠀⠀⠀⢠⣾⠃ ⠀⠈⠻⣦⣄⣀⣤⣴⠾⠛⠉⢹⡀⠈⠉⠛⠷⣦⣤⣀⣀⣠⣤⡶⡟⠋⠉⠀⠀⡼⠉⠛⠷⢶⣤⣤⣤⡶⠟⠁⠀ ⠀⠀⠀⠀⢹⡍⠁⢿⠀⠀⠀⠈⡇⠀⠀⠀⠀⡇⠈⠉⠉⠁⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⢰⠃⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⢸⡀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣇⠀⠈⡇⠀⠀⠀⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢠⡇⠀⠀⠀⡾⠀⢀⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⣇⠀⠀⠀⢻⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣸⠀⠀⠀⢰⠇⠀⣼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⢸⡄⠀⠀⠘⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡏⠀⠀⠀⣾⠀⠀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣀⠀⣇⠀⠀⠀⣷⠀⠀⠀⢸⡄⠀⠀⠀⠀⡟⠀⠀⠀⠀⡇⠀⠀⢀⡏⠀⣸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠳⢾⣤⣄⡀⢻⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⢸⠁⣀⣠⣼⠶⠛⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠒⠓⠒⠶⠖⠒⠓⠒⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣴⣌⠐⣄⠀⠀ ⠠⣖⡒⠂⠐⠂⠌⣉⡀⡱⢄⠀⠀⠀⠀⢹⢯⣷⣜⡆⠀ ⠀⠙⠋⠽⢟⣛⣛⣿⣿⠑⡄⢂⠀⠀⠀⢸⠚⠉⠱⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⡸⠚⠈⠉⠉⠉⠒⠤⡑⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠢⡀⠀⠀⡴⠋⠉⠢⡑⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⡔⠒⢌⠀⠈⡔⠈⡐⣠⠀⢱⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⡾⡶⣿⣄⡀⡻⡶⠿⣻⣧⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠛⣪⠝⣉⡀⠀⠉⠬⣙⡹⢆⣼⠁ ⠀⠀⠀⠀⠀⠀⠐⠒⠛⠪⠔⣼⣶⠶⣒⣒⣥⠒⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⣿⣻⡇⠀⠆⠀⠀⠀ ⠀⠀⠀⢀⣀⡀⢀⡀⠤⡴⠊⠀⠀⢈⠷⣷⠀⠹⡀⠀⠀ ⠀⠀⠀⠘⡸⣿⡅⢀⣊⠉⢷⡰⠈⠀⠀⢀⡦⠐⠗⣄⠀ ⠀⠀⠀⠀⠐⠛⠛⠒⠛⠢⣀⡿⠷⠤⠖⠛⠉⠈⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣽⣯⣿⣟⣻⣿⣿⣿⣿⣿⢿⣻⡋⢉⢹⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣤⣿⣿⣅⣀⣠⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⢛⠻⣿⠿⠛⢉⡉⠉⢻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠃⠘⣀⣀⠭⠒⠊⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣭⠽⣿⣿⣿⣷⣎⣍⣹⣀⣨⣤⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⣿⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠯⣍⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠉⠒⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢿⣯⡀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⢸⣽⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠏⠀⠈⡖⠒⢲⡞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⣄⠀⠀⠀ ⠀⠀⠀⣼⠀⠀⡜⠁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠈⠳⡀⠀ ⠀⠀⠀⣧⠀⢀⡇⣠⣏⣀⣀⣀⣀⣀⠀⠀⠀⠀⡠⠊⣠⠴⡇⠀⠀⠀⠀⢳⠀ ⠀⠀⠀⢹⡀⢸⣷⠏⠀⠀⠀⠀⠀⠀⠉⠳⢦⣎⣠⠞⣵⣴⡇⠀⠀⠀⠀⠸⡆ ⠀⠀⢠⢞⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠈⢻⡟⠋⠁⠙⣄⠀⠀⠀⢰⡇ ⠀⢠⠏⢸⣄⡴⢲⣤⡀⠀⠀⠀⢀⠂⢀⡴⢲⣤⡔⢳⠀⠀⠀⠀⠉⠒⠊⠉⠀ ⢀⡞⠀⢘⠏⠀⢰⡇⢹⡄⠀⠀⡌⠀⡎⠀⢀⡏⢯⠉⣇⠀⠀⠀⢠⡀⠀⠀⠀ ⢸⡇⠀⢸⡦⢤⣾⣧⢸⣿⠀⠀⠆⢰⣷⣦⣾⡀⣸⡄⢸⠀⠀⢠⣿⣷⡀⠀⠀ ⠀⢃⠀⠸⣧⣀⣿⢉⣽⠿⠂⢶⡶⠺⢿⣿⡏⣹⣿⡇⢸⠀⢠⣿⣿⠏⡇⠀⠀ ⠀⠘⣆⠀⠀⠈⠉⠉⠀⢤⣤⠼⢷⡤⠃⠈⠉⠉⢁⡴⠃⢠⣿⣿⠃⢀⠇⠀⠀ ⠀⠀⠈⠑⠦⢄⣀⠀⠀⠀⠙⢶⡞⠁⠀⣀⣠⣴⡋⠀⣠⣿⡿⠁⡰⠃⠀⠀⠀ ⢀⣀⠤⢴⠖⠊⠉⠉⣑⣤⣶⣿⣿⡟⠛⠋⢹⣿⣿⣶⣿⠋⠑⠊⠀⠀⠀⠀⠀ ⢸⠀⠀⠸⡄⠀⠀⡄⠹⣿⣿⢻⣾⣿⡄⠀⠘⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⣧⠀⠀⢧⣠⠞⣷⠀⠀⠀⠀⠉⡇⠉⠉⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣇⢱⣖⠉⠀⢰⡏⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣹⠈⠑⠶⣉⣀⣀⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⠀⠀⠀⠀⢹⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢧⣀⠀⠀⣈⣆⣀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠉⠀⠈⠉⠉⠉⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠙⠛⠓⠲⠶⠦⠤⢴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⢾⣟⠓⠶⣄⠀⢀⣿⠷⠾⢶⣤⣤⣤⣤⣤⣤⣀⣰⣇⣀⡀⣀⡤⠶⠒⠲⢦⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⡟⠻⢭⣑⣂⣈⣧⣸⣿⣾⣿⠿⠿⠿⣭⡉⠉⠙⠻⢿⣭⣿⣿⠋⢀⠴⠒⠒⣦⡌⢷⡄ ⠀⠀⠀⠀⠀⠀⠀⣸⠁⡏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠈⠻⠃⠰⠃⠀⠀⣾⠉⠉⣹⡷ ⠀⠀⠀⠀⠀⠀⠀⠸⡄⢃⣨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣆⠀⠀⠀⠀⢇⠀⠀⠀⠙⠛⣻⢿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠈⠳⣄⣀⣀⡴⣻⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠁⢀⣀⠀⠀⢀⡏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠹⡆⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀ ⠀⠀⠀⠀⠀⢀⡾⠇⢀⡞⠀⠈⠙⠒⢾⡇⠤⢀⣼⠟⣆⠀⠀⠀⠒⠀⠀⣀⠙⢦⣿⡀⠀⠀⠀⠀⠀⠰⣶⠒⠞⠃ ⠀⠀⠀⠀⣠⡾⠁⠀⡾⠀⠀⢀⢐⡴⠛⡇⠀⠀⢸⠀⠘⢷⣄⣤⠴⠒⠉⠁⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀ ⠀⣀⣤⡾⠿⠟⠀⢸⡇⠀⠠⣽⠟⠀⠀⢹⣆⢸⣿⠀⠀⠀⠈⠛⠶⣤⣀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢈⣧⠀⠀ ⠘⢿⣷⣅⡀⠀⠀⣾⠀⠀⣾⠃⠀⠀⠀⠀⠻⣿⣿⠀⠀⢀⣀⡀⠀⠀⠉⢻⣷⣶⣤⣤⣿⡆⠀⠀⠀⠀⠀⢻⡄⠀ ⠀⠀⠉⠻⣯⣠⣤⣿⠀⣸⣿⠀⢀⣰⣿⡷⠀⠈⢻⠀⠀⢿⡿⡇⠠⠤⠀⢸⠿⠿⣿⣿⠟⣿⠀⠀⠀⠀⠀⢸⣧⠀ ⠀⠀⠀⠀⠀⣨⠏⢹⣶⣿⣿⠃⠀⠉⢫⡀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⡟⣀⣴⠟⣱⣿⠃⠀⠀⠀⠀⠀⠀⢻⡄ ⠀⠀⠀⠀⢠⣯⣴⣿⣿⣿⣿⡀⠀⠀⠀⡇⠀⠈⠲⠞⠁⠸⠀⠀⣠⣴⠿⠛⠋⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⡷ ⠀⠀⠀⠀⠈⠉⠉⠉⣉⣿⣿⣿⣦⣀⡘⠁⠀⠀⠀⠀⠀⠀⠡⠀⣁⣠⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⢿⡿⢿⣷⣶⣶⡶⠶⠶⣶⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣺⡶⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡿⠿⢍⣈⣙⡶⠚⠁⠠⠤⢖⠒⠒⠒⠒⠲⠤⣄⣠⠤⠖⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣠⣿⡅⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣼⣣⠟⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣰⠋⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣼⠀⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⡼⠁⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⡀⠰⠃⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⣷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢹⣧⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⠋⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠶⣄⡀⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⣿⣶⣝⡦⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠖⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣟⣫⢿⢮⡳⢄⠈⠻⣆⠀⠀⠀⠀⠀⠀ ⣿⣯⡉⠉⠑⠒⠲⠒⠒⠋⠉⠁⠄⠐⠀⠀⠀⠀⢨⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣦⣝⣯⣷⠈⠛⡆⠀⠀⠀⠀⠀ ⠹⣿⣝⣶⡦⢤⣀⣀⣀⣀⣀⣠⡤⢶⣖⣭⣷⣤⡾⠃⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢩⣙⣿⣿⣿⠷⠶⢧⠀⠀⠀⠀⠀ ⠀⠉⠻⢦⣌⣉⡻⢲⠲⠶⠶⠚⠛⢛⣷⣿⣿⣿⠙⢷⡀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⠉⠀⠀⢹⡄⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠒⠒⠾⠿⢿⣿⣾⡏⠀⠀⠹⡄⠀⢷⠀⠀⢀⣀⣀⣀⣀⢸⣿⠀⠀⠀⠀⠀⡾⢀⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡀⠀⠀⠀⢹⣤⠼⠒⠋⠉⠉⠉⠉⠉⠙⠛⠳⢤⣀⣀⡾⢡⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣶⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠋⠓⠦⡀⠈⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠈⠻⣦⡀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠘⢦⠀⢹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⣀⣀⡀⠈⢻⡄⠀⠀⢠⡟⠁⣠⠤⠤⢤⣄⡀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢀⣾⠁⠀⠙⢦⡄⠁⠀⠀⠈⠀⣾⠉⠀⠀⣇⠈⠙⣶⡀⠀⠀⢿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡙⣧⡄⠀⣧⣹⡄⠀⠀⠀⣽⢹⡆⠀⢀⣿⣤⣾⣿⢿⡀⠀⣼⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢻⡟⢿⣿⣷⣾⣿⣷⠀⠀⠀⣿⠛⢿⡿⣿⣿⣿⠟⣿⣸⣇⣤⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡴⠷⣄⡻⣎⣻⡿⠟⠓⠓⠦⠼⣦⡈⠻⠦⣥⡤⣾⡿⠗⠒⠚⢻⣷⡤⠤⠤⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠓⢲⡤⣍⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⣉⣉⣩⠟⠉⣻⣟⠀⠀⣼⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢀⣿⡗⠛⠒⣾⣿⠟⠂⠀⠀⠀⠀⠀⠙⠓⢳⣴⠞⠋⠉⣹⣾⠿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⠤⠤⠽⠿⣄⡉⠳⢤⣀⣈⡦⡤⠤⣤⣤⣤⣤⡤⠖⠋⢁⣠⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢶⣮⣝⣿⣟⣍⣥⣤⣴⣶⣶⠿⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⢿⡟⢩⡿⠃⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠋⠻⣷⣮⣢⣿⣷⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠁⠀⠀⠀⠹⣿⣯⡍⣻⡇⠀⠀⠒⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⣀⣠⠴⢶⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⣸⣉⣻⣿⣷⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠁⣿⣾⣦⠴⠒⠋⠁⠀⢀⡴⢿⣤⣄⡀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠉⢻⡄⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡆⢸⣿⣿⣷⡄⠀⠀⠀⢾⠀⠀⠀⢻⣿⡶⢾⣉⡀⠀⠀⠀⠀⠀⠀⢀⣿⣤⠴⢛⠻⠿⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⡄⢿⣿⣿⣇⠤⠴⠒⣺⣷⡀⠀⠀⠹⣿⣦⣌⠁⠀⠀⠀⠀⠀⣀⣾⣿⣅⠐⢮⣐⣢⣘⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⠿⠿⠷⠴⠾⠿⠿⢷⡀⠀⠀⢻⣿⣿⣷⣦⣤⣤⣶⠾⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠞⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⡂⠰⠢⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠤⢔⡕⢱⠋⣴⣦⠂⢈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣔⠉⠉⢇⢸⡄⠿⡏⢳⣿⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⣙⣀⡼⠋⠁⢻⡵⠋⠙⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⡘⣀⠤⢤⣀⡀⠀⢠⣞⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⢀⣄⣷⣿⣿⣷⣑⡀⢠⣿⣟⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⢳⢦⠈⠛⢛⠧⡫⠊⠙⣍⢙⢶⡀⡠⢤⠀⠀⠀⠀⠀⢀⣾⣿ ⠀⠀⠀⠀⠀⢻⣘⢣⡀⠀⠹⡤⢀⣠⡼⢻⣧⡏⡳⠀⡆⠀⠀⠀⣠⣿⣿⠏ ⠀⢰⣖⡠⠄⣁⠪⠼⠈⠐⢢⠽⢶⣾⡇⣸⠞⠊⠀⠀⡇⠀⢄⣼⣿⠻⠏⠀ ⠀⠸⡌⢿⡢⡀⠉⠢⣀⡠⠊⠒⠐⠃⠀⣹⢶⡀⠀⢨⠃⢠⠿⣯⡹⠿⡁⠀ ⠀⠀⢣⠈⡿⣾⠦⠀⠙⡇⠒⠠⠤⢀⣈⣈⡆⠑⢤⠮⣰⣿⣿⡤⣻⠒⠇⠀ ⠀⠀⠀⡛⠀⠀⢣⠀⡸⠁⠀⠀⠀⠀⠀⠀⠢⡀⢀⣿⣿⣿⠏⠧⣄⠼⠀⠀ ⠀⠀⡰⠀⠀⢀⠀⡝⠐⢄⠀⠀⠀⢀⣀⢤⣤⣼⣿⣿⡿⢃⣀⡤⢮⣤⠀⠀ ⠀⡐⠁⠿⢀⠊⠌⠘⢄⠀⠑⠤⣴⣫⡋⣃⣿⣿⣿⣿⣿⡀⡙⢿⣶⠋⠀⠀ ⢰⣤⣀⠀⢂⠌⠀⠀⠈⠢⣀⣾⡝⢯⣱⣿⣿⣿⡟⠘⣗⣳⣸⡞⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⢠⠃⡠⠤⡀⠈⠂⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠔⠊⠉⠀⠀⡇⠀⡇⠀⢣⠀⠈⠆⠀⠈⠄⠀⠀⠀ ⠠⠒⠒⢄⠀⠀⠻⣄⠀⠀⠀⢸⠁⠀⢰⠀⠈⡄⠀⠘⡀⠀⠸⠀⠀⠀ ⠃⡖⠢⡀⠀⢄⠀⠘⢧⣀⣀⣼⢤⡄⡀⡆⠀⢡⠀⢠⠀⠀⢠⠀⠀⠀ ⡀⢣⠀⠑⠄⠀⠑⡀⡶⠿⠧⠼⠚⠋⠻⠼⣀⠈⣔⡝⠁⢀⠂⠀⠀⠀ ⢡⠀⠡⢀⠈⠢⡀⢐⠧⣀⢀⠀⠀⠀⠀⠀⠀⠉⠋⠉⢉⣉⢐⣀⡀⠀ ⠀⠑⠤⡀⠜⠓⢿⠃⡠⢲⢼⡄⠄⠔⠹⣱⣶⣄⠀⠀⢃⠑⠁⠀⠈⢆ ⠀⠀⠈⢉⠝⢆⠇⢰⠀⠈⢟⠿⢾⡀⠀⠙⠭⠁⠑⡀⠀⡄⠀⠀⠀⠈ ⠀⠀⠀⠃⠀⠀⡆⠈⠄⠀⠀⠉⠉⢣⠀⠀⠀⠀⢠⣃⠀⠃⠀⠀⠀⢠ ⠀⠀⠀⢄⠀⠀⢥⠒⠚⢦⣀⠀⢀⠌⠑⠤⠐⢪⣇⢀⡕⡀⢀⡀⠔⠁ ⠀⠀⠀⠀⡕⠈⡈⠂⠄⠋⡠⣴⣿⣷⣶⠦⠉⡿⠀⠀⡠⡁⠀⠈⠢⠀ ⠀⠀⠀⠀⠉⠘⠒⢄⠀⠘⠆⡈⠉⢡⣀⡤⠚⠀⣠⡮⠥⣮⠂⠠⠘⠀ ⠀⠀⠀⠀⠀⣴⠖⠒⣱⠦⢤⣀⣉⡉⢁⣤⠒⠛⢿⡖⠀⢸⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡀⠀⢀⣩⠷⡾⢧⣀⣼⠿⠦⣀⠀⣹⡤⡼⠀⠀⠀⠀

⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠆ ⠀⠀⠀⠇⢆⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⡠⢺⠈ ⠀⠀⢸⠀⠀⠣⡀⠀⠑⢄⠀⠀⠀⢀⢼⠀⠀⢠⡊⠁⠀⢀⠄⠀⡈⠀ ⠀⠀⠸⠀⡄⠀⢸⡦⡀⠀⠑⣀⡔⢁⠖⠈⠉⠉⠊⠴⣤⣹⡀⠀⠇⡆ ⠀⠀⠀⠆⢰⠀⡌⠣⢱⠀⠀⢹⠐⠁⠀⠀⠀⠀⠀⣀⠠⠖⣅⠜⢀⠃ ⠀⠀⠀⠐⠄⠲⣧⠀⠋⠀⣠⣋⠀⠀⠀⠀⠀⡀⡀⠉⢆⡘⢅⠠⠊⠀ ⠀⠀⠀⠀⠰⠖⠈⡠⣤⣾⣧⣤⣬⣦⡀⠀⣸⡯⠉⢻⡷⡏⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⡇⡇⣿⣿⢻⣿⡧⠠⣿⢷⠀⢈⣦⡦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣋⡜⠝⡿⠿⣿⠿⠃⠀⠉⠘⣢⣾⣨⠗⡂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⡈⠻⣅⡀⠘⠲⢤⣄⣀⣀⣹⣽⣫⠔⠁⠀⠀⠀ ⠀⠀⢀⠒⣴⠁⡆⠀⠈⠉⢉⣿⣿⡍⠑⠒⠙⠛⠉⡉⡁⢀⣠⣆⠀⠀ ⢸⠁⢌⡶⢻⡉⣇⠀⠀⠀⣤⣿⡟⠁⠀⢀⡀⡀⠀⣿⣯⣁⠘⢿⡆⠀ ⠀⠙⢉⣱⡚⠭⠛⠂⣰⠉⣿⣿⠏⠀⢠⡿⠋⢱⡄⣿⠧⠌⣣⣼⣿⠀ ⠀⠀⠀⠡⡀⠀⠀⠈⡨⠋⠙⣣⣵⣶⣿⣇⣃⣤⠗⠘⣿⣾⣛⣻⣿⡇ ⠀⠀⠀⠀⠈⠢⣶⣾⣦⢸⣟⡛⠉⣻⣿⣹⣿⠏⠀⠀⠹⣿⣿⣟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣖⡒⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣲⠶⠒⣀⣠⡍⠓⠀⠉⠲⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⠞⣡⠎⢠⡴⠋⠁⠀⣀⣀⣀⠀⠀⠘⣎⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠤⠤⠤⠚⣁⡾⠁⢠⣿⠁⠀⣴⣿⣿⣦⡈⠃⠀⠀⡘⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⠶⠶⠿⢿⡇⠀⢠⣿⠀⡸⣿⢿⣿⠻⢷⡀⣰⣾⣷⣾⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⠀⠀⣰⢷⠀⠘⣿⡄⠀⣿⣼⣿⠖⠾⢿⣿⣿⣿⣋⠁⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⣤⡆⣬⣥⠾⠀⠀⡇⣻⢦⡉⠉⢿⡇⣠⣴⢿⡿⣿⣿⡛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡉⠲⠖⠀⢀⡼⣱⠏⠀⠈⠀⠘⣿⣯⢠⣿⠁⠀⠙⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣴⣺⠯⠞⠁⠀⠀⠀⠀⠀⢟⣿⠟⠁⠀⠀⠀⢀⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⣡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠁⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⣴⣶⠛⠙⠛⠷⣦⣤⣄⣀⣀⠀⠀⢰⡟⣅⣤⣴⡞⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⣷⣽⣿⣿⣿⣿⣶⣍⠙⢯⡁⠀⠀⠈⢠⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣤⣈⣻⣿⡟⣿⣿⣿⢿⣿⣆⠈⣷⣀⠀⢀⣿⣿⣯⡇⢘⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣀⠙⠒⠛⠿⣧⣽⣟⣿⡿⠃⢹⡿⠁⣨⠿⣿⡿⢭⡽⠷⣛⡉⠋⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠛⣆⠀⠀⠈⠉⠛⠛⠛⠓⢛⣧⠟⠁⠀⠘⢿⣦⡀⠀⡙⢿⣿⣄⠀⢀⣤⠶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡇⢸⢹⡄⠀⠀⠀⠀⠙⢦⡴⠋⠁⠀⠀⠀⠀⠀⢻⣿⡄⣸⣦⠋⣯⢷⣿⡁⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⡇⠘⡎⢷⠀⠀⠀⠀⠀⠘⢿⣶⣄⣀⣀⡀⢀⣤⣾⡿⠷⣿⣿⣠⣿⠄⠈⣿⡆⠀⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢧⡙⠻⢷⡇⠸⡗⠦⣀⡀⠀⠀⠈⢿⣮⡉⠙⠻⢿⣿⣿⡥⠎⢹⠹⣿⠟⣠⡾⠃⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡟⠁⠀ ⠀⠀⠠⣶⣶⠦⠤⣄⣀⠀⠀⠙⠳⢤⣀⢀⡿⠀⠀⠙⠓⢦⣤⣀⣙⣛⣿⣛⣞⣻⡟⠀⢠⣼⣿⡷⠿⠉⠀⠀⠀⠀⢰⣿⠀⠀⠀⣀⠤⢀⣾⣿⣿⠿⢿⣿⡟⠀⠀⠀ ⠀⠀⠀⣿⢿⣶⣦⡀⠉⠙⠲⢦⣄⠀⠉⠉⠀⠀⠀⠀⠀⠈⢷⠀⠈⠉⠛⣿⢹⣿⠃⣀⣾⣟⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠸⣅⣰⣿⣿⣿⣿⣦⡀⢉⣄⠀⠀⠀ ⠀⠀⠀⣿⠈⢻⣿⡿⣦⣄⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⣠⠞⠷⣤⣄⣀⣼⡇⠀⠀⠀⢸⡿⣧⣱⣄⠀⠀⠀⠀⢘⣹⡇⠀⠀⢀⣴⣿⣿⡇⠈⠻⣿⢛⡏⠀⡆⠀⠀ ⠀⠀⠀⢿⡆⢸⠏⠿⣦⡙⢷⣄⠀⠀⠀⠀⠙⣦⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣷⠈⢿⣄⠂⠀⠀⠀⢈⡿⠀⠀⢠⣾⠟⠉⣙⣿⣦⡞⠉⠉⢳⣶⠁⠀⠀ ⠀⠀⠀⠘⣿⠄⠠⠞⢻⣷⣌⢿⣷⣄⠀⠀⠀⢹⣻⡗⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢢⠈⠻⡄⠈⠻⣧⡀⠀⢠⣾⠃⠀⣠⣿⣿⣷⣼⡃⠀⢙⣿⡧⠤⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠸⣤⠄⢀⣴⡿⢿⣦⠻⡟⠋⠀⠀⠀⢹⡇⠀⠀⠈⠉⠓⠒⠲⠤⢤⣄⣀⣈⡀⣀⣿⠀⠀⠈⠛⢶⡿⠛⢦⣼⣿⣿⣿⣿⣿⣿⡒⠋⣹⣷⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣞⣾⠋⠄⠀⠈⢷⡘⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣁⠀⠀⠀⠀⠀⠙⣶⣿⣿⣿⣿⣿⣿⡿⣿⠉⠛⠁⢸⠀⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⠃⠁⠀⠀⠀⠈⢻⡄⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠁⠸⣷⣦⣄⣠⡴⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡏⠐⠀⡀⠀⠀⠀⠀⢻⣦⣶⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣠⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⣹⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⠁⠀⢰⠀⠀⢀⡿⠁⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣀⣠⠾⣥⡤⢤⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⠟⠀⣄⣄⣐⠃⠀⣸⠀⢀⡏⢻⡀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣠⣶⠟⣻⣭⡙⢿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⠴⠖⢾⣿⣿⣷⡄⠈⣿⣬⠇⠀⠀⠀⠀ ⠀⠀⢠⠟⠀⠈⣿⢿⠁⠀⣴⠃⢀⡞⠀⠀⢿⡄⠀⠀⠀⠉⠓⢠⣀⣄⣴⡿⢁⣼⠟⠉⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡃⠀⠀⠀⠙⣿⣿⣿⣾⣼⠟⠀⠀⠀⠀⠀ ⠀⢠⠏⠀⠀⠀⠀⠈⠀⣴⠁⢀⡞⠁⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢉⣿⣿⣴⣟⡷⣄⠀⢦⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⣿⣄⠀⢶⡀⠈⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⢰⡇⠀⠀⠀⠀⠀⠀⢸⠁⢠⡞⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⣰⣿⡏⠸⣿⡉⠁⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⣿⣧⡝⣿⡄⠀⢿⣦⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣟⢻⢶⣤⣀⠀⡀⠁⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣼⡿⢯⣿⡄⠙⢿⣶⣵⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠸⣷⣀⣼⣿⣄⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⠠⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠊⠀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⢀⠇⡸⠉⠀⠀⠀⠀⠀⢀⠔⠒⢄⠀ ⠀⢸⠀⣌⡐⠠⠤⠄⣀⠀⡠⢊⠤⠂⠀⠀⠇ ⠀⠠⠂⠛⠁⠀⠀⠀⡐⠉⠲⡯⠛⢃⠀⠀⢸ ⢠⠁⡦⠒⠢⡀⠀⠌⠠⠒⢶⠵⠀⠀⠉⠉⠁ ⢏⠀⡧⢴⣆⣧⠀⠅⣷⣴⣀⡆⡇⢀⣾⡆⠀ ⠘⡀⠑⠛⠒⢉⡹⢏⠕⠓⠚⡣⢃⣾⠏⡰⠀ ⠀⠈⣐⠤⠄⣀⣱⣏⣠⢴⣮⣀⡾⢏⠔⠀⠀ ⡏⠀⡇⠀⡌⠿⠿⣿⢆⡘⣿⣿⠁⠀⠀⠀⠀ ⢛⢠⠐⢉⡇⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠇⠁⠋⠤⠰⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⠀⠀⠰⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⣁⣈⣉⣹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⣲⡒⢤⠀⡶⣚⣠⣤⣤⣤⣤⣭⣄⣠⠔⠒⠢⣄⠀ ⠀⠀⠀⠀⢀⠊⢣⠉⠚⠒⠓⠛⠋⠉⠉⠒⢄⠈⠑⠿⠡⠊⢡⠛⢺⡆ ⠀⠀⠀⠀⠀⢢⡴⠃⠀⠀⡄⠀⠀⠀⠀⠀⠘⢣⠀⠀⠣⡀⠈⢉⡿⠁ ⠀⠀⠀⠀⢠⠏⡡⣀⠀⡼⠀⢀⡀⠀⠀⠀⠀⢄⢧⠀⠀⠈⠉⠑⠣⡀ ⠀⠀⠀⣰⠋⡸⠁⠀⡨⢇⠁⢸⠑⢄⣀⠤⠒⠈⢻⡄⠀⠀⠀⣻⠉⠀ ⠠⣴⡞⠋⢀⡇⢠⠟⠀⠘⣤⡏⠀⠀⠙⠒⢤⣀⣀⠹⡀⠀⠀⠸⡆⠀ ⠀⠈⠻⢦⣼⣀⣾⠀⣰⡶⠈⠳⠀⠾⡇⠠⢀⡿⢿⣟⡳⠀⠀⠀⢷⠀ ⠀⠀⠀⣰⣥⣿⣿⠀⠀⠠⠀⠤⠔⠈⠀⣠⠾⠖⣩⠟⠁⠀⠀⠀⠈⡆ ⠀⠀⠀⠉⠀⣽⣿⣷⣦⣅⣀⣀⣀⣀⣨⠤⠒⠉⠀⠀⠀⠀⣀⡠⠚⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⠿⠭⣱⠖⠩⠄⡒⠒⠒⠠⢤⡤⠒⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⡰⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠈⢸⠀⠀⠀⠘⠀⠀⠜⠀⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⡄⠀⠀⢸⠀⠀⠀⠀⡀⠊⠀⠀⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠁⢱⡀⠀⢸⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⡇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⣠⡤⢤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⠸⠀⠉⠓⢶⣄⠈⠻⣄⠀⠀ ⠀⠀⠀⢀⣴⣋⠀⠉⠳⢤⡀⠀⠀⠀⠀⣸⢃⣿⡄⢣⠀⠀⠀⠀⠀⠀⠈⢷⡀ ⠀⢀⣠⠟⠋⠁⠀⠀⠀⠀⠙⢧⠀⠀⢀⡇⣾⣿⣿⣦⡤⣀⡀⠀⠀⠀⠀⠀⣧ ⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⠃⣸⣿⣿⣿⣿⡾⢽⡲⢄⠀⠀⠀⣿ ⠈⣷⠲⣭⣥⣐⠦⣀⠀⠀⠀⠀⠘⡆⢸⡀⣇⠹⣿⣿⡟⠁⠀⠉⠳⣆⠀⠀⣿ ⠀⠙⢷⣿⢻⣿⣿⣾⣧⣄⠀⠀⠀⡏⡍⠉⠉⠙⢻⣿⡀⠀⠀⠀⠀⠘⢦⣴⠇ ⠀⠀⠀⠈⠻⠶⣿⣿⣿⣿⣷⣶⣤⠇⡇⠀⠀⠀⡴⢿⡿⣦⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠟⠙⠿⣿⣿⣿⣿⠄⢿⠀⠀⠀⠉⠛⢻⣬⣧⣀⡶⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠀⢀⡀⠘⣯⠉⠁⠀⠈⢧⠀⠀⠀⢠⡿⣻⣿⣯⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⣏⣀⡀⢹⣶⡽⠟⠻⣶⣄⡈⢳⣄⠀⣾⡷⠿⣿⡿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣧⠀⠉⢻⡏⢀⣠⡼⣿⣿⣷⡀⠙⢦⣹⣷⣾⢿⣠⢷⠲⢦⡀⠀ ⠀⠀⠀⠀⠀⢻⡀⠀⠈⢿⣾⡿⣦⣾⣿⣿⣇⠀⠀⠈⣿⠗⠭⢒⣷⡀⠈⠉⠀ ⠀⠀⠀⠀⠀⠈⢧⡀⠀⠈⠛⠛⣻⠟⢛⠭⣄⣀⡤⢤⡼⣤⡾⠋⠀⠻⠶⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⣩⠷⣶⣤⣴⣇⣰⡏⣀⣈⣙⣤⣾⢹⡍⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⡀⠀⡰⠋⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⡟⠙⠛⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣧⡼⠁⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣄⢠⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠛⠁⠀⢧⣠⣴⣟⠨⣿⣿⣿⣿⣿⣿⣿⡇⠈⣹⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣻⠀⠀⠀⣸⣿⣧⠏⠀⠛⠛⠛⣿⡿⠻⠿⠴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠳⣶⣿⣿⠃⠀⠠⣄⢀⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⣿⣿⣿⡇⠀⠀⢈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣧⢸⣿⣿⣷⠶⠛⠉⠘⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣸⣿⣿⣿⠀⠀⠀⠀⢹⡿⠿⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣷⢿⣿⣿⡀⠀⠀⠀⠈⣷⣴⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⡟⠘⣧⠖⠋⣏⠑⠛⣯⣿⡾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠓⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣶⠔⢉⢂⠄⠀⣠⣶⣿⣿⣿⣿⣿⣷⣦⡀⠀ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⡟⠛⡁⢀⣣⣌⣢⣀⠝⠛⠿⡿⠟⠛⢿⣿⣿⣿⣄ ⠀⢠⣿⣿⣿⡏⠁⠀⠀⢃⣴⢾⣿⣿⣿⣿⣿⣷⣦⣀⠃⢀⣠⣾⣿⣿⣿⣿ ⠀⢸⣿⣿⣿⣿⣶⠆⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⡿ ⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢩⣿⠏⣼⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⠇ ⠀⠘⣿⣿⣿⣿⣾⠋⠉⠸⢿⣿⣿⣇⠁⠘⠿⣿⣿⣿⠀⠀⢻⣿⣿⣿⡟⠀ ⣦⡀⠘⣿⣿⣿⣿⠀⠀⢀⣤⣿⣿⡏⠀⢀⣤⣾⣿⡿⠀⠀⢸⣿⣿⡟⠀⠀ ⠸⣿⣦⣬⣿⣿⣿⠆⠀⠈⠛⠿⠛⢠⣤⡄⠙⢻⣛⡁⠀⠂⣾⣿⣿⣷⣾⠏ ⢰⣿⣿⣿⣿⣿⣇⠀⢰⣫⣴⣷⡄⠀⣠⠶⢰⣿⣧⣹⡆⠀⣾⣿⣿⣿⡿⠗ ⠀⠙⠻⣿⣿⣿⣿⡦⡘⠿⠿⠟⢸⡇⠃⢱⠋⠻⠿⠟⡡⢊⠙⢿⡿⠀⠀⠀ ⠀⠀⠘⠛⠛⣿⡁⠀⠈⠒⠠⣀⠀⠈⠉⠁⠀⣀⠔⠀⣤⣿⡀⠀⠀⠀⠀⠀ ⠀⠠⠚⡹⡍⠽⣿⣦⣄⡀⢀⡜⠈⠀⠂⠒⢹⣀⣠⣾⣿⡿⠒⡎⡀⢘⠉⠃ ⢀⠖⣃⣁⣁⢢⣿⣿⣿⣿⡍⠀⡀⠀⠀⠀⡠⢺⣿⣿⣿⠀⡀⠧⠧⠜⣀⠀ ⠐⠎⠀⠀⠀⡇⡼⣿⣿⣿⣷⡀⠈⠂⠔⠀⣠⣾⣿⣿⣿⠹⠉⠈⠉⠉⠰⠀ ⠀⠀⠀⠀⠀⠏⠀⢘⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⡟⠀⠑⡇⠀⠀⠀⠀⠆ ⠀⠀⠀⠀⠠⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠁⠈⠛⠛⠛⠛⠁⠉⠛⠛⢻⠁⠀⠑⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠉⠛⠲⢖⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⣒⠦⢉⢱⠀⠀⠀⠀ ⡄⣄⣀⣀⠀⠠⠤⢀⣀⠠⠵⣮⡳⡄⠀⢀⣀⡠⠊⡡⠐⠉⠀⠀⠸⠸⠀⠀⠀⠀ ⠇⢁⠀⠀⠈⠉⠖⢟⠐⠀⢒⡢⢵⠸⠁⠀⠀⠱⢸⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀ ⠸⠈⠄⠀⠀⠀⠀⢰⢸⢴⡣⠊⠀⠀⠀⠀⠀⠀⣧⠡⠀⠀⠀⠀⡇⡜⠀⠀⠀⠀ ⠀⢣⠘⡀⠀⠀⢀⢆⠏⠸⠀⠀⠀⠀⠀⢀⠤⠀⠡⠕⣕⠒⠒⣈⡠⠁⠀⠀⠀⠀ ⠀⠀⢣⡑⢂⣀⡡⡜⢄⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠱⡀⠀⢀⢎⢔⢶⡲⢤⡀⠀⠀⠀⠀⢰⡠⢺⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⠀⣇⡖⠒⠴⡀⠈⡆⡖⠁⠀⣦⠸⡀⠀⠀⠀⠉⠠⠃⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠱⡌⢣⠁⠀⠀⠐⡀⠰⡡⡀⠀⠀⢀⠇⠀⠀⠀⠀⠁⡩⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⡢⠕⢄⡀⣠⣴⣶⡟⠛⢲⡴⠊⠀⠀⣀⣠⣴⣇⢠⢲⠴⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⢈⣵⡦⠬⡯⣝⢫⡀⡤⣺⡏⡏⠉⠉⡄⢫⠙⡘⣟⣻⣩⣢⡌ ⠀⠀⠀⠀⠀⠀⡴⢋⡉⠁⡀⢰⢿⣮⠼⠻⠋⣁⡇⠀⠀⡄⡼⣀⢃⢄⣊⠲⢄⢠ ⠀⠀⠀⠀⠀⢰⡿⠥⠀⠤⣈⡆⡸⢎⢷⣶⣿⣿⠇⢀⣴⣽⡉⢶⣌⠉⠸⠑⠀⠁ ⠀⠀⠀⠀⠀⢰⢸⡀⠀⡆⠈⣯⣒⡋⠵⢻⠿⠧⠞⢋⡷⡈⠉⠀⠈⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡈⠁⡰⢁⡐⠓⠒⡤⠧⡎⠀⢀⠴⠋⠀⠈⢐⠒⢒⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠊⡹⠁⠀⠉⠀⠀⢸⠀⠀⠛⠩⠴⢤⣀⣋⣒⣫⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢔⣩⠋⡀⠁⠉⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡠⠐⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⢣⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠖⢁⡌⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠠⢄⣀⠄⠀⠀⠀⠑⠒⠒⠁⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠚⠁⠀⠀⠀⡇⠀⡠⠀⠀⠀⢀⠈⠢⣀⣴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡃⡀⠌⣐⠒⠒⢊⣴⠞⠒⠚⠂⢴⡣⠂⠀⠈⣏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡆⠲⡖⠉⠈⡙⢀⢰⠁⠐⡆⡄⠀⠀⠑⡀⠀⠀⠀⠣⡀⠀⠀⠀⠀ ⠀⠀⢠⠇⠠⡁⠀⢸⣿⢦⢹⡀⡏⣷⢸⠀⠀⠀⢡⠀⢸⡇⠀⠀⠑⢄⠀⠀ ⠀⢀⠃⡾⠀⢣⠀⠘⢼⣿⢸⢣⠐⢌⡿⠀⠀⢠⠋⠀⡆⠘⢄⠀⠀⠀⠑⢄ ⢀⠆⢠⡑⠁⠙⡧⢀⠀⢀⠜⠀⠁⠤⢤⠤⠾⠤⡀⠸⠀⠸⠀⣨⠐⠂⠠⠄ ⠘⠀⢸⠑⠤⢠⣃⣀⣀⣤⣤⠖⢄⠀⡆⠀⠀⢀⠇⢘⡀⠀⠃⠈⢆⠀⢸⠀ ⢠⠀⠀⠣⡐⠀⠈⠙⠻⡉⠀⣀⣀⢆⠈⠒⠒⣉⠴⠁⠱⡀⠀⠀⠀⠀⠁⠀ ⠈⢆⠀⠀⠈⠓⠊⠭⡅⠀⠀⠀⠤⠤⣥⠶⠛⠁⣀⣣⢀⢀⡦⠂⠉⠱⡄⠀ ⠀⠀⠑⠤⠀⣀⠠⠔⠁⢠⠒⠒⠒⠒⠂⠵⣴⠁⠀⠈⣿⣭⠖⠊⠉⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠉⢉⡔⠋⡹⠒⠐⠊⠑⠢⠭⣉⣀⣀⡜⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣤⣄⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠖⠉⢀⡇⣠⠖⠢⣄⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣠⠊⠀⢧⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠉⡆⠀⣀⣉⣽⣦⣤⣽⣆⣀⡎⠉⠉⠙⠻⣿⠟⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠈⡆⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⢀⡅⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⠀⣼⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣼⣿⢟⣯⣿⣿⣿⣿⣿⣿⣿⣶⣶⣯⡻⣿⣿⣮⡀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣠⣾⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣮⣿⣿⣿⣦⣤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣳⣿⣿⡿⢻⣿⣿⣿⠋⣿⣿⣿⣽⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⡿⠁⣰⣿⣿⣿⣿⣿⣿⠏⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣶⡿⠉⠉⠀⠼⣿⣿⣿⣿⣿⣿⡌⠉⠀⠰⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀ ⣷⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⠇⠀⠀⠀⣠⣶⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⢻⣿⣷⣄⠀⠙⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠀⠀⠀⣀⢀⣿⣿⣿⣿⣿⣤⣤⣶⡿⠀ ⠈⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠋⠉⠀⠀⣀⣀⣉⡋⠉⠁⠠⣶⣿⣿⠇⠀⠈⢉⣭⣥⣤⡀⠀⠀⠈⠹⣿⣿⣿⣿⣿⡿⣿⣿⠃⠀ ⢶⣼⡿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣾⢉⣠⣤⣿⣦⠀⠀⠀⠀⡠⣔⡄⢰⣿⣿⣧⡈⢻⡆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟ ⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠸⣿⣿⣿⣿⣿⣿⢀⢴⠒⡞⠳⡌⢳⢸⣿⣿⣿⣷⣾⡇⠀⣠⣾⣿⣿⣿⣽⠛⠛⠉⠁⠀⠀ ⠀⠀⠈⠙⠿⣟⣿⣿⣿⣿⣿⣿⠦⡀⠙⠻⠿⠿⠛⠁⢸⣸⠀⢹⠀⢈⡞⠀⠙⠿⠿⠿⠋⣠⠞⢁⠀⠙⠻⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠴⠿⠿⠿⢿⣽⠟⠛⠁⠀⠈⠒⢤⡀⠀⠀⠀⠀⠉⠓⠚⠓⠊⠀⠀⠀⠀⢀⠴⠊⠀⣠⣾⡆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⣠⣾⣿⣿⣧⠀⠀⢀⣀⣀⡀⠀⣀⠀⠀ ⠀⠀⣠⢲⠃⣍⣏⠉⣹⣿⣿⣷⣤⣀⠀⠀⠀⠀⣰⠁⠈⠉⠓⠒⠤⠔⠊⣇⠀⠀⣠⣾⣿⣿⣿⣿⠗⠒⢺⠁⠀⠀⢸⠀⠉⡇⠀ ⠀⠀⣇⣸⣀⡟⢼⣀⡁⠘⣿⣿⣿⣿⣿⣶⡴⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡑⣾⣿⣿⣿⣿⡿⠛⠀⢠⡞⠐⡇⠀⣼⠀⢀⠀⠀ ⢀⡞⠋⢉⣀⣀⣀⣀⡉⣶⣿⣿⣿⣿⣿⣿⣧⠈⠳⢄⠀⠀⠀⠀⠀⠀⢀⡴⠃⣿⣿⣿⣿⣿⣆⠀⢀⣰⠧⠤⠖⠤⠭⣀⡘⠀⠀ ⠈⣠⠊⠁⠀⠀⠀⠀⡏⠀⢻⣿⣿⣿⣿⣿⣿⣄⠀⠀⠙⠢⣄⣀⡠⠒⠁⠀⣼⣿⣿⣿⣿⣿⡿⣿⡟⠒⠊⠉⠉⠉⠑⠢⣱⠀⠀ ⠀⠘⠀⠀⠀⠀⠀⠀⡇⡰⠋⠹⣿⣿⣳⣿⣿⣿⣦⣄⠀⠀⠀⠁⠀⢀⣤⣾⣿⣿⡽⣿⣿⠟⢦⡈⢇⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠙⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣹⠋⠀⠀⠙⢾⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠘⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢹⠛⠻⠿⠿⠟⠛⠁⠀⠀⠙⠛⠛⠛⢻⡅⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠒⠂⠐⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⡖⠖⡆⣀⠀ ⠀⠀⠀⠀⠀⠇⠀⢠⣾⣷⣦⡀⠀⣴⣾⣷⡄⠀⠘⡗⢄⠧⢤⠋⢠⠀ ⠀⠀⠀⠀⢰⠀⠀⠸⣿⣿⣿⠇⠘⣿⣿⣿⠇⠀⠀⡏⣧⢄⠀⡏⣩⠇ ⠀⠀⠀⠀⢠⢗⡤⣀⣈⡉⠀⠀⠀⠀⢉⣁⣀⣤⡾⡝⠁⠀⡏⠁⠀⠀ ⠀⠀⠀⠀⠈⠣⠍⡑⠚⠯⠿⠻⠟⠿⠽⠛⢊⣉⣴⣁⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡝⠉⠁⠀⠉⠈⠉⢹⠉⠁⠀⢀⠧⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠊⠀⠃⠀⠀⠀⠀⠀⠀⠀⡇⣀⠔⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠞⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡎⠀⠑⠤⢔⢪⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠀⠀⠀⠀⡘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⡠⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠋⠑⠂⠯⢄⢠⠋⠑⢄⠀⠀⠀⠀⢠⠂⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡀⠀⠀⠀⠀⡼⠁⠀⢀⡤⠤⢤⣀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠾⠛⠋⠉⠉⣿⡇⠀⠀⠀⣾⡇⠀⠀⢸⡄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⠛⠛⠁⠀⠄⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠸⡇⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢿⡇⠀⠀⠀⢻⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠖⠛⠲⢦⣀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⡇⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀ ⢀⡾⠁⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠻⣷⡦⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⣼⠁⢀⡖⠲⣄⠀⠀⠀⠀⠓⣄⠀⠀⠀⠀⠘⢷⣷⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠈⡇⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⡏⠀⢸⡇⠀⠈⢷⡀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠙⢷⣄⣀⣤⣴⣿⣿⠗⣿⣿⣿⢀⣤⡀⢳⡀⠀⠀⠀⢹⡀⠀⠀⣰⠏⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀ ⡇⠀⠈⣇⠀⠀⠀⠹⣆⠀⠀⠀⠀⠙⢆⠀⠀⠀⣠⣴⣿⣿⣋⠡⠤⠏⣀⣼⣿⣿⢫⡾⣧⠜⢧⠀⠀⠀⠘⡇⢠⡾⢛⣿⠃⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠹⡄⠀⠀⠀⠈⢷⡀⠀⠀⠀⠈⢷⡀⠀⣻⠟⠛⠻⠾⠿⠟⠛⠋⠉⠀⠀⠀⠉⠙⠓⠾⣦⣀⠀⠀⣿⣄⡼⠟⠁⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡄⠀⠀⠻⣄⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠹⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣿⡿⠿⠓⠢⠶⠖⠛⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡀⠀⠀⠘⠲⣄⠀⠀⠀⠘⢷⡀⠀⠀⠀⢹⡿⣤⡀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢀⡀⠀⠀⣠⠏⢀⣀⠀⠀⠀⠀⠀ ⠀⠀⠳⣄⠀⠀⠀⠈⠛⠒⣲⡶⠃⣹⣷⣄⣴⠋⠀⠀⠉⠓⢒⡟⠁⠀⠀⢠⠀⠀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠙⡏⢉⡵⠋⠉⠉⠙⢦⡀⠀⠀ ⠀⠀⠀⠉⠳⢄⣀⣀⣀⣠⠛⠛⠋⣿⣶⡟⠁⠀⣠⠶⠒⣶⣦⣽⣤⣀⣠⠎⣠⠎⠁⠀⢯⠉⢿⣿⣷⣦⣀⠀⠀⠀⠀⠀⢻⡉⢠⠏⠀⠀⠀⠀⠀⠀⠹⣄⠀ ⠀⠀⠀⠀⠀⠀⣠⣞⣉⡠⣴⠂⠀⢀⡾⠀⠀⣰⠃⠀⠀⣿⢈⣿⣷⣄⠀⠀⡟⠀⠀⠀⠘⢶⣿⠿⣿⣿⠼⣷⣄⠀⠀⠀⠈⢧⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣟⠛⢹⠇⠀⠀⡿⠀⠀⠀⠘⣿⠛⢿⣿⣷⣄⣧⠀⠀⠀⠀⠀⠛⢤⡀⠁⠀⣿⠘⣆⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣ ⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠈⠳⡞⠀⠀⢰⣧⠀⠀⠀⠀⠘⢷⣉⠉⠁⢹⣿⡀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠉⠀⢸⡀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣧⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠉⠙⠒⠋⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⡤⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇ ⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠘⡇⢀⣠⠤⣌⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⢧⡀⠀⠀⠀⣀⣤⠴⣿⠋⠀⠀⠈⢷⡀⢸⠃⠀⠀⠀⠀⠀⠀⣰⠋⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⣼⢡⡏⠀⠀⠀⠉⢻⡶⢄⡀⠀⠀⠀⣀⡼⠃⠀⠀⠉⠓⠒⠋⠉⠀⣦⢻⣄⠀⠀⣀⡾⠃⣼⠀⠀⢀⣀⣠⠴⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣤⡤⡇⠘⣧⡀⠀⠀⠀⣼⠇⠀⠉⠉⠒⣺⣭⣤⣖⣒⣒⣛⡃⠒⠒⠤⣤⣿⠀⠉⠛⠛⠉⠀⢠⡟⠀⠀⠈⠉⠓⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣧⠀⠈⠙⠓⠶⠚⠁⠀⢀⡴⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣨⡿⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣀⣠⠿⣆⠀⠀⠀⠀⠀⢸⣷⡋⠀⠻⠿⠿⠿⢿⡿⠟⠛⠉⠀⠀⠀⣠⡟⠁⠀⠀⠀⢀⡴⢯⡀⢳⣄⠀⠀⠀⠀⠀⢀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⢦⡀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⢳⣄⣀⣀⣀⡤⠞⠋⠀⠀⠀⢀⣴⣋⣠⣤⣽⣭⡈⠙⠳⠤⡤⠤⠚⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠉⠓⠦⣤⣀⣠⣼⣻⣭⠽⠃⠀⠀⠀⢀⣠⣾⣿⣿⠋⡉⠉⠉⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡶⡶⠶⣶⣭⣷⣦⣄⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣠⡴⠚⠛⠻⢿⣿⣴⡿⠋⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠀⠀⠀⠀⢶⣯⣉⣙⠙⠛⠿⣶⣶⡶⠿⠟⠛⠛⢿⣿⣿⠁⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠈⠙⠛⣻⣿⣿⣿⣿⡁⠀⠀⠀⣠⣸⣿⣿⣧⡀⠀⠀⠀⠀⠈⢿⡟⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⢀⣠⣴⡟⠋⢉⣿⠟⠙⠿⢶⣦⣤⣿⡿⠛⠋⠉⢙⣦⠤⠤⠤⠤⣌⣿⠟⠛⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠲⠶⣾⣶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠒⢒⠚⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢤⣙⠛⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⠛⢉⣀⠤⠖⠚⠋⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⠉⠀⣀⡴⠖⠉⠁⠀⠀⠀⠀⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠛⢫⣍⣉⣉⣉⠉⠙⠛⠛⠛⠛⠲⠦⣤⣄⣀⣀⣤⡤⠤⠤⢬⣿⣦⡀⠙⣦⡀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠸⡇⠀⠀⠀⠉⠉⠙⠒⠶⢤⣀⣀⣴⣞⣉⣥⣤⣀⣀⣀⣀⠀⠉⠻⢄⠈⣷⠶⠞⠋⠉⠉⠉⠉⢻⡆⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠛⠻⢤⡀⠀⡇⠀⠀⠀⢈⣹⣿⠦⣼⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢰⡇⠀⣠⡾⠋⢀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⡀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢸⣧⡞⣿⣡⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣧⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣷⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣿⠏⢸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⢷⡀⠳⣄⠀⠀⠀⠀⢀⣀⣴⠇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣧⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣸⠇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠒⠀⠈⠳⣄⠳⣄⠈⠉⠉⠉⠉⠉⠉⠁⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣇⠀⠸⣆⠀⠀⠀⠀⣀⣀⡴⠃⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠈⠙⠛⠛⠶⠤⠤⠤⠴⠖⢲⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⡀⠙⠓⠉⠉⠉⠉⠁⢀⣴⣿⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢷⣤⣤⣤⠤⠴⠖⠛⠋⢸⡇⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⣴⠏⢀⣠⠶⢶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀⡴⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⣸⠃⣴⠋⢠⠞⣉⡴⠚⠛⠛⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠾⠋⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢺⡀⢠⠶⠶⠶⢤⡘⠆⠀⠀⠀⠃⢰⠃⢠⣏⠞⠁⠀⠀⢀⣤⡄⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⢦⣄⠀⢸⣷⣻⠀⠀⠀⠀⠙⢶⡄⠀⠀⠀⢸⡀⢸⡟⠀⠀⠀⠀⠈⣿⣷⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠈⠳⢾⣇⠙⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠈⣧⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠯⠶⠚⢛⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠘⢧⡘⣧⡀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡿⣦⣀⠙⢳⣄⠀⠀⠀⠀⠀⠀⣈⣧⣤⣤⣬⡿⢦⣷⣦⣄⣀⣀⣀⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠀⠀⣠⡤⠤⢤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡉⠲⢤⡙⠷⣄⠀⠀⣠⣾⡿⠿⣿⣻⣿⠇⠀⠆⠉⠙⣿⣿⡟⠋⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣏⣿⣧⡀⠀⢰⠏⢉⡷⠶⠿⢃⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣀⠀⠈⠙⢿⠭⠟⣿⣿⣿⠿⠃⠀⠀⠐⢀⣴⣿⡎⢻⡦⠤⠤⠴⠒⠛⣏⠁⠙⣿⠻⣾⣽⠋⣙⣷⣾⣍⢻⡥⠴⣟⠉⠙⡌⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠛⠶⠶⣾⣿⣶⣦⣭⣉⣷⣤⣠⢴⡶⢏⣻⣹⢱⠀⣷⠀⠀⠀⠀⠀⠘⡇⠀⢹⡇⠀⠀⢰⠇⣿⣀⡏⠹⣄⣴⢚⣛⣒⠦⣌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣯⣯⡥⠗⠀⠀⠀⠓⣌⢻⡹⡄⢻⡄⢳⣌⢷⣼⣿⡿⢸⠀⣿⠀⠀⠀⠀⠀⠀⢹⠀⢸⡇⠀⠀⣿⠀⡇⠀⠈⣻⢿⣉⡁⠀⠈⠛⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⣀⣀⣀⣀⣀⠀⠀⠀⢸⣾⣿⣿⣦⣿⡶⠿⠻⠏⠉⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⡼⠀⣾⣧⣀⠀⢹⡄⠳⣒⣋⣅⣀⡹⣟⢦⣀⠀⡡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣠⡔⠋⠉⠁⠀⠀⠉⠛⢦⣠⠟⠀⢹⡈⢿⣣⡀⠀⢀⣀⡠⣶⢿⣧⣿⠀⠀⠀⠀⠀⣼⠃⣼⢿⣤⡙⠓⠲⠽⠦⠾⠋⢹⡿⠄⣸⠀⠙⣤⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠞⡽⣧⡤⠤⠤⠤⢤⣀⡀⢸⣿⠀⢀⣸⣷⡈⠳⣝⢿⣾⣎⡳⣝⣧⣿⡿⠀⠀⠀⣠⣾⣧⡾⣧⠤⢎⡻⣷⣄⠀⠀⠀⠀⠸⠷⠞⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡟⢸⠇⠀⠀⠀⢠⠀⠈⢻⣿⣯⡴⠋⢁⣨⣿⣦⡈⠳⣝⣾⣯⣥⠾⠋⠀⣀⡴⢾⣽⡿⠿⠷⣬⣯⣭⠄⢻⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡟⠀⠀⠀⠀⢸⡄⠀⠀⢸⡏⣠⠜⠛⠒⠤⣌⣻⠷⠤⣭⣿⣿⣿⡯⠭⠿⠛⠋⢉⡿⣄⠀⠀⠀⠈⠙⠋⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣷⢣⡇⠀⠀⢸⠇⠀⠀⢀⣷⠟⠒⠒⠒⠦⢤⣽⠀⢠⡟⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠁⠀⢠⡟⠀⠀⢀⡾⠓⠒⠲⠤⣄⣀⣴⣃⣤⡟⠁⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠈⠛⠲⠦⠤⠤⠖⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⣰⣏⣀⣠⠶⢯⣀⣀⣀⣀⣠⠴⠟⠋⠁⣼⠃⠀⠀⠀⢀⣴⣟⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⣠⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠛⠁⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢿⣧⣌⣉⠓⠲⠤⣤⣤⣤⣤⣿⣥⣴⠞⠫⣝⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢁⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠷⠷⠦⠤⢤⣬⣷⣦⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⣩⠟⠉⠉⣩⠟⠉⠉⠙⠒⠢⢤⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣸⣃⣀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⣤⠄⡀⠀ ⠀⢀⠤⠁⠢⠄⠀⣜⣧⡀⠀⠀⠑⡄ ⢰⢥⣀⡀⠀⠈⡄⣹⢿⡿⠛⢆⠀⡇ ⠀⠙⠿⣿⣦⣄⡴⠀⢉⣧⡀⠀⠑⠁ ⠀⠀⢠⠉⡙⣛⡁⢆⠀⣸⣷⡋⠀⠀ ⠀⠀⢸⠐⢟⣥⢿⡆⠣⢿⣿⡕⠠⠀ ⠀⠀⠀⠢⣈⣛⢛⠩⠄⣼⠔⠉⠒⠀ ⠀⢴⣄⠊⣺⣿⣿⣿⣟⣉⡇⠀⠀⠀ ⠐⠁⢘⣾⠟⠿⣿⠿⠣⠋⠀⠀⠀⠀ ⠀⡽⣿⡀⣑⣾⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⢣⣿⡇⠀⢹⠛⡄⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⠡⠒⣐⠿⠇⠀⠀⠀⠀⠀⠀

⣼⠷⢶⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠶⢶ ⢻⠀⠀⣄⠈⠙⠻⢷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠛⠉⢀⠀⠀⣾ ⢸⡄⠀⣏⠙⠦⣄⡀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠋⠁⠀⣀⡴⠞⢹⠀⠀⣿ ⢸⡇⠀⢹⡀⠀⠈⠙⠲⣤⡀⠀⠈⠙⠻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠀⠀⣠⡴⠋⠉⠀⠀⢸⠀⠀⡿ ⢸⣧⠀⢸⡇⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠙⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣿⠀⠀⠀⣀⣤⣤⠄⠀⠀⠀⠀⢠⣴⡿⠋⠁⠀⢀⣠⠖⠛⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇ ⠈⣿⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡄⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢸⡇⠀⣠⡾⢫⡿⠋⠀⠀⠀⠀⠀⣿⠁⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⡇ ⠀⣿⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣿⢀⡞⠁⣴⡿⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣾⠃ ⠀⢹⣧⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣿⠟⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⣿⠀ ⠀⠈⣿⡀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡟⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣼⠇⠀ ⠀⠀⢹⣇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣿⠀⠀⠀⣠⣤⣤⣄⡀⠘⣧⠸⠀⣾⠃⠀⢀⣀⣠⣤⣤⡀⠀⠀⣿⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢠⣿⠀⠀ ⠀⠀⠀⣿⡄⠀⢧⣄⣀⡀⠀⠀⠀⠀⠀⢀⡴⠋⢁⣴⠟⢀⣴⡿⠋⠉⠉⠉⠉⠛⠻⠆⠼⢉⣉⣉⣭⠿⠏⠉⠙⠿⣷⣄⠙⢷⣄⠉⠷⣄⡀⠀⠀⠀⠀⠀⣀⣀⣴⠃⠀⣸⠇⠀⠀ ⠀⠀⠀⠸⣷⣤⣄⡀⠉⠉⠛⠒⠒⠶⠚⠉⣠⡾⠛⢷⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⣤⣶⣿⣿⣷⣾⠛⢷⣦⡌⠑⠒⠒⠒⠚⠉⠉⠁⣀⣤⣼⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⢶⣤⣤⣀⣴⣿⠋⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠉⠀⠈⠻⣷⣄⠈⣻⣷⣤⣠⣤⣴⠶⠿⠛⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠘⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠈⠻⣿⡏⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣾⣿⣿⠋⠀⠀⠀⣠⣤⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣶⣄⣀⠀⠰⢶⣶⢦⣤⣀⡀⠀⣿⠇⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣰⣿⣿⠿⠿⠿⠿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢻⡆⠀⣀⣠⣤⢶⣶⠖⠀⢀⣀⣴⡖⠀ ⠀⠀⠸⣯⡙⠷⣶⣄⡙⢷⣌⠉⠛⠶⣟⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡿⠥⢤⣤⣤⣀⣈⠙⢿⣿⣿⡄⠀⠀⠀⠀⢸⡷⠚⠋⣁⡴⠛⣡⣤⡾⠛⣹⡟⠀⠀ ⠀⠀⠀⠸⣷⡄⠀⠈⠛⠳⠿⣷⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢻⣿⣄⠀⠀⣤⣤⠉⠉⠛⢿⣿⣿⣆⠀⠀⠀⠀⠀⣠⣾⡿⠾⠛⠉⠀⠀⣴⡟⠁⠀⠀ ⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠻⣿⣶⣄⣈⠁⠀⠀⣀⣾⣿⣿⡿⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢀⣀⣀⣀⣈⠛⢿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⢩⡿⡿⠟⠋⠉⠉⠉⣉⣉⣉⡉⠉⠉⠙⠿⠿⢿⣍⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⢠⣿⣸⢀⡷⠀⣰⣞⣋⣩⣭⣿⣿⣿⣶⠀⢰⣶⣶⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠶⣤⣤⣤⣤⣿⣿⣟⣀⣸⣿⣧⢾⠀⠃⠈⠛⢿⣿⣿⣿⣿⠟⠋⠈⠃⢿⠔⣾⣏⣀⣀⣠⣤⣤⣤⣤⣤⡴⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣩⡿⢻⣿⣶⣦⣄⣀⠀⠀⠈⠉⡉⠀⠀⣀⣠⣤⣶⣿⡟⠻⣯⡉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢸⣯⣄⢹⣏⢹⡟⠛⢷⠶⢶⠟⠛⣿⢉⡝⢀⣼⡷⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⣧⣿⠀⠘⠛⠛⠦⠾⣦⠿⠦⠞⠛⠋⠀⢸⣦⡇⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⣿⣸⡆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣿⣨⡇⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣿⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿⠃⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠸⣿⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢻⡿⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢿⡞⢹⣠⢶⠀⠀⠀⠀⠀⣴⣦⡞⠹⣾⠁⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠈⣧⢸⠏⢸⣅⡀⣀⡀⣀⣹⠈⡇⢰⠏⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠘⣿⠀⢸⠋⣿⠉⢻⠏⢿⠀⢱⡏⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠘⠷⣼⣤⣯⣤⣼⣤⣾⠴⠋⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⣤⣤⣤⣤⣤⣤⣤⡤⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⢲⡢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢔⡿⢋⡥⠒⠀⠈⠀⠈⠳⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣧⢀⡠⠖⣱⠋⢠⡏⠀⣰⣾⣯⡑⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡙⠲⠶⠟⢇⠀⢿⡇⠸⣿⣿⡟⢧⣠⣾⣷⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠰⢻⠄⢸⢷⡀⠿⢿⣏⠉⣻⣿⣿⣦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⢻⡓⠯⠉⢀⣼⡼⠉⠂⠀⢿⡟⢩⡟⠉⠻⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡶⠿⠛⠀⠀⠀⠀⠸⠿⠋⠀⠀⢀⣨⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⣀⡤⣤⣄⡀⠀⠀⠀⠀⠀⣰⠏⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣾⣻⣶⣶⣾⣝⡛⢶⠂⠀⠘⢋⣾⣿⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣤⣹⣿⡟⣿⣿⣻⣷⣈⣧⣀⣀⣾⣿⣿⢉⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣯⣤⣈⠉⠙⠷⢿⣿⣯⣀⡿⣠⠞⠻⣯⡛⠛⢭⣤⡍⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⢸⡆⠀⠀⠀⠠⣄⡠⠚⠁⠀⠀⠈⢷⣄⢰⣽⢿⢦⣴⠋⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢸⢹⣇⠘⢹⡄⠀⠀⠀⠘⣷⣤⣀⣀⣀⣤⣾⠿⣾⣧⣼⡇⢉⡷⠀⠸⡆⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠃ ⠀⠀⣀⣀⠀⠀⠀⠘⠮⡙⠻⠈⡏⠒⠤⣀⡀⠈⢷⣦⣉⣻⣿⡿⠂⢸⣿⣿⡴⠛⠀⠀⢀⡇⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠁⠀ ⠀⠀⣿⣯⣍⡙⠒⠤⣄⠈⠑⠒⠃⠀⠀⠀⠹⡟⠚⠻⢿⡾⣿⠇⢠⣿⠟⠉⠀⠀⠀⠀⢸⡇⠀⢠⡊⣰⣿⣿⣯⠉⠻⠁⠀⠀ ⠀⠀⣿⠙⣿⣿⣦⡀⠀⠉⠒⢤⡀⠀⠀⢀⡤⠻⠤⣄⣠⡧⠉⠀⠉⣿⣦⣤⠀⠀⠀⠀⣸⠇⠀⢀⣽⣿⣏⠉⢻⣟⡎⠁⠀⠀ ⠀⠀⢹⡄⠋⢙⣯⡙⣦⡀⠀⠀⠘⣷⣔⠉⠀⠀⠀⠀⠀⠀⠀⢀⠑⣿⠈⢷⡀⠀⠀⢀⡟⠀⢠⣾⡏⣨⠟⢷⣇⠀⢹⡏⠀⠀ ⠀⠀⠀⢯⡀⠁⣹⣿⣌⢿⡦⠀⠀⠘⣿⠉⠓⠒⠤⠤⣀⣀⡀⠀⠃⠈⡇⠀⠙⢦⣤⡿⣄⣰⣿⣿⣿⣷⡤⠔⢿⡉⢻⠁⠀⠀ ⠀⠀⠀⠈⢷⣶⠫⠀⠉⢧⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⣁⠀⠀⠀⠈⢳⣾⣿⣿⣿⣿⢿⡛⠚⠉⠅⣾⠀⠀⠀ ⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⢳⡀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⣰⣿⣿⣿⣿⣿⠋⠀⠻⠶⣤⠖⠃⠀⠀⠀ ⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢻⠏⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀⣰⣃⣀⠀⠀⠀⠀ ⠀⠀⢠⠏⢀⣀⠀⠀⢠⠀⢰⠻⡄⠀⠘⢦⡀⠀⠀⠀⠀⣤⡶⣾⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⡡⠤⢶⣾⣯⡉⠻⣯⡇⠀⠀⠀ ⠀⢠⠏⠀⠸⠿⠁⢠⠃⢠⠃⠀⠹⣄⠀⠀⠈⠃⠤⣤⣾⢫⣾⠋⢙⢀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠹⣿⣿⣷⠟⠀⠀⠀⠀ ⢠⠋⠀⠀⠀⠀⠠⠃⣠⠃⠀⠀⠀⠙⢦⠀⠀⠀⣰⡿⣷⡟⠟⠂⣸⣿⣿⣿⣿⣿⣿⠋⣿⡏⣿⡄⠹⣄⣸⡿⠃⠀⠀⠀⠀⠀ ⣿⣶⣦⣄⡀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠈⠳⢤⣼⠿⣷⡈⢷⣦⣼⣿⣿⣿⣿⣿⣿⡇⠀⠹⣏⣨⣷⡀⣿⠟⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡤⢊⣦⠀⠀⠀⢀⠠⠐⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠡⡉⢸⠀⡾⢸⠀⠀⠔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢹⠮⠈⠀⠋⢠⣸⢰⠁⠀⡰⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⡀⢸⡁⡄⡂⠤⠒⠼⣿⡿⢂⢀⠡⠃⠀⠀⠀⠀⠀⠀ ⠀⢀⢔⠲⣄⠀⠀⠀⠘⡈⠎⢺⣇⡕⣲⣄⠀⠀⠉⠷⠤⢔⠆⡀⠔⠆⠀⠀⠀⠀ ⢠⠁⡆⠀⠘⠀⣖⣺⡯⡍⠀⠈⠋⣧⢬⣽⣤⡀⠀⠄⠐⠉⠁⡠⠊⠀⠀⠀⠀⠀ ⢸⠀⡇⠀⠀⠀⢯⡁⠀⠀⠀⢀⣀⣤⡾⠋⠀⠡⣀⡀⣀⠠⠊⠀⠀⠀⠀⠀⠀⠀ ⠈⡄⠘⢄⣀⠀⠀⢹⣭⣏⣇⡷⠟⠊⣀⣤⣴⣎⢳⣿⣥⣒⣠⡤⢞⣲⡶⠀⠀⠀ ⠀⠈⠒⠠⢀⠱⡀⠶⠠⠀⠠⠄⠲⠉⢣⠐⠂⠀⠀⠚⣻⡏⠂⢍⣼⠕⠂⢄⠀⠀ ⠀⠀⠀⢀⠤⠅⢓⠀⢢⠀⠀⠀⢇⡠⠤⢻⡀⠀⣼⡑⡟⡇⠀⢾⠁⠀⠀⢀⡡⠀ ⠀⠀⠀⠈⠧⣉⡁⠤⡎⠀⠀⠀⡾⠁⡀⠆⠰⡀⣷⡏⠏⠀⠀⣸⡗⢋⠁⠈⠆⠀ ⠀⠀⠀⠀⠀⠈⢠⠈⠈⠢⡀⠰⠀⢰⢱⠀⠀⠱⠈⠱⠀⠀⠰⢻⠀⠘⡀⠀⠘⡀ ⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠈⢣⠀⢇⠃⠀⠀⠀⠃⠀⠀⠀⠀⡈⠀⠀⢱⠀⠀⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⢘⡠⠃⠀⠀⠀⠀⠸⢄⠀⠀⣀⣴⣶⠁⠀⢧⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠀⠑⠉⠉⠀⠀⠀⠀⠀⠁⠀

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

⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢻⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣟⣋⠉⠉⠛⣆⠀⠈⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣿⣿⡇⠀⣶⣾⡿⢿⣿⣿⣿⣷⢶⣄⠀⠀⠀⠀⠈⢡⣾⣿⣿⡯⣭⡓⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⢻⣍⡿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣩⣿⣿⣿⡇⠀⣿⣋⣾⣿⠿⣿⠿⠛⠟⠻⣧⠀⠀⠀⠀⠘⠁⠙⠉⠡⠞⠃⠀⠀⠀⠀⣿⢳⠀⡄⠀⠀⠀⠀⠀⣿⠑⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢨⠉⡿⣧⣿⣧⠀⠁⠈⠈⠉⠛⠁⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠆⠘⠀⠀⠀⠀⠀⠀⠻⣆⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣠⠟⢸⡃⢻⣞⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡀⠀⠀⠀⠀⣀⣠⡴⠾⠿⠛⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⣼⣿⣿⣻⢋⣤⣿⣿⣄⢳⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡾⠁⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣽⡇⣀⠀⠀⠀⠀⠀⠀⠀⣇⣰⣄⠀⢀⣤⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣠⣾⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢦⡀⠀⠀⠀⠀⠀⠉⠙⠛⣷⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣾⣿⣿⣿⣿⠿⠟⠛⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⢳⠀⠀⠀⣄⣄⣀⣀⣀⣀⣀⣠⣤⠤⠴⠂⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⣿⣿⣿⣿⡄⠀⠈⢳⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣄⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣷⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣻⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⣸⣿⠿⣿⡿⠃⢻⣿⣿⣷⣦⣄⣀⣀⣄⣀⣄⣤⣴⣿⣿⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣸⣿⣿⠀⢿⠁⠀⠀⠛⢿⣿⣿⣿⣿⣿⣭⣻⣭⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠙⠻⢹⡇⠘⡆⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠈⡇⠀⠉⠀⠀⠀⠀⠀⠀⣴⢿⣿⣿⣟⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢀⣾⣿⣄⣿⣿⣷⣾⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

🟪🟪🟪🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪🟪 🟪⬜️⬛️🟪⬜️⬛️🟪 🟪🟪🟪🟪🟪🟪🟪 🟪⬛️⬛️⬛️⬛️⬛️🟪 🟪🟪⬛️⬛️⬛️🟪🟪 🟪🟪🟪🟪🟪🟪🟪

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢠⣄⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣯⣝⠻⣦⡀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣷⣤⣴⣾⣿⡛⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣽⢃⣴⣿⣿⠟⠛⡋⠑⠀⠀⠀⠐⠘⠛⠛⡉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠉⠩⠈⣿⣿⣾⣿⣿⣿⡤⠶⠿⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠁⠈⣿⣿⣿⣟⠛⢿⣿⣿⣿⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⢿⣷⣄⣸⣿⣿⣿⣿⣯⣹⣿⣶⣏⣤⣶⡦⡀⠀⠀⠂⢀⡀⠀⠀⠐⢿⣿⣿⣿⣄⣠⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣦⣶⣾⣿⣿⣿⣷⡀⡀⠀⠛⣿⣿⣿⣿⣿⣿⣿⡿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣐⠀⠀⠀⣉⣭⣿⣿⣿⠫⠀⢠⣴⣄⡈⣻⣿⣿⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣟⠙⣿⣿⣦⡀⢰⣿⠛⢻⣿⣿⣷⡀⠈⠉⠟⢽⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣾⣿⣧⣈⣉⣼⣿⠃⠀⠀⠴⠛⣍⡉⣛⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣄⡀⣀⠀⠀⢬⣙⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠋⠋⡿⣿⣿⣿⣿⣿⡿⠟⠋⠛⠛⠩⠍⡝⣻⣆⣀⣀⣀⣽⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢀⠀⠈⠀⠀⢹⠟⠉⠀⠀⠀⠰⢧⠴⠆⠀⠀⣿⣿⣿⣿⡟⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣽⡂⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⡀⠓⠀⢀⣼⣿⣿⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣷⣆⣤⣄⣸⣆⣤⣤⣤⣴⣴⣷⣶⣶⡾⣿⣿⡿⠃⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣾⣿⣿⣿⣿⣟⠛⣿⠿⠿⣿⡟⠻⢿⠛⠛⣿⣩⣾⠿⠿⠂⢘⣿⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣩⢿⢿⠿⠷⢾⣿⣷⣶⡿⠗⠚⠛⠛⢙⡀⣾⣴⣿⣿⠛⠟⠿⠙⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⢾⣿⠀⠀⠀⢀⣼⣶⣾⣿⣽⣿⣿⣿⠏⠀⢀⣠⣴⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⢠⣬⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⣿⣿⣿⡟⠋⠘⣿⣏⣥⣶⣿⣿⣿⣿⡿⣿⣙⢿⣷⣬⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡟⣋⣉⣩⣿⣶⡄⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣏⠀⠸⣇⠀⠀⠹⠿⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡼⣿⣿⣿⠉⠉⠉⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠹⢿⣿⣿⣿⣿⣿⠀⠉⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡛⣤⠀⣹⠀⠀⣀⢠⠈⡚⣿⣄⠀⠀⠀ ⠀⠀⣠⣶⠟⢋⣻⣽⣿⣧⣤⣠⣤⣼⣷⣿⣿⣿⣿⣿⣿⣿⠟⠿⢿⠁⠀⠀⠀⠀⠀⠈⠛⠛⠋⠙⣇⠀⠀⢐⠚⠺⣿⣿⣿⣿⣿⣿⣿⣧⠛⣦⢠⠀⠀⠉⡟⠀⠛⣸⣿⡆⠀⠀ ⢀⣼⣿⣿⣷⣾⡏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠄⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⡙⢸⡄⠀⠀⠀⠀⢀⠍⠹⣿⡀⠀ ⣼⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⡀⠀⠁⢀⠀⠀⠀⠀⠀⠐⢿⡀⢈⡀⠀⠈⠿⢿⣿⣿⣿⣿⣿⣯⡍⢈⣷⡔⠀⡀⠀⡄⠀⣦⢻⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⣗⠃⠀⠂⣀⢿⣻⣿⣿⣿⣿⣿⣷⣟⢿⣆⠃⠀⢀⣴⣶⣿⡏⠀ ⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠷⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢀⡀⣭⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣷⣾⣿⣿⣿⡟⠁⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⢻⣿⣿⣿⣿⣿⡏⠀⠀⠁⠀⠀⠁⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⡦⠃⠀⠀⣀⠄⠀⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡋⠋⠙⠋⢳⠂

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡠⠖⠒⠒⠒⠢⢤⡀⠈⢷⣍⡓⠲⢤⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣁⡤⠔⢊⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠋⡤⠒⠉⠉⠓⠢⢄⠈⢳⡌⠳⣌⡓⠲⠼⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡸⠧⠔⢊⡵⠏⠀⠀⠀⠀⡴⣧⠀⠀⠀ ⡞⢸⠁⠀⠀⠀⠀⠀⢀⠇⣸⣄⠀⣨⠟⠲⢤⣀⡀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⢀⣠⡤⠞⠿⣤⠤⠤⠶⠶⠴⠿⡇⠀⠀⠀ ⢸⡈⢇⠀⠀⠀⠀⢠⠊⢠⠏⣨⠟⠁⠀⠀⠀⠈⠉⠙⠓⠒⠲⠶⠦⠤⠤⠤⠴⠶⠒⠒⠛⠉⠉⠀⠀⠀⠀⠈⢻⣍⡩⠭⣍⢫⡁⠀⠀⠀ ⠀⠳⣄⠳⢄⡀⡴⠁⡴⢃⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠂⠚⡆⡟⡄⠀⠀ ⠀⠀⠈⠓⠦⣉⣠⠮⣄⣾⠁⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢸⣼⣹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠙⠶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠴⠀⠀⠀⠸⣇⡸⣧⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⣿⠷⢹⠸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⡆⡿⡄ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣈⡻⣿⣆⠀⠀⠀⠀⠀⣴⡿⣋⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⡇⡜ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣦⡹⡆⠀⠀⠀⣸⢋⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣾⠃⢰⡥⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⡟⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⢀⠀⠀⠀⢸⡿⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠃⣀⠔⡿⠭⢗⣲⣺⢗⣽⣿⣿⣿⣿⣿⡟⠀⣀⣀⣀⣀⡀⠈⢿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡏⠀⠀⣿⣶⠮⠿⣿⣾⠷⠿⠛⠛⠉⣿⣿⡟⠋⠉⢙⣿⣿⣿⣿⣿⣿⣯⠙⠛⠛⠷⠦⣤⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣷⠀⠀⠋⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⢀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢀⣠⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣸⡀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⣧⡴⡟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠉⣷⡀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠁⠀⢀⡾⠉⢠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡴⢿⠇⠀⢸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢠⠞⢿⣄⣹⡶⢤⣤⣤⣤⠶⠶⢲⣿⡟⠉⢻⣷⡖⠶⢦⣤⣤⣤⡴⣾⣏⣠⡿⢲⡄⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠣⣬⣿⣿⣿⣦⣤⣼⣿⣦⣤⣿⣿⣿⣷⣿⣿⣷⣤⣼⣿⣧⣤⣶⣿⣿⣿⠥⠞⣸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢹⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣉⠇⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠈⢩⠞⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢳⡍⠁⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠙⠒⠋⢰⣉⠉⣻⠛⠻⡟⠛⢻⠛⠛⡏⠉⢹⡄⠑⠒⠋⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠈⠉⠁⠀⠀⠉⠉⠉⠀⠀⠈⠉⠁⠀⢀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠓⠶⠤⣤⣤⣤⣄⣀⣀⣤⣤⡤⠴⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪 🟪⬜️⬛️🟪⬜️⬛️ 🟪🟪🟪🟪🟪🟪 🟪⬛️⬛️⬛️⬛️🟪 🟪🟪⬛️⬛️🟪🟪 🟪🟪🟪🟪🟪 🟪🟪 🟪🟪🟪🟪🟪 🟪🟪🟪🟨🟨🟨 🟪🟪🟪🟪🟨🟨🟪 🟪🟪🟪🟪🟨🟨🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪 🟪🟪 🟪🟪🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪 🟪🟪 🟪🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪 🟪🟪 🟪🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪🟪🟪 🟪🟪🟪🟪 🟪🟪🟪🟪🟪 🟪🟪 🟪🟪🟪🟪🟪 🟪🟪🟪🟪🟪 🟪🟪🟪🟪 🟪🟪🟪🟪 🟪🟪🟪🟪 🟪🟪🟪🟪 🟪🟪🟪🟪 🟪🟪🟪🟪 🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣲⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣿⠁⠀⠀⠀⠀⠀⠀⢀⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣿⡟⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡘⣏⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⡇⠀⠀⠀⠀⠀⢀⣾⣿⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢱⡘⣦⣿⣞⢷⡀⠀⠀⠀⠀⠀⢀⣽⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠳⣦⣀⣠⣴⢞⣿⡿⢡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡌⢿⣿⣧⡻⠦⠤⣤⣤⠶⠛⠁⣠⡿⠆⠀⠀⠀⠀⣀⣀⣀⣀⣀⠠⠤⠤⠤⠤⣅⣹⣷⣦⣤⣀⣈⣉⣉⣭⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠆⢳⣾⡛⢶⠞⠋⠀⠀⣠⣾⠇⠀⣀⣤⠴⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⠻⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣦⣤⣶⣶⣿⣿⣿⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣦⣤⣄⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⢀⣠⣤⣶⣶⣤⣤⣤⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢧⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢨⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣧⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣼⣿⣿⣿⣿⣿⠿⢿⡿⣿⣻⣷⠀⠀⣾⣟⣉⢠⡟⢛⣿⣿⡆⢀⣙⣿⣿⡀⠘⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⡇⠀⣿⣿⣿⢟⡽⠗⠀⣿⣤⣿⣿⣿⣿⣿⣿⡇⠀⠸⢿⣟⣿⡿⠃⠀⢈⣿⣿⡇⠀⠀⢈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢱⡟⠀⠀⢿⣿⡿⠋⠀⠀⠀⠙⠛⠛⠋⢸⣿⣿⠿⢷⣀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡗⠀⠀⠀⣿⣇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⡟⠃⠀⠀⣼⣿⣿⣄⠀⠀⠀⠀⠀⢀⣤⣾⣿⣶⣶⣾⣿⣗⣶⡤⣤⣤⡾⠿⠿⠛⠋⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠈⠻⢿⣿⣷⣦⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠛⠓⠶⣤⣄⡀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠉⣩⡿⠛⠉⠁⠈⠛⠻⠿⢿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⣦⣠⠾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣾⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⢧⣤⣀⣀⣀⣀⣀⡤⠴⢛⣡⡾⢇⠘⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠿⠛⢻⣿⡇⢿⣷⣦⣤⣤⣀⣀⣤⣤⣖⣻⣭⣤⡾⠟⢻⠿⢷⣶⣶⠶⠾⠿⠛⠉⠀⢸⣷⣟⣀⡤⣤⣤⡶⠒⠦⠤⢤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⢶⡾⠋⠆⠀⠀⠈⡿⣷⡌⠛⠿⣿⡿⠿⠿⠿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠉⠙⢿⣮⣻⣿⣄⠀⠀⠀⠈⠻⣆⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⣸⡿⠁⠀⠀⠀⢠⣿⣿⣿⣷⣄⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠶⠶⣶⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠹⡆⠀ ⠀⠀⢀⣤⣲⡟⢠⡧⠇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣽⣶⣶⣤⡌⣝⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢳⡀ ⠀⣰⢋⡼⢳⣿⡄⠃⠀⠀⠀⣠⣿⣿⣿⣿⣿⠟⣿⡟⠛⠛⠛⠻⢿⣿⣿⣉⠛⢛⣻⣟⡛⠉⢁⣤⣾⠟⠋⠉⠁⠀⠀⣿⣿⠁⢹⣆⠙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃ ⠘⠁⠞⠁⢸⣿⣿⣆⠀⢀⣴⣿⣿⣿⣿⠟⣀⢾⣿⠁⠀⠀⠀⠀⠀⠀⢉⢻⣿⡟⠋⡙⠻⣾⣟⣭⣶⠀⠀⠀⢰⣄⢀⣿⠃⠀⠀⣿⣇⢿⣿⣿⡇⠀⠀⠀⠀⡰⠃ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⠇⢺⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⢁⣼⡿⠿⣿⠏⠀⠀⠀⠈⣿⣾⠏⠀⠀⠀⠀⢹⣿⣿⣿⠁⠀⣠⡴⠛⠁⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣟⡃⣸⣿⢸⡟⠀⠀⠙⠿⣦⣯⣀⠀⠀⠹⠿⢩⣿⣿⠿⠟⢿⣷⣄⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠈⣿⣿⣿⡴⠟⠁⠀⠀⠀⠀ ⠀⠀⠠⣄⣀⣀⣘⣿⣿⣿⣿⣿⣿⣇⣸⡁⣀⡀⠀⠀⢹⣿⣋⣀⣈⣀⣴⣿⡟⠁⠀⠀⠀⣹⣿⣤⣀⣀⣀⣀⣼⡿⣁⣀⣀⣀⣀⣀⣤⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠛⠛⠉⠉⠉⠉⠉⠉⠈⠉⢻⣍⠉⣉⣩⠟⠉⠀⠀⠉⠉⠉⠉⠀⢉⣉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪 🟪🟪⬜⬜🟪🟪🟪🟪🟪⬜⬜🟪🟪🟪🟪 ⬛⬛⬜⬜⬛⬛🟪⬛⬛⬜⬜⬛⬛🟪🟪 ⬛⬛⬜⬜⬛⬛🟪⬛⬛⬜⬜⬛⬛🟪🟪 🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪 🟪⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛🟪🟪🟪 🟪⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛🟪🟪🟪 🟪🟪⬛⬛⬛⬛⬛⬛⬛⬛⬛🟪🟪🟪🟪 🟪🟪⬛⬛⬛⬛⬛⬛⬛⬛⬛🟪🟪🟪🟪 🟪🟪⬛⬛⬛⬛⬛⬛⬛⬛⬛🟪🟪🟪🟪 🟪🟪⬛⬛⬛⬛⬛⬛⬛⬛⬛🟪🟪🟪🟪 🟪🟪⬛⬛⬛⬛⬛⬛⬛⬛⬛🟪🟪🟪🟪 🟪🟪⬛⬛⬛⬛⬛⬛⬛⬛⬛🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪

⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⣿⠆⠀⠀ ⠀⠀⢠⣾⣿⠋⢀⣿⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠋⢀⣾⠋⠀⠀⠀ ⠀⣠⣿⡿⠁⠀⣼⠇⠀⠀⠀⠀⠀⣴⣿⡿⠋⢀⣴⠟⠁⠀⠀⠀⠀ ⢠⣿⣿⠁⢀⣼⠏⠀⠀⠀⠀⠀⣴⣿⠯⠴⢿⡟⠁⠀⠀⠀⠀⠀⠀ ⢻⣿⣯⣼⡿⢿⡀⠀⠀⠀⠀⢸⣷⡏⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀ ⢺⣿⡏⠁⠀⠸⣧⠀⠀⠀⠀⣾⣿⡇⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⠀⠀⠀⣿⠀⢀⣀⣤⣽⠿⠧⣤⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣧⠀⢀⣿⣿⡿⠛⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣷⣿⠋⣿⠀⠀⢀⣀⡀⠀⣰⣶⣦⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⣿⣿⡏⢠⣿⣿⡿⢷⠀⢻⣿⣿⢹⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⡇⠘⣿⡿⢇⣼⡟⣾⣿⣷⣿⠟⠿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠹⣦⣀⠈⠉⡽⠋⠀⠛⠛⠋⠁⠀⠀⠈⡇⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣶⣄⠉⠛⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣍⡛⠛⠛⢶⣄⠤⡤⠤⠒⠃⠉⢙⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣦⣀⣀⣠⣴⣖⡋⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⡿⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⢦⠀⠀⠀⠀ ⠀⠀⣼⣿⠃⠀⠀⢸⣷⣿⣿⣿⡟⠛⠉⠀⠀⠉⢻⣷⣬⣧⠀⠀⠀ ⠀⠀⡧⢸⡄⠀⠀⠀⣿⡇⠙⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⡉⢧⠀⠀ ⠀⢠⡿⠾⣷⣤⡴⠾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣧⠘⣆⠀ ⠀⣾⡇⢠⡟⠁⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣆⣼⡀ ⠀⢿⣷⣾⡇⠀⠀⢀⣿⣷⢀⠀⠀⠀⠀⡀⠀⠀⣀⣤⠤⢿⡿⠟⠃ ⠀⠀⠈⠁⠉⠉⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣀⣀⣀⣀⣠⣤⣾⣿⠃⣿⠃⢸⠟⠻⣿⣿⣿⣿⣇⠀⠀⠀⠘⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠿⠛⠙⠛⠻⢶⡄⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⡿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣤⣌⣀⡇⢻⣿⣿⣿⣿⡆⠀⠀⠀⢻⣷⠀⠀⢹⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣰⣾⡿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀ ⠗⠀⠀⣴⣿⣿⣿⣷⣤⣄⣉⠛⢿⣿⣷⣼⣿⣿⣿⣿⣷⠀⠀⠀⠘⣿⣧⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣼⢯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣟⣿⠟⠁⠀⠀⠉⢿⣷⣆⠙⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡟⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⢸⣟⣾⠁⠀⠀⠀⠀⠀⠈⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣤⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠏⢻⡇⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⠿⠿⡟⣛⣭⣭⣶⣿⡿⣟⣯⣶⡿⠟⠋⠀⠀⠈⢿⡄⠈⢷⣤⡀⠀⠀⠤⠔⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⢟⣛⣿⡿⠷⠿⠛⠋⠁⠀⠀⠀⠀⢀⠀⠈⢿⣄⠀⠈⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⣯⠻⣧⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠙⠛⠟⠿⠿⠿⠟⠻⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠻⣿⡻⣶⣤⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣦⠉⠻⣶⣤⣴⣶⣿⢿⣟⣵⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡹⣷⣾⣿⣿⠛⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣴⣿⣷⣾⣿⣿⣿⣿⣿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡘⠿⢿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠟⠛⣻⣿⠿⠛⢹⣿⣿⣵⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢢⣴⣾⡿⠷⠶⠶⣦⡀⠀⠀⠀⠀⠘⢷⠀⠀⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠐⠿⠁⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢷⣿⣿⣋⠀⠀⠀⠀⠈⠻⣦⢰⡄⠀⠀⠘⣧⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢟⣿⡿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠙⢷⡀⠀⠀⣿⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⢰⠀⠀⠀⠀⠀⢠⣿⣯⡏⣷⣆⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⣀⣤⣾⣿⡟⢙⠋⠀⠀⣀⢀⠀⠀⠀⠀⠀⠘⣷⠀⣠⠏⢀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⣷⣸⣆⠀⠀⢀⣠⣾⣿⣿⣿⢿⠛⠿⣶⣦⣀⣀⠀⠀⠻⣦⣿⣴⣾⡟⠻⢿⣿⠟⣛⣤⣶⣶⣿⠿⠷⢶⡄⠀⠀⠀⢿⡦⠏⠀⢈⡀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⡿⠷⠿⠛⠉⠀⠸⣿⣷⢸⡀⠀⠀⠈⡉⢻⣿⣿⣾⣿⠛⠛⢿⣿⡟⠉⠀⣾⡋⠙⣿⣻⣯⣴⣾⡿⠃⠀⠀⠀⣸⠁⠀⠀⢸⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⣠⣭⣿⣿⡿⢿⡏⠀⠀⠀⣿⡅⠀⠈⠛⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣶⠚⢻⣧⣿⣿⣤⣾⣧⠀⣀⣴⡿⣿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⡇⠀⠀⣾⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣿⡿⢦⣀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠉⠉⠛⠛⠛⠋⠀⢠⣿⡟⠉⠀⠀⠳⢶⡈⠉⠛⠛⠛⠻⠶⢶⣤⣄⠀⠀⠀⠋⠀⡇⠀⠀⣿⣿⠿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⠁⠀⠉⠛⠷⠶⠶⠖⠛⠉⢻⡇⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣀⢀⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣄⠀⢠⡇⠀⢀⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⠀⠀⠀⢀⣠⠾⠋⠀⢠⣴⣾⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠐⠀⠈⠛⣶⣾⢀⣠⠞⢻⡇⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣍⡻⣿⣷⣶⣶⣶⣶⣾⣿⡿⠿⠋⣿⡆⣠⡞⠋⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠿⠛⠁⠀⣸⡇⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠳⣶⣿⣿⣿⣿⣯⣭⣶⣶⣚⣿⣿⣿⡋⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⡭⠽⠟⠋⠉⠉⠉⠀⠉⠻⣦⣀⠀⠀⠠⠀⠀⠙⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⡟⠀⠀⠀⠀⢠⢸⣿⡇⠀⠀⠀⠀⠀⢻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⣸⣯⣧⣤⣀⠀⢀⣀⣀⣀⣠⣄⣀⣨⣿⣷⣦⡀⡆⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣾⠿⢷⣿⡇⠀⠀⠀⠀⣏⣾⡟⢻⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⣴⣶⣶⡴⠶⠟⣛⣯⣿⡿⠷⠶⢾⣿⠁⠀⠀⢻⠁⠀⠀⠀⠈⣿⡟⠀⢸⣇⠤⣤⣤⣤⣧⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽⣿⣿⠉⠉⠀⠈⠉⠁⠀⠀⢀⣠⣶⣿⠏⠀⠀⠀⠀⠀⠀⠀⣀⣼⡟⠀⠀⢸⣿⡀⠀⠀⠀⠉⠛⠶⣤⣀⣀⡤⠖⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣦⣤⣤⠤⣤⣶⣾⣯⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⣼⣻⣿⠀⠀⠀⠘⢿⣿⢦⣄⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡎⠉⢛⣛⡿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣘⣵⣿⣷⠀⠀⠀⠀⠸⣿⣷⣍⡣⣄⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⣀⣀⣀⣀⣀⣤⣶⠿⠛⠛⢿⣔⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣺⣾⡿⠿⢻⣷⠀⠀⠀⡇⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠛⠋⠉⣭⣿⠟⠉⠁⠀⠀⠀⠀⣠⣿⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣿⠟⠁⠀⠀⠀⣿⡄⠀⠀⣤⣹⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠟⠋⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣦⣀⡐⢄⣀⣀⣀⢀⣤⣼⣽⣿⠁⠀⠀⠀⢀⠰⠛⢿⠀⠀⠸⠟⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠁⠀⣠⣿⠋⠀⠀⠀⠀⣤⠞⠉⠀⠀⠀⠀⠀⠀⡀⠀⣼⣿⣿⣿⣿⣿⡟⠛⠿⣿⡿⣿⡿⠿⠋⠉⢣⠈⠁⢘⣋⠁⠀⠀⢸⣆⠀⠀⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣾⠓⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠖⢻ ⣿⠀⢰⢤⡈⠙⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⢉⣠⢤⠀⢸ ⢻⠀⢸⠀⠈⠓⠦⣀⠀⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠁⢀⡤⠒⠉⠀⡄⠀⣸ ⢸⡆⠈⡇⠀⠀⠀⠀⠙⠢⢄⡀⠈⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⢀⡞⣹⠀⠀⣀⣤⡶⠀⠀⠀⢀⣴⠟⠉⠀⣀⠔⠊⠁⠀⠀⠀⠀⡀⠀⣿ ⠸⡇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁⡏⣠⠞⣩⠟⠀⠀⠀⠀⢸⡇⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⡇ ⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣿⠀⠀⠀⠀⠀⠀⢰⡇⢸⡷⠃⣴⠏⠀⠀⠀⠀⠀⢸⠇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣸⠃ ⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⡀⠀⠀⠀⠀⠀⠸⡇⢸⠁⡼⠃⠀⠀⠀⠀⠀⠀⣿⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀ ⠀⠀⣿⡀⢹⡀⠀⠀⠀⠀⠀⠀⢀⡽⠀⣸⠇⣀⣴⠶⠶⠦⢤⣷⠀⡼⠥⠤⣴⡶⠶⢶⣄⠀⣿⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⡰⠀⣸⠃⠀ ⠀⠀⠘⣧⣀⡉⠓⠒⠦⠤⠤⠔⢉⣴⢾⣥⡾⠛⠁⠀⠀⠀⠀⠀⠐⠒⠚⠉⠉⠀⠀⣠⣿⣷⣮⡿⢦⣌⠳⠤⠤⠤⠖⠒⠉⣁⣰⡏⠀⠀ ⠀⠀⠀⠀⠉⠙⠛⠶⠦⣤⣤⣶⡏⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠋⠀⠙⢿⣄⣙⣷⣤⣤⡴⠶⠚⠛⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠙⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⡀⠀⣠⣶⣾⣿⣶⣶⣤⡀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢀⣀⡀⠀⠀⢀⠀ ⠀⠘⣿⠶⣤⣉⠻⣍⠓⠶⣴⡏⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣋⣉⡈⠉⠻⢿⣿⣆⠀⠀⠀⠘⣧⠴⠞⣋⡽⢋⣠⠴⣾⠏⠀ ⠀⠀⠘⣷⡀⠉⠛⠺⢷⣤⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⣿⡄⠀⢨⡍⠉⠚⢻⣿⣧⠀⠀⠀⠀⣠⡾⠿⠚⠉⠁⣴⠏⠀⠀ ⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠙⢿⣶⣤⣤⣤⣤⣾⣿⡿⠀⠀⠀⠀⠁⠀⠀⠀⢀⣼⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⣻⣿⡿⠿⠖⠒⠒⠒⠒⠲⠾⢿⣿⣟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⣰⣿⡟⢰⣏⡄⣆⠀⣖⣚⣫⣽⣿⣶⡄⢰⡶⡾⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⠿⢿⣤⣼⣿⡾⠀⠀⠉⠻⠿⠿⠿⠋⠀⠉⢻⣷⣿⣤⣤⠴⠶⠶⠶⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⣿⡟⢿⠶⣦⣤⣄⣐⣤⣤⡶⣿⠛⣿⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣽⠈⠛⠛⠦⠿⡼⠧⠞⠛⠁⣸⣽⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢸⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⣧⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢻⡞⣧⣤⠀⠀⠀⠀⣤⣴⠻⡿⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢧⡟⢸⣧⣠⢄⣠⡇⢹⣴⠃⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⢧⣸⣁⡇⠈⡇⣧⣸⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣬⣉⣉⣉⣉⣁⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣠⣴⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣦⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⠟⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠋⣠⣾⠋⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⠃⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⣰⡿⠃⠀⠀⠀⠀ ⠀⢠⣾⣳⡿⠁⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⢀⣿⣷⣿⠁⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣥⣴⣶⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣿⣿⡏⠤⣶⣿⡏⠀⠀⠀⠀⠀⠀⢀⣾⢫⡿⠈⠉⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⡿⠿⠛⠁⣿⡄⠀⠀⠀⠀⠀⢸⣿⣼⠇⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⢿⡇⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣼⣧⠀⠀⠀⠘⣿⠀⠀⢀⣠⣤⣼⣿⠿⣦⣤⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣷⣿⣆⠀⠀⢀⣿⣶⣿⡿⠛⠉⠁⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣦⣠⣿⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠿⣿⣿⣤⣽⠇⢀⣠⣴⣶⣦⡀⠀⢸⣿⣿⡿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢠⣿⣿⣿⣿⠛⢷⠀⠸⣿⣿⡿⢀⣿⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣷⣿⡇⠀⢻⡿⠿⠿⣀⣾⠘⣷⣿⣿⣾⣿⠿⠿⠾⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⢿⣆⠀⠀⠙⠙⢛⡽⠊⠀⠻⠿⠛⠛⠋⠀⠀⠀⠈⣶⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⣀⠙⠻⠶⣤⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣻⣶⣤⣤⣤⣿⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⣈⠉⠉⠉⠻⣷⡄⠦⠤⠴⠞⠋⠁⠀⠀⣸⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣤⣶⣛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⠟⠉⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⡟⠀⠀⠀⢹⣿⠻⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⣿⣷⣄⠙⣦⠀⠀⠀⠀ ⠀⠀⢰⡏⣿⠃⠀⠀⠀⠀⣿⣿⠿⣿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡿⣄⠀⠀⠀ ⠀⠀⢼⡇⢿⣇⠀⠀⠀⠀⣻⣿⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢻⡆⠘⣇⠀⠀ ⠀⠀⣾⠿⣶⣿⣄⣤⣴⠾⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢿⡄⠸⡆⠀ ⠀⢸⣿⠀⢀⣼⠋⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⣧⠀⢹⠀ ⠀⢸⣿⣆⣾⡏⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣏⣿⡇ ⠀⠘⢿⣿⣿⣧⣄⣀⣀⣤⣼⣿⣧⣠⣤⣀⠠⠤⠤⠤⠄⠀⠀⠒⠒⠒⠒⠛⠾⠛⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⠖⠒⠺⣿⣯⠟⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣭⣿⠃⠀⠀⠈⠁⢀⡎⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠉⠉⠓⠲⣶⠴⠚⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠈⢧⡀⠀⠀⢀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⡇⠀⠀⠀⢸⡿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⢻⠀⠀⠀⠘⡇⢩⠑⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠀⠀⠒⢲⠛⢦⣀⠀⠀⠀⠹⡆⢀⣀⣀⣀⣠⠴⠋⢸⡇⠀⠀⢘⡇⠀⠀⠀⣧⠘⢦⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⡟⠙⡄⠀⠀⡏⠉⠁⠀⠀⠀⠀⠀⠈⢧⠀⠀⡾⠻⣄⠀⠀⠘⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡾⠀⠀⢱⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣧⠀⠈⢳⣄⠀⠘⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢸⠁⠀⠀⠈⡇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠸⡄⠀⠀⠘⢷⡀⠈⢳⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡜⠀⠀⠀⠀⢳⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣰⠃⠀⠀⠀⠀⢹⡀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡼⠁⠀⠀⠀⠀⠈⢧⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⠁⣰⠃⠀⠀⠀⠀⠀⠀⢇⠈⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡼⠀⠀⠀⠀⠀⠀⠀⠘⡄⢻⠀⠀⠀⠀⠀⠀⠀⡈⢀⠇⠀⠀⠀⠀⠀⠀⠀⠈⡄⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⡄⠀⠀⠀⠀⠀⠀⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠈⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠠⣇⠀⠀⠀⠀⢀⣼⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⡼⠂⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡯⡦⠤⠞⠁⠀⠀⠀⠀⠀⠀⢰⣯⣦⡤⢽⠃⠀⠀⠀⢛⣛⠒⠖⠋⠀⠀⠀⠀⠀⠀⢸⡡⣦⠤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣚⣋⣉⡻⠶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣠⠞⠁⠀⠀⠛⡆⠹⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠑⡶⠁⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⠁⢠⡀⠀⠀⠀⠀⡸⢸⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠚⠫⢟⣮⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡦⢌⣓⡤⣹⡆⠀⠀⣰⢣⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠛⠛⠲⣄⣸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣡⠔⠒⠒⠬⡹⠚⢯⣉⣵⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⡤⠚⠉⠙⡍⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡰⠁⠀⠀⠀⠀⠈⢆⠀⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣤⢀⠀⢹⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣲⠁⠀⠀⠀⠀⢀⣀⣸⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡔⠀⠀⢀⣽⣿⠃⠀⡇⠸⡄⠀⠀⠀⠀⠀⠀⠀⣸⣅⡇⡟⠑⠀⠀⠀⠀⠀⣸⢣⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠸⡿⠛⠀⣾⣉⣶⣃⠀⠀⠀⠀⠀⠠⣿⣿⠿⣆⡼⡄⠀⠀⠀⠀⡴⠁⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⣀⡤⠋⠀⣁⣈⣇⠤⠤⠤⠤⠤⣾⣿⣭⣀⠈⠉⠢⢄⣀⡞⠁⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⢉⣉⣥⣔⠾⠛⠉⠁⠀⠀⠀⠀⠀⠰⣿⣟⡏⠻⣕⠢⢤⣀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠙⢶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⡜⠀⠀⡴⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣠⡼⣤⡤⣞⠀⠀⠀⠀⠀⠘⣆⣀⣀⡇⠀⣰⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢰⣞⡕⠉⠁⠉⠙⢷⡤⠂⠐⢤⣠⠿⠓⠒⠫⣝⣅⠀⡀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢸⡜⢀⡴⠚⠉⠒⢜⣆⡀⠀⢠⢇⡠⠤⠤⡀⠈⣟⡏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡞⠉⢿⣃⣜⠰⣶⣴⠀⡸⠿⠝⠒⠿⡏⠀⡄⠠⠈⣆⢸⡟⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠈⠻⣺⣄⣈⡠⠞⠃⢀⣀⠀⠀⠙⢦⡙⠚⠀⣾⣿⠁⠀⢰⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢠⠄⠀⣡⠂⣀⠴⠊⠁⠀⠉⠙⢲⠠⣍⠑⠚⠊⠉⠉⠀⡏⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⢀⠇⠀⡞⠁⠀⣹⠂⠀⠀⠀⠀⢀⡞⠀⠈⢳⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢤⢻⠁⠀⡀⡙⠋⠉⠉⠒⠢⡎⠀⢀⠀⠀⠇⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡈⣞⠲⠼⢻⣀⣀⠀⠀⢀⡼⠁⠀⣼⣆⠀⠀⢠⡶⣯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢎⠪⣝⡒⠾⣀⣉⣹⡳⠿⠒⢓⡖⠉⣓⡶⣖⣟⣷⡟⢀⡤⠤⢤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣈⠉⠷⢬⣵⡞⠛⠒⡟⠛⠛⣯⠞⠛⣷⣯⢠⠿⢷⡿⠋⠀⠀⠀⠈⠛⣶⣤⡈⡹⢦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠒⠛⠛⠒⢾⡿⠦⣀⠀⠀⠹⠤⣨⠧⠒⠟⢧⣀⠞⠁⠘⠃⣠⢿⡁⠀⠀⠀⠀⠀⠀⠈⢳⡈⠳⡄⠙⣆⠀⠀ ⠀⠀⠀⠀⣀⣠⣴⠏⠀⢷⡄⠀⠀⠀⠀⣿⠦⠈⠓⡤⢄⣀⣆⣀⣀⣀⣀⣀⣠⠤⠴⡞⠓⠚⣇⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠘⡄⢹⡄⠀ ⠀⢀⡴⢛⡽⠚⡿⢧⣀⡼⠃⢠⡆⠀⠀⡿⠒⠁⠸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠇⢸⠷⡀ ⠀⡾⢡⡏⠀⣠⢷⡀⡞⠀⠀⢯⠉⢦⣴⠁⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠳⣄⡀⠀⠀⠀⢠⠏⣠⠾⢚⡟⠀⢧ ⢸⠁⡏⡇⠀⢧⣈⢻⣇⠀⠀⠀⢷⡽⠁⠀⠀⠀⣠⢧⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠸⡅⠀⠀⠀⣠⣼⠛⠒⠲⣾⠛⠚⣡⡴⠋⠀⠀⢸ ⡾⠀⠣⠽⡦⠒⠁⠀⣈⡷⠦⢤⡞⠀⠀⠀⣀⠔⠁⣸⠀⠀⠀⣠⢴⡏⠳⢄⡀⢀⣀⣠⠗⠀⠠⣶⣾⠋⢠⠒⡆⢹⠎⠉⠁⠀⠀⡇⠀⢸ ⢷⠀⠀⠀⠘⠦⠟⠉⠉⠀⠀⡾⠁⠀⠀⠈⠁⠀⠀⠘⠉⠉⠉⠁⠀⠀⠀⠀⠻⢏⠀⠀⠐⠁⠀⠁⠺⠶⢋⣀⠓⠻⡄⠀⠀⠀⠀⠀⠀⡏ ⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢳⡀⠀⠀⠀⢀⠼⠀

⬛🟪🟪🟪🟪🟪⬛⬛ 🟪🟪🟪🟪🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪🟪🟪 ⬜⬛🟪⬜⬛⬛🟪🟪 🟪🟪🟪🟪🟪🟪🟪🟪 🟪⬛⬛⬛⬛⬛🟪🟪 🟪🟪⬛⬛⬛🟪🟪🟪 🟪🟪⬛⬛⬛🟪🟪🟪 ⬛🟪🟪🟪🟪🟪🟪⬛ ⬛⬛⬛⬛⬛🟪🟪🟪 ⬛⬛⬛⬛⬛🟪🟪🟪 ⬛⬛⬛⬛⬛⬛🟪🟪 ⬛⬛⬛⬛⬛🟪🟪🟪 ⬛⬛⬛⬛⬛🟪🟨🟨 ⬛⬛⬛⬛⬛🟪🟪🟨 ⬛⬛⬛🟪🟪🟪🟪🟨 ⬛⬛⬛🟪🟪🟪🟪🟪 ⬛⬛⬛🟪🟪🟪🟪🟪 ⬛⬛🟪🟪🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪🟪🟪 🟪🟪🟪🟪⬛🟪🟪🟪 🟪🟪⬛⬛⬛🟪🟪🟪 ⬛⬛⬛⬛⬛⬛🟪🟪 ⬛⬛⬛⬛⬛⬛🟪🟪 ⬛⬛⬛⬛⬛⬛🟪🟪 ⬛⬛⬛⬛⬛⬛🟪🟪 ⬛⬛⬛⬛⬛⬛🟪🟪 ⬛⬛⬛⬛⬛⬛⬛🟪 ⬛⬛⬛⬛⬛⬛⬛🟪 ⬛⬛⬛⬛⬛⬛⬛🟪 ⬛⬛⬛⬛⬛⬛⬛🟪 ⬛⬛⬛⬛⬛⬛⬛🟪 ⬛⬛⬛⬛⬛⬛⬛🟪 ⬛⬛⬛⬛⬛🟪🟪🟪 ⬛⬛⬛⬛⬛🟪🟪🟪

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠉⠉⢢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠂⠐⠠⢀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠳⠦⢶⣤⡤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢤⡀⠀⠑⡀⢀ ⠀⠀⠀⠀⠀⠀⠀⣔⠐⠃⠈⠨⡁⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⠌⠈⠘⢢⠥⡆ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢡⢸⡠⠤⠤⠤⢄⣀⠀⢀⣮⠂⠀⠀⠀⡸⢠⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢄⣀⠼⠃⠢⠝⢃⣀⠀⠤⡍⠇⠃⠀⠀⠀⠐⢉⠎⠀ ⠀⠀⠀⠀⠀⠐⠶⠔⡾⢁⠠⠑⡄⠫⠀⠐⢁⠤⢒⠦⠁⠀⠆⢀⡀⢈⠔⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠩⡡⠊⡀⡈⠀⣱⠔⣈⠭⠉⠶⡀⠰⢊⡡⠔⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⡇⠁⢸⡱⠡⢴⠁⠌⠀⢠⣴⠀⡗⠐⠈⠉⢠⠃⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣀⣀⢹⡱⡷⢎⣁⠨⠛⣼⡀⠀⢈⣡⠊⠃⠀⠀⣠⠎⠀⠀⠀⠀⠀ ⠀⡠⠏⡩⣭⠑⠒⢩⣷⡧⠤⣤⣶⣾⡯⡏⠉⠁⠈⡀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀ ⠸⠁⣎⡉⡺⢦⣼⠀⢡⢈⢲⠤⡤⠄⠚⠓⠒⠒⠖⠙⠇⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⢙⣿⠄⢼⠳⠒⠽⠂⡾⢷⠇⢎⠊⢉⠕⡲⠊⡌⠙⣷⡿⣍⠻⠀⠀⠀⠀⠀⠀⠀ ⠀⠡⠤⠂⠃⠄⠊⠒⠁⣸⡄⠌⠣⣨⣘⣄⣠⠧⠶⠁⢊⣼⠠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⢾⢿⠘⢌⠂⠔⠁⠀⢇⠀⣠⣷⡓⣿⣎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠴⡟⣓⣩⠄⠓⠎⠉⠐⠒⠒⠚⢿⢮⣤⠬⠼⢴⢳⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⡆⢇⠀⠳⠤⠤⡤⠊⠀⠀⠀⠀⠀⣔⠛⠠⠤⢔⡑⠇⢿⠇⠀⠀⠀⠀⠀ ⠀⠀⣴⣛⣭⣕⣲⣐⢲⠃⠀⠀⠀⠀⡠⠚⢉⢩⠭⠬⠭⠭⣶⠗⠀⠀⠀⠀⠀⠀ ⠀⠮⠈⣈⣀⣉⣉⡈⠏⠀⠀⠀⠀⠀⠉⠁⠒⠒⠒⠒⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⠏⠀⢀⡤⣄⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠋⠉⠉⣿⠀⠀⠀⣿⠀⠀⢸⠀⠀⠈⠳⡀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡖⠛⠉⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠈⡆⠀⠀⠀⢱⡀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⢀⡤⠦⠤⣀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⢹⠀⠀⠀⢣⠀⠀⠀⠀⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⢠⠏⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⢷⡆⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⡆⠀⠀⠘⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⠀⡜⠙⢦⡀⠀⠀⠑⢄⠀⠀⠀⠙⢷⡀⠀⠀⣀⣼⣧⣤⣤⠀⠀⢳⠀⠀⠀⢣⠀⠀⠀⡞⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀ ⡇⠀⢳⠀⠀⠙⣄⠀⠀⠈⠳⡀⠀⠀⣈⣿⣿⡟⠋⣽⢁⣿⣿⣶⣿⡈⢇⠀⠀⠘⡆⢀⡾⣷⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀ ⢧⠀⠘⣆⠀⠀⠈⢣⡀⠀⠀⠙⣄⠀⡿⠛⠛⠿⠗⠚⠋⠉⠉⠀⠉⠛⠺⠦⣀⠀⣷⣤⡞⠁⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀ ⠘⡄⠀⠘⢦⠀⠀⠀⠱⣄⠀⠀⠈⢦⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣟⠉⠉⠋⠉⠙⢲⡄⠀⠀⠀⠀⠀ ⠀⠹⣄⠀⠀⠙⠢⠤⣤⠌⢳⣄⣀⠜⠉⠓⠤⢤⡖⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠑⢄⠐⢦⠒⡾⠒⠒⠢⣄⠀⠀ ⠀⠀⠈⠲⠤⣀⣀⡘⠛⠛⣿⣾⠋⠀⡠⠒⣶⢬⣧⣄⡠⢃⡔⠉⠸⡍⢻⣷⣦⣄⠀⠀⠀⠈⢫⠉⠞⠀⠀⠀⠀⠈⢦⠀ ⠀⠀⠀⠀⠀⠚⠥⠒⣎⣀⢴⠇⠀⢸⠁⠀⢹⣼⣿⣷⣄⢸⠀⠀⠀⠙⢿⠛⠿⠋⠳⢄⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠈⣇ ⠀⠀⠀⠀⠀⠀⡠⠊⠙⢢⡼⠀⠀⡇⠀⠀⠀⠻⣌⠟⠛⢺⡄⠀⠀⠀⠀⠙⠦⠤⠏⠈⡆⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⢧⠀⠀⢻⠀⠀⠀⠀⠈⠓⠒⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⢀⣠⡾⠒⠢⡀⠀⡇⠀⠀⠀⠀⠀⢠⠇ ⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢰⢣⠖⠉⠚⢷⣄⡀⠀⠀⠀⢀⡼⠁⠑⠤⠠⠄⠒⣉⢽⠀⠀⠀⣽⠀⠇⠀⠀⠀⣠⠔⠁⠀ ⠀⠀⠀⠀⠀⠀⠑⠦⣄⡤⡇⠸⣀⠀⠀⢠⡇⠈⠑⢒⣒⣭⣤⣒⣒⣒⠒⠢⢤⣿⠊⠑⠒⠋⠁⡸⠀⠀⠉⠛⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⣧⠀⠈⠙⠋⠉⣀⡠⢲⣿⣿⣿⣿⣿⣿⠿⠛⠀⢠⡟⠀⠀⠀⠀⡴⢁⠀⠀⠀⠀⠀⢱⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠯⢧⠀⠀⠀⠀⠻⣆⠀⠉⠉⠉⢻⡁⠀⠀⢀⡠⠞⠀⠀⢀⡠⠊⣑⣾⠓⠦⣀⣀⣀⠜⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠈⠓⠤⣀⣀⣠⣿⡿⠟⠉⠀⠀⣀⣴⣿⡟⠛⠋⠙⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠓⠲⠾⣷⣤⣄⣀⡀⠀⢀⣀⣀⣀⣀⣴⡖⠉⠙⠻⣿⣿⠃⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠛⠳⠦⣤⣭⣿⣿⠋⠉⠀⠉⣿⣿⡄⠀⠀⠀⠈⢿⡦⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢀⣠⡶⠛⣻⡿⠻⢶⣦⣤⣿⠿⠛⠛⢦⡤⠤⠤⣌⣷⠶⢶⡟⠀⠀⠀⠀⠀⠀⠀

🟪🟪🟪🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪🟪 🟪⬜⬛🟪⬜⬛🟪 🟪🟪🟪🟪🟪🟪🟪 🟪⬛⬛⬛⬛⬛🟪 🟪🟪⬛⬛⬛⬛🟪 🟪🟪🟪🟪🟪🟪🟪

⠀⠀⠀⠀⠀⠀⠀⣠⡾⡿⠿⠿⢿⡿⡿⠿⡿⠛⠛⢍⢢⣀⣱⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠙⢸⠃⣀⣠⣼⣧⣷⣶⣾⣶⣾⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⢠⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⠁⠁⣾⡿⠋⠉⢹⣿⡇ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠉⢉⠩⠿⡻⡋⠀⠀⡜⣡⣅⢆⢸⡟⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⡆⣾⣷⢸⠀⠀⠀⠡⢛⡋⠜⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠒⠒⠁⠀⠀⠀⠡⠀⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠲⠛⣀⠄⠀⡸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄⠀⠈⠀⠀⠀⠈⠁⠀⠀⡰⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠿⣌⡳⠦⣄⡀⠀⠀⠀⢀⠜⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢳⡒⠛⠨⢭⣲⠮⠭⣴⡌⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠶⣷⠤⠤⢀⡈⠉⠒⢺⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠤⡀⡰⢁⠔⠊⢀⣠⣄⣀⣌⡑⢤⠼⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣿⡕⠁⣠⠶⠋⠁⠀⠀⠀⠈⠢⡱⡜⡄⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⣤⢤⡏⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⡌⢆⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⡿⣿⢿⢿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟⢸⣷⠉⣿⡇⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣇⣿⣿⣤⣿⣿⣸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣭⣈⢪⢆⠀⡧⣂⣨⣭⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢻⣻⣏⠫⣋⠻⠁⠀⢙⣦⢠⠈⠻⣻⡯⢫⢉⣿⣳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢕⢻⣿⣄⠀⠀⠀⠘⠀⠀⠉⠂⠀⠀⠀⣤⡞⣁⡽⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠛⢯⠛⠶⡄⠀⠀⠀⠀⠀⠀⠀⢨⡗⠚⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠈⠉⠉⠉⠁⣠⠔⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⣾⠈⠒⠤⠤⠔⠊⢻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡜⡁⢿⣿⠀⠀⢀⠀⠀⠀⢸⣿⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡋⢀⣇⣸⠋⠀⠀⠘⠆⠀⠀⠘⢻⣳⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣋⡸⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣙⣆⡀⠀⠀⠀ ⠀⢠⠖⠉⠀⢠⣿⣿⣿⣿⣿⠈⠉⠲⠦⠠⠶⠊⠁⢸⣿⣿⣿⣿⣯⠉⠉⠑⢆⠀ ⢠⠃⠀⠀⠀⣿⣿⣿⣿⠛⢿⣷⣄⡀⠀⠀⠀⣀⣤⣿⠟⣿⣿⣿⣿⡇⠐⠀⠀⢣ ⠇⠀⠀⠀⣎⡠⣿⣿⣿⠀⠯⡽⣿⣛⣷⣶⣟⣻⡿⡭⠆⢸⣿⣿⣃⢨⡆⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⡏⡹⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣤⠤⠤⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢰⢃⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠓⠒⠤⣄⡉⠉⠛⠛⠳⠶⢶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢶⣤⣄⣀⠞⠀⠀⡎⡸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⣤⣀⠀⠀⠀⠀⠉⠁⠒⠂⠤⠤⣀⡀⠀⠀⠀⠀⠀⠉⠑⠒⣤⠽⠋⠀⣀⡼⢿⣧⣄⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠉⢒⣦⠤⣀⡀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠶⢖⣈⠉⠁⠀⠀⢀⣠⣿⠗⠒⠬⠩⠝⣛⣛⣶⣶⡦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠎⠁⠀⠀⠀⢹⡗⠢⢤⣀⣀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠾⢯⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠒⠈⠉⠒⠤⠤⠠⠤⠟⠛⠂⠉⠁⢈⣿⠖⠒⢤⣄⡀⠀⠀⠀⠀⠈⠓⠤⣉⠐⠢⢤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣡⣴⡾⠝⠋⠁⠉⠑⠂⠠⠄⣀⠀⠀⠉⠑⠒⠤⢍⣑⠲⢤⣄⣀ ⠀⠀⠀⠀⠀⠀⢿⣵⣶⡿⣟⡆⠀⠀⠀⠀⠀⠀⣀⣀⢤⣾⡛⣿⠯⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⢄⣀⡀⠀⢉⣻⡿⠿ ⠀⠀⠀⠀⠀⠀⠀⠙⠯⣟⠻⠟⣦⣤⣤⣔⣚⣿⡷⠖⠊⠉⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⡏⠁⠈⢻⡿⠀⠀⠀⠀⠀⠈⢿⣶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀