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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢉⠴⣚⠉⣙⠢⢄⡤⢞⡂⢀⣐⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡤⣞⢁⠊⢀⣀⠐⢿⡄⠰⢁⡀⠈⠺⣦⢡⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣗⣟⡸⠀⠻⡿⠃⢸⣇⢃⠿⠿⠀⠀⣽⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⢷⣴⡀⠀⠠⣪⣾⣷⡄⡀⠠⣐⢕⠁⠀ ⠀⢰⡦⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠲⡖⠓⠉⠁⠈⠉⠒⠀⠈⢸⠀⠀ ⢶⣿⣷⣤⢀⣀⡀⠀⠀⣏⡑⠢⢄⠀⠀⠀⠈⠐⠀⠐⠀⠀⠀⠀⠀⡸⡀⠀ ⠛⠛⠛⠟⠀⠤⠤⠌⢉⠀⠈⠓⢬⣿⣦⡤⣤⣤⠤⠤⣤⣤⣤⣤⣚⣔⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡤⠂⠀⠀⢀⠤⠤⢄⡨⠔⠒⢍⠉⢁⣯⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢤⡤⣬⠀⠀⠀⢇⠀⠀⠀⠁⠀⠀⡸⢰⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⡿⣽⡀⠀⠀⠈⠒⢄⡀⠀⢀⠔⠁⠈⠙⡋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠳⢧⣠⣤⣄⣠⣀⣈⣱⡥⠤⠴⠦⠴⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬜⬛⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜🟨⬛🟨⬛🟨⬛🟨⬛🟨⬛⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜🟨🟨🟨⬛🟨🟨🟨🟨🟨🟨⬛🟨🟨⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🌫️🌫️🌫️🌫️🌫️🌫️🟨🟨🟨🟨⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬛⬜🟨⬛🟨🟨🟨🌫️🌫️🌫️🟨🟨🌫️🌫️🌫️🌫️🟨⬛⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🌫️🌫️🟨🟨⬜⬜🟨🟨🌫️🌫️🟨🟨🟨⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🌫️🌫️⬜⬜⬜⬜⬜⬜⬜🟨🌫️🌫️🟨🟨⬛⬛⬜⬜ ⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🌫️⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🌫️🌫️🟨🟨⬜⬜⬜ ⬜⬜⬜⬜⬜🟨🟨🟨⬛⬛🌫️🌫️⬜⬜⬜⬜🏾🏾⬜⬜⬜⬜🌫️🌫️🟨🟨⬛⬛⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛🌫️🌫️⬜⬜⬜🏾⬛⬛🏾⬜⬜⬜🌫️🌫️🟨🟨🟨⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛🌫️🌫️⬜⬜⬜🏾⬛⬛🏾⬜⬜⬜🌫️🌫️⬛🟨🟨⬜⬜ ⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🌫️🌫️⬜⬜⬜⬜🏾🏾⬜⬜⬜⬜🌫️🌫️⬛⬛🟨⬜⬜ ⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🌫️🌫️⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🌫️🌫️⬛⬛⬛⬜⬜ ⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🌫️🌫️⬜⬜⬜⬜⬜⬜⬜⬜⬜🌫️🌫️🟨⬛⬛⬜⬜ ⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🌫️🌫️🌫️🟨⬜⬜⬜⬜🟨🌫️🌫️🌫️🟨🟨🟨🟨⬜⬜ ⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🌫️🌫️🌫️🟨🟨🟨🟨🌫️🌫️🌫️🟨🟨🟨🟨🟨⬜⬜ ⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🟨🟨🟨🟨🟨🟨⬜⬜ ⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🌫️🌫️🌫️🌫️🌫️🌫️🟨🟨🟨🟨🟨🟨🟨⬜⬜ ⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜ ⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🟨🟨🟨⬜⬜⬜ ⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟧🟧🟧🟨🟨🟨🟨🟧🟧🟧🟨🟨🟨🟨⬜⬜⬜ ⬜⬜⬜⬜🟦🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🟧🟧🟧🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜ ⬜⬜⬜⬜🟦🟦⬛⬛🟨⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜ ⬜⬜⬜⬜🟦🟦⬛⬛⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟦🟦⬜⬜ ⬜⬜⬜⬜🟨🟦⬛⬛⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟦🟦🟦🟦🟦⬜⬜ ⬜⬜⬜🟨🟨🟨⬛⬛⬛⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🏽⬛🟦🟦🟦🟨⬜⬜ ⬜⬜🟨🟧⬛⬛⬛⬛⬛⬛⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🏽🟦🟨🟨🟨🟨⬜ ⬜🟨🟧🟨⬛⬛⬛⬛⬛⬛⬛🟦🏽🏽🏽🏽🏽🏽🏽🟦🟦🟦🟦🟨🟨🟨🟨🟨⬜ 🟨🟨🟨🟨⬛⬛⬛🟦🟦🟦🟦🟦🏽🟦⬛⬛⬛🟦🏽🟦🟦🟦🟦🟨🟨🟧🟨🟨⬜ 🟨🟨🟨⬜🟨🟨🟨🟦🟦🟦🟦🟦🏽⬛🟦🟦🟦⬛🏽🟦🟦🟦🟦🟨🟨🟧🟨🟨⬜ 🟨🟨⬜⬜🟨🟨🟨🟦🟦🟦🟦🟦🏽⬛🟦⬛⬛🟦🏽🟦🟦🟦🟦🟨🟨🟧🟨🟨⬜ ⬜⬜⬜⬜🟨🟨🟨🟦🟦🟦🟦🟦🏽⬛🟦🟦🟦⬛🏽🟦🟦🟦🟦🟨🟨🟧🟨🟨⬜ ⬜⬜⬜⬜🟦🟦🟦🏽🟦🟦🟦🟦🏽🟦⬛⬛⬛🟦🏽🟦🟦🟦🟦🟨🟨🟧🟨🟨⬜ ⬜⬜⬜⬜🟦🟦🟦🏽🟦🟦🟦🟦🟦🏽🏽🏽🏽🏽🟦🟦🟦🟦🏽🟦🟦🟦🟨🟨⬜ ⬜⬜⬜⬜🟦🟦🏽🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🏽🟦🟦🟦🟨🟨⬜ ⬜⬜⬜⬜🏽🏽🟦🟦🟦🟦🟦🟦🟦🟦🏽🏽🟦🟦🟦🟦🟦🟦🟦🏽🟦🟦🟨🟨⬜ ⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦🏽🏽🟦🟦🟦🟦🟦🟦🟦🟦🏽🏽🟨🟨⬜ ⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🏽🏽🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛⬛⬜ ⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦🏽🏽🟦🟦🟦🟦🟦🟦🟦⬜⬜⬛⬛⬛⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦🏽🏽🟦🟦🟦🟦🟦⬜⬜⬜⬛⬛⬛⬛⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦⬜⬜🟦🟦🟦🟦⬜⬜⬜⬜⬛⬛⬛⬛⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬛⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟪🟪⬛⬛⬜⬜⬜⬜⬛⬛⬛🟪🟪⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜

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

⬜⬜⬜🟨🟨🟨🟨🟨⬜⬜⬜ ⬜⬜🟨🟨🟨🟨🟨🟨🟨⬜⬜ ⬜🟨🟩🟩🟨🟫🟫🟨🟨🟨⬜ ⬜🟩⬛⬜🟫⬛⬜🟫⬛⬛⬜ ⬜🟩⬜⬜🟫⬜⬜🟫⬛⬛⬜ ⬜🟨🟩🟩🟨🟫🟫🟨🟨🟨⬜ ⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜ ⬜🟨🟨🟨🟨🟨⬛🟨🟨🟨⬜ ⬜🟨🟨⬛⬛⬛🟨🟨🟨🟨⬜ ⬜🟦🟨🟨🟨🟨🟨🟨🟨🟦⬜ ⬜🟨🟦🟦🟦🟦🟦🟦🟦🟨⬜ ⬜🟨🟨🟦🟦🟦🟦🟦🟨🟨⬜ ⬜🟨🟨🟦🟦🟦🟦🟦🟨🟨⬜ ⬜🟨🟦🟦🟦🟦🟦🟦🟦🟨⬜ ⬛⬛🟦🟦🟦🟦🟦🟦🟦⬛⬛ ⬜⬛🟦🟦🟦🟦🟦🟦🟦⬛⬜ ⬜⬜⬜⬛⬛⬜⬛⬛⬜⬜⬜ ⬜⬜⬛⬛⬛⬜⬛⬛⬛⬜⬜

➖🟪🟪🟪🟪🟪🟪🟪🟪 🟪🟪⬜️⬜️⬜️⬜️⬜️⬜️🟪 🟪🟪⬜️⬜️🟪⬜️🟪⬜️🟪 🟪🟪⬜️⬜️🟪⬜️🟪⬜️🟪 🟪🟪⬜️⬜️⬜️⬜️⬜️⬜️🟪 🟪🟪🟪🟪⬜️⬜️🟪🟪 🟪🟪🟪🟪⬜️🟪🟪 🟪🟪🟪🟪🟪🟪 ➖➖🟪🟪

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠾⠛⠉⠉⠉⠉⠛⠿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠁⠀⢀⣠⣤⣤⣄⡀⠀⠈⢿⡆⠀⠀⠀ ⠀⠀⢀⣿⣁⣀⣠⡿⠋⠀⠀⠙⢿⣄⣀⣈⣿⡀⠀⠀ ⠀⠀⢸⣿⠛⠛⢻⣧⠀⠿⠇⠀⣼⡟⠛⠛⣿⡇⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠙⢷⣦⣴⡾⠋⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⣸⣿⠀⠀⠀⠛⠷⠶⠶⠾⠛⠀⠀⠀⣿⣇⠀⠀ ⠀⣸⣿⣿⢷⣦⣀⣀⣀⣀⣀⣀⣀⣀⣴⡾⣿⣿⣇⠀ ⢠⣿⢸⣿⠀⣿⡏⠉⠉⠉⠉⠉⠉⢹⣿⠀⣿⡇⣿⡄ ⢸⡏⢸⣿⣀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣀⣿⡇⢹⡇ ⢸⡇⠀⢿⣏⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⣹⡿⠀⢸⡇ ⢸⣿⣤⣌⠛⠷⣶⣶⣶⣶⣶⣶⣶⣶⠾⠛⣡⣤⣿⡇ ⠘⠿⠿⠇⠀⠀⠀⢿⡾⠇⠸⢷⡿⠀⠀⠀⠸⠿⠿⠃ ⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⡠⠬⡡⠬⡋⠀⡄⠀⠀⠀⠀⠀⠀⠀ ⡀⠁⠢⡀⠀⠀⢰⠠⢷⠰⠆⡅⠀⡇⠀⠀⠀⣀⠔⠂⡂ ⠱⡀⠀⠈⠒⢄⡸⡑⠊⢒⣂⣦⠄⢃⢀⠔⠈⠀⠀⡰⠁ ⠀⠱⡀⠀⠀⡰⣁⣼⡿⡿⢿⠃⠠⠚⠁⠀⠀⢀⠜⠀⠀ ⠀⠀⠐⢄⠜⠀⠈⠓⠒⠈⠁⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀ ⠀⠀⢀⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡀⠀⠀⠀⠀ ⠀⠀⢸⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀ ⠀⠀⠸⢸⣳⠦⣍⣁⣀⣀⣀⣀⣠⠴⠚⠁⠇⠀⠀⠀⠀ ⠀⠀⠀⢳⣿⠄⠸⠢⠍⠉⠉⠀⠀⡠⢒⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠣⣀⠁⠒⡤⠤⢤⠀⠀⠐⠙⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⡀⡼⠀⠀⠈⠱⡒⠂⡸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢒⠁⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠙⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣠⡶⠞⠛⠉⠉⠉⠙⠳⣦⡀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢾⡧⣆⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⠀⠀⠀⠀⠀⠀⠉⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠾⢶⡄⠀⠀⠈⢷⡹⣆⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣤⠞⠁⢀⣴⠞⠉⢿⣜⣀⣀⣤⡴⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣴⠛⠃⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠿⠛⠋⠛⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣄⣠⣤⣴⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⠿⠟⠛⠋⠉⠉⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⢛⣿⣉⣁⣀⣠⣠⣤⣴⣶⣶⠿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠻⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣿⣯⣵⣶⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⠀⠀⠀ ⠟⠛⠛⢿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⡿⣷⣶⢶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⣀⣀⣤⣤⣴⣶ ⣠⣤⣴⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠉⣀⣀⣤⣬⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⡶⠖⢻⡟⠉⠁⢸⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⢧⠈⢷⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀ ⢀⣀⣠⣤⡤⠴⠖⠖⣞⠛⠋⢩⠏⠀⠀⠀⠀⣾⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢻⢳⠀⠀⠀⠀⠀⠀⠈⢧⠘⡆⠀⢠⡀⠀⠀⠀⠀⠘⣆⠀⠀⠹⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⡞⠀⠀⠀⠀⠀⣿⣇⠀⠀⢸⡀⣦⠀⠀⠀⠀⠀⢸⢰⣧⠀⠀⠀⠀⠀⢷⡜⣧⣧⠀⠀⣿⡀⠀⠀⠀⣤⠸⣆⠀⠀⠹⡄⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢠⡇⠀⠀⠀⠀⢰⣿⣿⠀⠀⠘⡇⣿⠀⠀⠀⠀⠀⠸⣦⣿⡀⠀⠀⠀⠀⠈⢿⣜⣿⠀⠀⣿⢳⡀⠀⠀⠘⣧⡹⡄⠀⠀⢹⡀⠀⠀⠀⠛⠛⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠃⠀⠀⠀⠀⣾⠹⣿⡆⠀⠀⣇⣿⡆⠀⠀⠀⠀⠀⣿⡏⣷⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⣿⣈⣧⠀⠀⠀⠸⣷⣳⠀⠀⠀⢧⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡞⡇⠀⢸⠀⠀⠀⠀⠀⣿⠀⠈⣷⡀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠸⣇⣿⣤⣤⣶⠶⢦⣄⣿⢻⡆⠀⡿⠉⢻⣤⠞⢷⢦⣷⢻⣇⠀⠀⠘⣇⠀⠀⠀⠀⠀⢸⡀⣠ ⠀⠀⠀⠀⠀⠀⣸⣷⢻⡀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠘⢷⠀⠸⣿⣿⠀⠀⠀⠀⠘⣷⣿⡿⠟⠉⠁⠀⠀⠈⠙⡎⣿⢸⠇⠀⠀⠉⠀⢸⡇⢻⡘⣿⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠋⠁ ⠀⠀⠀⠀⠀⠀⣿⣿⣎⢧⠘⡇⠀⠀⠀⠀⢹⣦⣤⣀⣨⣷⡸⣿⠻⣇⢀⣴⠶⠾⠿⠿⡆⠀⣀⣤⣴⣶⣿⠟⠟⠻⣏⠀⠀⠀⠀⠀⠀⢻⠀⠁⢹⡇⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠆⠀⠀⠀⠀⠀⡇⠀⣙⣟⡄⢧⠀⠀⠀⠀⢹⡀⠀⠀⠀⢿⡳⣿⣄⡽⠋⠀⠀⠉⢠⡀⠀⣈⣥⡾⢋⣩⣤⣶⣾⣿⣿⣿⣷⣶⣤⣀⣀⠸⡆⠀⠀⠁⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠄⣧⣾⠛⠙⢻⣾⣄⡤⠶⠶⢦⣇⠀⠀⠀⠀⣷⣌⠛⢷⠒⠚⠛⠚⠚⠷⢺⡿⢋⣶⣿⣿⣿⠛⣻⠀⠀⠈⠉⠙⠻⣿⣯⣤⣿⠀⠘⡃⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⣧⡈⢃⠀⠀⠈⠛⠀⠀⠀⠀⢙⠂⠀⠀⠠⠽⣷⡆⠀⠀⠀⠀⠀⠀⠀⡟⣴⣿⣟⠙⠉⠉⢠⠋⠀⠀⠀⠀⠀⠀⢸⣿⠁⣿⠀⢸⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⡘⡇⣏⠃⠀⢁⣠⣴⣶⣟⣛⣛⣙⣿⣷⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠙⠷⢶⠞⠉⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⣿⠀⣿⠀⠀⡇⠀⠀⠘⣿⡆⠀⠀⠀⠀ ⠿⠋⠀⢸⣿⣿⣿⣄⣴⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣀⡠⣖⣒⣛⣻⣿⣿⡶⢂⡴⣣⢄⢹⢠⣿⠀⠀⡇⠀⠀⠀⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⢘⣿⣝⣿⣿⣿⠟⠁⠀⠀⠻⢦⣈⣙⣊⡷⠁⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⢾⢟⡯⠋⣠⡬⢀⡬⢃⡴⢫⡞⣱⢋⣼⣾⣾⡆⢠⠇⠀⠀⠀⢹⢿⣷⡄⠀⠀ ⠀⠀⢀⢸⣿⠛⢿⣿⣿⡆⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢀⠜⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⡿⠋⣰⡿⢀⡴⠋⡴⢋⠴⢪⣜⡵⢛⡟⠁⢻⡇⢸⠀⠀⠀⠀⠘⡆⠹⣿⡆⠀ ⠀⠀⢸⠀⣿⡄⠀⠙⣿⡿⢀⣤⣶⡾⢿⡟⠉⣭⢫⢁⡴⠃⠀⠈⢧⠀⠀⠀⠀⠀⠀⣠⢞⡵⣿⠋⣠⠞⢁⡴⠋⡰⢊⣠⢆⡴⡿⠛⡤⢋⠀⠀⠈⢳⡇⢀⡆⠀⠀⠀⡇⠀⢿⣿⠀ ⠀⠀⢸⡄⢹⣧⡄⠀⣼⠋⣲⡏⠀⣰⠟⣠⡞⣱⢏⠞⠡⠈⠀⠀⠀⡃⠀⠀⠀⢀⠞⡵⠯⠎⣠⠞⢁⡴⠋⣠⠞⠑⡝⣡⠏⠀⠀⢺⣇⡟⠀⠀⠀⡞⠁⢸⡇⠀⠀⠀⡇⠀⢸⣧⢧ ⠀⠀⠀⣧⠨⣿⣇⠀⠐⢻⠏⡼⡿⠛⣾⢋⡼⡡⠏⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠞⠡⠢⣊⠞⠁⠀⠀⠀⠈⠛⠁⠀⢀⡾⠁⣠⣾⡇⠀⠀⠀⡇⠀⠀⣿⣌ ⠀⠀⠀⣿⣸⡘⣿⡆⣠⢏⢾⡟⢁⡜⢡⢞⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⢟⣠⠞⣿⢿⡇⠀⠀⠀⣧⠀⠀⣸⣿ ⡆⠀⠀⣿⣿⣿⣾⣧⢁⢮⠏⣠⠟⠀⣡⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠒⠛⠛⠒⠲⢤⣄⡀⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⢀⣠⣴⠮⠗⠋⠀⢠⡿⢸⡇⠀⠀⠀⡟⡄⢰⠏⢻ ⣇⠀⠀⠸⡾⣿⣿⡙⢿⣇⡰⠋⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⣠⣴⣶⣾⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠘⣿⢸⡇⠀⠀⠀⡇⢳⠁⠀⠀ ⢿⡄⠀⠀⢻⡿⣿⣧⠀⠈⠙⠲⠶⠂⡀⠀⠀⠀⠈⢳⣶⣶⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⡇⠀⠀⠀⡇⠈⣇⠀⠀ ⠀⣿⣄⠀⠀⠻⣼⣿⣆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠿⠛⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⣿⣿⡆⣧⠀⠀⠀⡇⠀⠸⡄⠀ ⠀⣿⡟⠳⢤⡀⠙⠿⣿⣦⠀⠀⠀⣆⣘⡄⠀⠀⠀⠀⠀⠘⣿⣿⡟⠀⠀⠙⣿⣿⠟⠁⠀⠀⠀⢆⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⠈⡄⠀⠀⠀⣠⣾⣿⣿⣿⣿⠀⠀⠀⡇⠀⠀⢹⡄ ⣾⣿⡇⠀⠀⠉⣶⣤⣌⡙⠧⣤⣀⣈⣉⡴⠀⠀⠀⠀⠀⠀⠹⣿⠃⠀⠀⠀⣿⡏⠀⢀⠂⢲⠀⣾⣽⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⠀⢠⣼⣿⡧⣿⣿⠹⣿⡄⠀⠀⡇⠀⠀⠀⢻ ⣿⡟⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣯⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠄⠀⠈⠀⢸⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡄⣈⣧⢀⣶⣷⡀⠀⠀⠀ ⢯⣄⣠⣴⣛⠿⠿⠿⢿⢟⠿⣿⣏⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡏⠀⠄⠀⠰⠉⢉⡖⠻⡆⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠿⣿⣿⣷⣿⣿⣿⠈⣻⣷⠇⣿⣧⡀⠀ ⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣤⣾⡇⠀⢀⣿⣿⣦⣄⠀⠀⠀⠀⣷⠀⠀⠀⢺⡧⠀⠀⠠⠀⢀⡞⠛⠚⠃⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⡿⢠⣯⣿⢷⡌⠛⣿⣦ ⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⡿⠃⠠⣾⣿⣿⣿⣿⣷⣦⣀⠀⢹⡀⠀⠀⠈⠁⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⣾⣿⡿⢫⣿⣆⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣧⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⣀⣴⡾⠿⠛⢛⣻⣿⣿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⢸⣿⣿⡟⢂⡀⢻⣧⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣍⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡠⢀⣀⢾⠃⠀⠀⢀⣠⣴⢾⣻⣥⡶⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣏⠐⢂⠐⢂⡘⢷ ⠀⠀⠀⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠉⠁⠀⠀⠉⠀⠈⠻⣄⠀⠸⣶⣾⣿⢟⣫⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢃⠐⢀⠐⢂⡀⢆ ⠀⠀⠀⠈⠦⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣳⣄⣀⣀⡀⠀⣀⠀⠀⠀⢹⡄⠀⣿⣉⡈⠋⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢀⠰⢀⠰⠆⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⣩⣿⣛⣯⣽⣿⣿⡟⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣴⠶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣀⣤⠶⠟⢛⣻⣿⠏⢻⣿⣿⣿⣆⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⢀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡜⣁⠀⣙⠓⠤⠙⠻⠛⠁⣠⣄⢙⣧⣻⣿⠀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠱⣿⠏⢸⠀⠀⠀⠀⠀⠀⠀⢸⠁⣼⡿⠟⠛⠲⢴⢶⣶⣿⣿⣿⠿⠗⠉⠉⠀⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠛⠓⢸⠀⠀⠀⠀⠀⠀⠀⢸⣦⣭⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⣀⢈⡆⠀⠀⠀⠀⠀⠀⢸⣾⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠠⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡆⠙⠛⠀⡇⠀⠀⠀⠀⠀⠀⣠⢿⣿⠀⠀⠀⢀⣠⣤⣀⣀⢰⠀⠀⢀⣠⣴⣶⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⡇⠀⠀⠀⣇⢀⡀⠀⠀⠀⠀⣟⣢⠹⠇⠀⠶⣻⣿⣿⠿⡿⠋⡀⠀⣿⠟⠛⠋⠹⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠁⠀⡇⠀⠀⠀⢹⠉⠉⢳⡀⠀⠀⢻⣿⠛⢇⠀⠀⠈⠀⠠⠚⠁⠀⠳⠀⣿⡀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣧⠤⠤⡟⠀⠀⠀⣾⡧⠶⢤⣿⣉⣷⡌⢧⡇⢸⢦⡀⠀⠀⠀⠀⢀⡀⠄⠀⢱⠿⣆⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡜⣿⠀⠀⣶⠀⠀⠀⠈⠁⠀⠀⠙⠀⠉⠻⡆⠳⣌⣇⠳⡀⠀⠀⣰⠏⠙⢶⣤⣼⣿⣿⣦⡀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡞⠀⢸⠆⠘⠋⠁⠀⠀⠀⠀⠀⠀⡶⠛⠂⢀⡇⠀⠀⢘⡄⠀⠲⡀⢿⣤⡤⠤⠤⠽⠛⢛⣿⠃⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠁⠀⢸⠀⢷⠀⠀⢆⠀⠀⠀⠀⠀⡇⠀⠀⠘⡇⠀⣠⣾⠿⣄⠀⠑⠀⠘⢿⣶⣶⣶⣿⡿⣿⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⡀⠀⣾⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⡇⠀⠀⠐⣧⣾⣿⣿⡇⠈⠢⡀⠀⠀⠀⠹⣗⣊⣭⡼⠃⠀⣼⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢣⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄⠀⠈⠢⣄⠀⠀⠀⠁⠀⠀⠀⣰⢿⠀⠀⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣦⡀⠀⠈⠑⠦⠤⠤⢤⣴⣚⡁⣼⣴⣦⣄⡈⢿⣷⣦⣄⡀⠀⠀⠀⠀ ⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡝⢷⠄⠀⠀⠀⢀⣴⠛⠙⣻⣿⣿⣿⡙⠻⠉⢿⣿⣿⣿⣶⣄⠀⠀ ⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⢷⣄⡀⣠⡾⠻⢿⣯⣤⣤⣉⣻⠇⠀⠀⠈⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠑⢢⣤⣄⠀⠀⠀⠀⠖⠀⣼⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⠿⠟⠀⠀⠀⠉⠻⣍⣉⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⣻⡆⠀⠀⢀⣠⠴⠛⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣸⡵⠟⣳⡄⠀⠀⠀⢿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⣠⣺⡿⠷⠒⠉⠁⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⡏⣰⣿⠟⢙⣆⠀⠀⢸⣿⣿⣿⠿⠋ ⠀⠀⠀⠀⢀⡞⠋⠁⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣀⠀⣿⣿⠁⣰⣿⠿⣆⠀⠸⠿⠋⠁⠀⠀ ⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠈⠁⠀⠀⠀⠈⠉⠛⠃⠒⠛⠉⠀⠀⠀⠀⠀⠀

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⬜🟨🟨🟨🟨⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜🟨🟨🟨🟨 🟨🟨🟨⬜⬜🏽🏽🟨🟨🟨🟨🟨🟨⬜⬜🏽🏽🟨🟨🟨🟨 🟨🟨⬜🏽🏽🏽🏽🏽🏽🟨🟨🟨⬜🏽🏽🏽🏽🏽🏽🟨🟨 🟨⬜🏽🏽⬜⬜⬜⬜🏽🏽🟨🟨🏽🏽⬜⬜⬜⬜🏽🏽🟨 ⬛🏽🏽⬜⬜⬜⬜⬜⬜🏽🏽🏽🏽⬜⬜⬜⬜⬜⬜🏽🏽 ⬛🏽⬜⬜⬜🟧🟫⬜⬜⬜🏽🏽⬜⬜⬜🟧🟫⬜⬜⬜🏽 🏽🏽⬜⬜🟧⬜⬛🟫⬜⬜🏽🏽⬜⬜🟧⬜⬛🟫⬜⬜🏽 🏽🏽⬜⬜🟫⬛⬛🟫⬜⬜🏽🏽⬜⬜🟫⬛⬛🟫⬜⬜🏽 ⬛🏽⬜⬜⬜🟫🟫⬜⬜⬜🏽🏽⬜⬜⬜🟫🟫⬜⬜⬜🏽 ⬛🏽🏽⬜⬜⬜⬜⬜⬜🏽🏽🏽🏽⬜⬜⬜⬜⬜⬜🏽🏽 🟨🟨🏽🏽⬜⬜⬜⬜🏽🏽🟧🟧🏽🏽⬜⬜⬜⬜🏽🏽🟧 🟨🟨🟨🏽🏽🏽🏽🏽🏽🟧🟨🟨🟧🏽🏽🏽🏽🏽🏽🟧🟨 🟨🟨🟨🟨🟨🏽🏽🟨🟨🟨🟨🟨🟨🟧🟨🏽🏽🟧🟧🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨

⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬛⬜⬜⬛⬛⬜⬜ ⬛⬛⬛⬜⬛⬜⬜⬛⬜⬜⬛⬜⬜⬛⬜⬛⬜ ⬛⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛ ⬛⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛ ⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛ ⬜⬜⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛ ⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛ ⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜ ⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜ ⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜ ⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜ ⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜ ⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜

➖➖➖🟩🟩➖🟩🟩 ➖➖🟩🟩🟩🟩🟩🟩🟩 ➖🟩🟩⬜⬛⬜⬜⬛🟩 ➖🟩🟩🟩🟩🟩🟩🟩 🟩🟩🟩🟩🟥🟥🟥🟥 🟩🟩🟩🟩🟩🟩🟩 🟦🟦🟦🟦🟦🟦🟦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢞⡵⠟⠉⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣴⡄⠀⠀⡷⢦⣄⣠⣄⠈⠳⣌⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⢳⡟⠀⠀⢀⣠⣄⣀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⡇⠀⠈⠉⢟⠳⢦⣽⣧⠈⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠀⠘⠓⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀ ⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⢲⡿⠋⠉⢱⠟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠛⠉⢀⡴⢫⡅⠀⣠⣏⣀⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⢸⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢞⠋⠀⠀⣠⣤⠞⠓⢺⠋⠉⡿⠀⠀⡇⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠙⢷⣸⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⢀⣼⡴⠚⠋⡽⠃⠀⠀⡆⠀⣸⠁⠀⠀⡇⠀⠀⡏⠀⠀⠀⠀⠀⠀⢠⠀⠀⢹⣦⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀ ⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⣡⡴⠚⣩⡇⠀⢀⡞⠡⣄⡀⠀⡇⢠⠇⠀⠀⠀⣇⠀⢰⣟⢸⡇⠀⠀⠀⠀⢸⠀⠀⢸⠈⢷⡀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠗⣋⠁⠀⣰⢻⠀⣠⠏⠀⠀⠀⠈⠉⡏⡟⠒⠒⠒⠚⢻⠁⣸⢿⡘⡏⠀⠀⠀⠀⣾⠀⠀⣸⡆⠀⠹⣄⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠋⠀⠀⡟⠀⢠⠇⢸⣰⠏⠀⠀⠀⠀⠀⠀⣷⠃⠀⠀⠀⠀⢸⢀⡇⠈⣷⠃⠀⠀⠀⣼⢹⠀⢀⡟⣧⠀⠀⢹⣧⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡟⢹⡇⠀⠀⢸⡇⠀⡟⠀⣼⣇⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⣾⠀⠀⣿⠀⠀⠀⢰⠏⢸⡀⡼⠀⢸⠀⠀⢸⠈⢧⡀⣷⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠸⡇⠀⠀⣿⡇⢸⠁⠀⠈⠛⢿⣷⣶⣤⣀⡀⠲⠦⣄⡀⠀⠀⠀⠀⠛⠀⠀⢻⠀⠀⢠⠏⠀⢸⡼⠧⣄⠘⡆⠀⡞⠀⠈⢳⣽⡇⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⢻⡀⠀⡿⣿⡏⠀⠀⠀⠀⢸⣿⠉⠙⠻⠿⢿⣶⣶⡾⠀⠀⠀⠀⠀⠀⠀⡾⠀⣠⠏⠀⠀⡞⠁⠀⠈⠑⡷⢤⣇⡀⠀⠀⢻⣿⠀⠀⠀⠀⠀⢸⠁ ⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠈⣷⡀⡇⢹⡇⠀⠀⠀⠀⠘⣿⣆⠆⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⢠⣇⡴⢣⣀⠀⠀⠀⠀⠀⠀⠀⣇⣾⠀⠀⠀⡀⠈⢿⡇⠀⠀⠀⢀⡎⠀ ⠀⠀⠀⠀⣸⣿⡆⠀⠀⠀⠀⠀⠀⢻⣧⡙⢿⡁⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡾⠏⠀⢸⣿⣭⣑⡂⠀⠀⠀⠀⡟⢸⠀⠀⢀⡇⠀⢸⡇⠀⠀⠀⣾⠁⠀ ⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣷⡸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠿⢿⣷⣶⣶⣤⣼⡀⠀⢸⡇⠀⣿⣇⠀⠀⣴⠇⠀⠀ ⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⡿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⠁⣨⣿⡟⡛⠀⢀⣿⠀⢸⣿⡏⠀⣼⡏⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢿⡇⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣤⣾⡿⠋⢀⡇⢀⣼⡇⠀⣾⢿⡇⢠⡟⠁⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣸⢃⡞⢩⠁⣼⠃⢸⢧⡾⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⡟⢧⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⢠⣞⡼⠃⢀⣿⣾⡇⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣧⢀⠀⠀⠀⠀⠀⢸⡇⠈⣷⣄⠀⠀⠀⠀⠀⠀⢸⠛⠛⠷⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣥⢀⣴⠟⢀⡾⣼⠏⡿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣇⠀⣿⠙⢦⡀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠈⠻⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⢡⡞⠁⢠⡟⣹⠏⢸⠇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⡆⣼⠀⣾⠙⢦⡀⠀⠀⠀⠈⠛⠲⠤⠤⠤⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡁⢸⡟⠀⣴⢟⣴⠟⠀⣾⡇⠀⠀⠀⠀⠀⠀ ⠙⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣾⣿⣷⣹⠀⡿⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⣹⢟⡇⠘⢡⣾⣷⠟⠁⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⢠⡇⠀⠀⠀⠀⠙⠦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡴⠖⠛⠋⠁⣠⠞⠁⢸⢀⣴⠿⠋⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣇⣼⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣽⠛⣉⣴⣿⣿⡏⠀⠀⠀⢀⣠⠞⠁⠀⠀⣿⠟⠁⠀⠀⠀⠀⠀⢀⣀⣾⡇⠀⠀⠀⠀⠀⠀ ⢷⣄⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⢠⡟⠿⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠛⠉⠉⠛⠿⣿⡀⠀⢀⣴⠟⠁⠀⠀⠀⣼⣏⣀⣀⣤⣴⣶⣾⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠙⠳⣿⠁⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠚⣿⣦⡀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⣀⣤⣴⡿⠀⣰⠟⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⣀⣀⡀⠈⢛⢷⣤⣀⣤⡴⡛⠁⠀⠀⢀⡲⠶⠞⠛⠉⠁⣸⡇⣶⠋⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠈⠉⣻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣴⣶⣶⠿⠟⠛⠻⠷⣶⣶⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠁⠰⠆⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣇⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢾⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣦⡀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⣿⣦⠙⠻⠟⠛⠀⠀⠀⠀⠀⠀⣶⣿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣶⣤⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⣀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡍⠛⠻⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣶⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠻⠛⣿⡿⠁⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣷⣦⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣷⣶⣶⡶⠀⠀⠀⠀⠀⣼⣿⡇⠀⢸⣿⠇⠀⣠⣴⣾⠟⠛⠉⠉⠉⠉⠛⠻⣶⣤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣶⠃⠀⠀⠐⠿⠿⠀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣀⣀⣀⡠⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣿⡇⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⣿⡿⠿⠟⠛⠛⠀⠀⣀⣀⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢣⣾⣿⣥⣾⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⣀⣤⣶⠿⠛⠛⠛⠻⣿⣧⠀⠀⠀⠀⠀⣠⣶⣿⣶⣤⣾⡟⠁⠈⢱⣿⠁⠈⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⡿⠋⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⣿⣿⣿⣿⠟⠁⠀⠀⣠⣿⡟⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠶⠿⠿⠛⢋⡉⠁⠀⠀⣠⣾⡿⠋⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷⣦⣤⣶⣿⣛⣋⣠⣴⡾⠟⠋⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢀⣤⣶⣶⣄⢀⣴⡿⠋⠀⠀⣸⡟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠈⣿⣿⣿⣿⠿⠋⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⠛⠛⢛⡉⠁⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⣿⣧⣤⣤⣤⣶⡾⠟⠉⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⢩⡥⠄⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠿⢻⣿⣾⣷⣤⣴⣶⣾⣿⣿⣿⣿⣟⣟⣻⣿⣿⠿⠛⠉⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠛⠁⠀⠰⣿⡟⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⣀⣀⣀⣀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆ ⠀⠀⢠⣾⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⡇ ⠀⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇ ⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⣶⣶⡆⠀⠀⣿⣿⡇ ⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⡇ ⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⡇ ⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠛⠛⠃⠀⠀⣿⣿⡇ ⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇ ⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠃ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠘⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜ ⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜ ⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜ ⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜ ⬛⬛⬛⬛⬛⬛⬜⬛⬛⬜⬜⬜⬜⬛⬛⬜⬜⬜ ⬛⬛⬛⬛⬛⬜⬛⬛⬜⬛⬜⬜⬛⬛⬜⬛⬜⬜ ⬛⬛⬛⬛⬛⬜⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬜⬜ ⬛⬛⬛⬛⬛⬜⬜⬛⬛⬜⬜🟨🟨⬛⬛⬜⬜⬜ ⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨⬜⬜⬜ ⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨⬜ ⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜ ⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜ ⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜ ⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜ ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛⬛ ⬛⬛⬛⬛⬛⬜⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛⬛ ⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜ ⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜ ⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜ ⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜ ⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜ ⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠿⠿⠿⢿⣿⣿⠋⠁⣠⠶⠶⣤⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣠⡴⠀⠀⠘⡿⠀⠘⣅⡀⠀⠘⠧⠘⣿⣿⣿⡟⠿⠟⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡾⠋⢀⣀⣠⣀⡀⠀⣰⠟⠿⣶⡀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⠿⠟⠋⢁⣿⣿⣿⣿⡇⠘⠀⣰⠟⠉⠀⠙⣷⣰⡇⠀⠀⠘⣷⡀⠀⠸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡅⠀⠀⣯⠀⠀⠀⠀⢻⡟⣧⢀⣤⣄⣸⡇⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⢻⣆⢰⣿⣶⣾⡇⠸⣿⣿⣿⣍⡇⠀⢠⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡄⠀⠀⠹⣯⣻⣿⣿⣿⣴⣿⣿⠿⣿⣷⣤⡜⠋⠉⠉⠙⠻⣿⣷⡀⠀⠀⠀⢠⡟⠉⠙⢿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢿⣿⣄⠀⠀⣸⠿⠋⣹⣿⣿⣿⣿⣷⣆⠈⢉⢛⡂⠀⠀⠀⠀⠀⠙⣷⠀⠀⢠⡿⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠀⠀⠈⠛⢃⡜⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⢻⡟⠛⠇⠀⠀⢀⣿⠀⠀⢸⠇⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠈⢿⣿⣿⣿⣿⡿⠃⠀⢀⣴⠟⠀⠀⠀⠀⢠⣾⠏⠀⠀⢸⠀⠀⠀⠀⢸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⣰⠟⠻⣶⣄⡀⠀⠀⠀⠈⠉⠉⠉⠀⣀⣤⡞⠁⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⢸⣇⠀⠀⠀⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣤⣀⡀⠀⠀⠀⠀⠉⠛⠿⣶⡶⠶⠶⣶⣟⣛⣁⣽⠃⠀⣠⣴⠿⠋⠀⣀⣀⣤⠾⠿⠿⣿⡄⠀⠀⣿⣤⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢶⣦⣤⣤⣄⡀⠉⠷⣿⣿⣿⣿⣿⠟⢁⣤⡾⠋⠁⢀⣴⠞⠉⠉⠻⣧⠀⠀⠙⡷⠀⠀⠻⠆⠙⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠴⠞⣿⠇⠀⣼⡿⠛⠲⢤⣤⣭⣭⣭⣤⡾⠟⠙⢷⡀⠀⣾⠁⢰⣶⠀⠀⠙⠃⢀⠞⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠉⠉⠁⣀⣴⣾⣋⣀⣾⡟⠁⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠘⢷⡸⢿⣦⣾⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⣠⠞⠋⠘⠛⠛⠛⠛⠳⠶⣤⣄⡀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⢿⣦⡿⠁⠀⠀⠀⠀⢠⡄⠀⢠⠀⠀⠀⢠⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢀⡼⠋⣠⣾⣦⡀⠀⠀⢀⣠⣤⡀⠈⠙⠻⢿⣏⠀⢠⣤⡀⠀⠀⠀⢈⣿⡀⠀⠀⠀⠀⠀⢸⡇⢠⡿⢀⡟⢠⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡿⠀⣼⣿⣿⣿⠇⠀⣠⣿⣿⣿⣿⠀⠀⠀⠈⠙⢷⣿⠈⢳⡄⠀⠀⣾⠉⢻⣄⡀⠀⠀⠐⡿⣥⣟⣴⠟⣰⡞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢸⣿⣿⣿⡟⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣆⠘⣧⠀⠀⣿⡀⠀⠙⢿⣦⣄⡀⠀⣋⣸⣯⠾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠙⠛⠋⠁⠀⢾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢹⡆⠸⡆⠀⠈⢿⣦⣄⣀⢈⣽⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠻⣄⣀⣀⣠⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣷⣄⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣧⣤⣤⡤⢤⣤⣤⣤⣄⣀⣤⡶⠶⠾⠷⢶⣦⣤⣽⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣀⠀⠀⠀⠉⢻⡁⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠉⠙⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢿⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠘⣧⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⢻⡇⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣀⠀⠀⢠⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣾⠟⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⡿⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣧⡀⣿⡇⠀⠀⠀⢠⣤⠀⠻⣷⡄ ⠋⠀⠀⠀⠀⠀⠸⣆⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣬⡉⠙⣷⡄⠀⠀⠀⠀⠈⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡁⠀⢀⣤⣤⡈⡆⠀⠹⡇ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⢿⣶⣮⣿⣦⡀⠀⠀⠀⠀⠳⣆⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠿⣿⣿⣿⣷⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⣀⠀⠀⠀⠻⢿⣴⣞⡛⠿⢿⣿⣦⡀⠀⠀⠀⢹⣿⠳⣤⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⡀⠈⠙⠛⠿⣤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⠀⠈⠷⡀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣽⠷⠶⠶⠒⠀⠈⣁⡀⠰⠶⠿⣽⡀⠀⠀⠀⢿⣷⣮⣁⠀⠀⠀⠀⠙⣿⣷⣦⣤⣶⣊⣉⣉⣛⣶⣶⣶⠿⣍ ⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⠉⠻⢦⣀⣀⠙⢦⡀⠀⠀⣀⡤⢖⡏⠀⠙⠳⣄⠀⠀⠀⠀⠉⠙⠛⠓⠒⠾⣧⠀⠀⠀⠀⠙⠊⠙⢷⡄⠀⠀⠀⠈⠻⣿⡟⠀⠀⣨⣿⣿⣍⠉⢿⡟⠉ ⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⠀⠀⠀⠉⠳⣝⡲⢤⣤⣠⣞⠛⠁⠈⠣⣀⠀⠈⠙⢦⡀⠀⠀⣰⠗⠂⠀⠀⠈⠃⠀⠀⢹⣦⣀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢷⣠⢾⣇⡙⠛⠻⢷⡄⠻⣆ ⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣇⠀⠀⠀⠀⠀⣽⣿⣾⣿⠉⠑⠒⠲⢦⣌⣶⣤⠶⠂⢈⣰⣾⣁⣠⣀⣤⣴⡖⠁⠀⠀⢸⡟⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⡿⣄⠈⠓⠶⣄⠀⣿⠀⠨ ⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢹⡄⠀⠀⠀⠘⠁⣸⡏⠀⠀⠀⢀⡤⠚⢻⣤⣿⣯⣿⣿⣽⣾⣿⣿⡏⠉⣿⢉⠀⠀⠀⢸⡇⠀⠀⠉⠓⢆⠀⠀⠀⠀⠰⣦⡉⠘⢦⡀⠀⠈⣷⣿⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢣⠀⠀⠀⣠⣾⣯⣁⠀⠀⣼⡿⣳⣶⣿⣿⡿⠿⣿⣿⣿⡟⠁⣽⠇⣸⡿⣋⡀⠀⠀⠈⠁⠀⠀⠀⠸⣆⠻⣄⠀⠀⠀⣯⠙⢦⡀⢳⡀⠀⢸⡌⢀⣾ ⡇⠀⠀⢰⡆⠀⠀⠀⠀⠻⣆⠘⣇⠀⢰⣿⣿⣿⣿⡷⢾⣿⠧⣴⣿⠛⢁⡄⠈⠉⠉⠁⠀⣠⡿⣰⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠻⡗⡄⠀⢹⠀⠀⠙⢾⣷⡀⠀⡇⢾⣿ ⡇⠀⠀⢸⣿⣀⣸⣄⠀⠀⣙⢷⣜⠦⠈⠻⣿⣯⡀⠀⠨⠃⢀⣿⠇⠀⠘⢿⣀⣀⣀⣠⣾⣵⡾⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠹⡾⡆⣸⠀⠈⣦⣀⣙⣷⡰⣷⠈⣿ ⣿⡀⠀⠈⣿⣿⡟⢿⣷⣄⠈⢳⣌⠷⣄⠀⠈⠉⠁⠀⠀⠰⢿⡟⠀⠀⠀⣀⣽⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢳⡄⡟⡆⢰⣿⠟⠉⠀⠹⡏⠀⢸ ⣿⣷⠀⠀⢿⣿⣷⣌⣿⣿⣿⣦⣜⣷⣈⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠁⠀⠀⠀⠀⠀⣰⠃⠀⠘ ⣿⡝⣧⢠⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⠀⠀⢀⣀⣀⣤⣴⠋⠀⠀⠀ ⠁⠙⠙⢷⣷⡸⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠀⢠⠏⠉⠁⡇⣿⠀⣼⣃⡀ ⡆⠀⠀⠀⠻⠀⢹⣿⣿⠉⢏⣹⠟⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⣾⡷⠋⠀ ⡟⠄⠀⠀⠀⠀⠀⢻⣿⣄⠈⠛⠷⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀ ⣧⠀⢀⠀⠀⠀⠀⠀⠘⠻⣿⠦⢴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡹⣆ ⢿⡄⠈⢦⡀⠀⠀⠀⠘⢶⣍⣁⡾⢤⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢸ ⠈⢻⡄⠀⢳⣄⢀⡀⠀⠀⠀⠙⠿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧ ⠀⠀⠻⠀⠈⣿⣮⡻⢦⣀⡀⠀⠀⠈⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿ ⠀⠀⠀⠀⠻⣿⢸⣿⣦⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿ ⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣛⡻⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⢠⣤⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠸⢸⣿⣿⣿⢻⣿⡟⢧⡀⠀⠀⠀⠀⠀⠘⣯⣥⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿ ⠀⠀⠀⠀⠀⡄⢸⣿⣿⣿⡜⣿⡇⠀⣿⣦⡀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⢠⡇⠈⢿⣟⢿⣷⣻⣷⠀⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠙⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⢠⡞⠀⠀⠀⠸⣄⠁⢀⣿⣄⠸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿ ⠀⠀⢀⡟⠀⠀⠀⠀⠀⠙⢶⣿⣷⣝⠀⠻⢿⣿⣿⣿⣿⣷⣤⣤⣤⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣤⡼⠿⠛⠛⢉⣦⡶⣿⡉⡉⠉⠛⠶⣤⣄⠀⠀⣀⢀⣠⣴⣿⣿⣝⠛⠛⠿⣿⣿⣦⡤⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡇⠀⠀⠀⢰⣤⠀⠀⠀⠀⠈⠻⣿⣤⣤⣤⣤⣶⣿⣿⣿⣿⣾⣿⣭⣒⠦⠬⠿⠷⣀⠈⠻⣿⣿⣿⣿⣿⣷⣦⡀⠈⠉⠉⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛ ⠀⠀⡇⠀⠀⠀⢸⣿⣤⠀⠀⠀⠀⠀⠻⣿⡟⡿⠿⣤⣿⣿⣿⠟⠻⣯⣙⠛⠻⣶⣤⣄⠀⢄⠀⠘⣿⣿⡿⠿⣿⣿⣿⣄⣠⣾⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣟⣿⣷⣄⠰⣷⣄⣀⣀⣙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢙⠿⡿⣾⡇⠀⢹⣭⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣧⣤⣶⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⠞⢋⣁⣠⡤⠀⠀⠀⠀⠀⠨⠿⠿⢶⣶⣤⣄⠀⠀ ⠀⠀⣴⢋⣥⡾⢛⣭⠶⠶⢤⡄⠀⠀⠀⠀⢠⡴⠛⢛⣿⣿⡃⠀ ⠀⣸⠁⠉⠉⢠⡟⠀⠀⠀⠀⢹⡆⠀⠀⢠⡏⠀⠀⠈⠉⢸⡇⠀ ⢀⡏⠀⠀⠀⢼⣇⢿⠿⠀⠀⣸⠇⠀⠀⠈⢧⣤⣀⣤⣤⣟⣷⠀ ⢸⠃⠀⠀⠀⠀⠈⠛⠲⠶⠞⠁⠀⠀⢀⣀⣠⡼⢋⣤⢤⣌⠻⣆ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣾⢁⡾⡗⡶⣾⡆⣿ ⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⠏⠉⠉⠉⡇⡿ ⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⣸⢱⡇ ⠀⢹⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⡏⢸⡇ ⠀⠈⣧⠀⠹⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡇⣿⠒⠤⡀⢿⠀⡇ ⠀⠀⠘⣇⠀⠁⠀⠀⠀⠀⠐⠲⢤⡀⠀⣼⠀⣧⣤⣤⡼⣾⠀⡇ ⠀⠀⠀⠘⢧⡀⠁⠀⠀⠀⠀⠀⠀⠈⠳⣿⠀⢿⡛⠻⣷⠏⢠⡇ ⠀⠀⠀⠀⠀⠛⢦⣄⠀⠐⠢⠄⣀⠀⠀⠹⣦⡀⠉⠉⢉⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣄⡀⠀⠀⠀⢀⣉⡿⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⠈⠊⠊⠈⠃⠂⠀⠃⠊⠊⠀⠈⠈⠑⠄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠶⠚⢻⠏⠁⢸⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠹⡄⢣⠀⠀⠀⠀⠀⠘⣆⠀⠙⡄⠀⠀⠀⠀⢹⠀⠀⠀⠀ ⠐⠒⠒⠊⠉⠉⡿⠀⢠⠃⠀⠀⠀⣾⡄⠀⢸⢀⡀⠀⠀⠀⢸⣳⡀⠀⠀⠀⢠⡹⣌⡀⠐⣆⠀⠀⠀⡘⣆⠀⠘⣄⠀⠀⠀⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠀⠀⢀⣿⡇⠀⢸⡀⡇⠀⠀⠀⠈⣽⣧⠀⠀⠀⠀⢻⣿⡇⠀⢹⣆⠀⠀⠱⣼⡄⠀⠘⡄⠀⠀⠻⠢⣄⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⠀⡀⠀⠀⠀⢸⠙⢿⠀⠀⣇⣧⠀⠀⠀⠀⢿⢼⡆⠀⠀⠀⠘⣿⡇⠀⣸⣼⡄⢀⡀⢻⣷⠀⠀⠹⡀⠀⠀⠀⠘⡄⠀ ⠀⠀⠀⠀⠀⣾⣧⠀⡇⠀⠀⠀⢸⠀⠘⣧⠀⢻⣿⡀⠀⠀⠀⣸⣶⣷⠾⠛⠙⠲⢯⣿⢀⡇⠀⠻⠋⢻⢻⡿⡇⠀⠀⢧⠀⠀⠀⠀⠣⠴ ⠀⠀⠀⠀⢰⣿⣾⡄⢡⠀⠀⠀⢸⣄⣀⣈⣧⣸⡿⣇⢀⣤⠴⠿⢿⠀⢀⣀⣤⣴⠾⠿⣿⠁⠀⠀⠀⠘⡆⠃⢻⠀⠀⠸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⣹⣿⣸⡀⠀⠀⠘⡍⠁⠀⢻⡿⣧⡹⠋⢀⠈⢠⠀⣈⣽⢟⣩⣴⣶⣾⠿⣶⣶⣦⣄⡀⢷⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⢸⠟⠋⠈⠻⣷⠚⠉⠙⢧⠀⠀⠐⣷⡈⠙⠉⠉⠉⠉⢉⣟⣵⡿⡿⠿⢉⠇⠀⠀⠀⠈⢻⣷⢺⠀⢸⠀⠀⠀⠸⣇⠀⠀⠀⠀ ⠀⠀⡀⢸⣼⠇⠀⢀⣀⣤⣴⣶⡶⣶⣄⠀⠀⠉⡇⠀⠀⠀⠀⠀⠈⣾⠟⠷⢤⡤⠊⠀⠀⠀⠀⠀⣼⠃⢸⠀⡞⠀⢠⠀⠀⢿⡄⠀⠀⠀ ⠟⠉⢹⣿⣿⣧⣴⣿⠿⠿⣿⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣤⣶⢶⡶⢶⡶⢆⣵⣤⡈⣧⣷⠀⡘⠀⠀⢸⣷⠀⠀⠀ ⠀⠀⢠⣿⣾⣿⣿⠁⠀⠀⠙⠢⠬⠤⠃⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣯⠟⣡⠒⡠⢎⡴⣛⢫⢟⣴⡿⣿⠀⡇⠀⠀⠸⡟⣷⡄⠀ ⠀⠀⡈⣿⠈⠻⣿⡆⢀⣠⣤⣴⠖⢠⡄⢀⠞⠈⢣⠀⠀⠀⠀⠀⣠⣾⣿⠟⣡⠞⡡⢊⡴⢋⢈⣽⠿⣩⠏⠀⠸⣿⠀⠀⠀⠀⡇⠸⣿⠀ ⠀⠀⡇⢹⣄⠀⡸⢓⡾⢁⡰⢃⡶⡻⡷⠣⠀⠀⠀⠀⠀⠀⢀⠞⠿⠝⠡⠊⡡⠊⡠⠋⡾⡡⠋⠀⢺⣷⠃⠀⢠⠇⢀⡇⠀⠀⡇⠀⣿⢷ ⠀⠀⢳⣘⢿⡄⠀⣝⣴⡟⣩⢏⣞⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⢸⠞⠀⠀⠀⠀⠉⠀⣠⠋⣠⣾⡇⠀⠀⣇⠀⢸⣧ ⡀⠀⢻⣿⣾⣷⠊⣾⠏⡴⠃⡻⠋⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⣀⡀⠀⠀⠀⣠⠃⠀⠀⠀⠀⢀⣠⣶⠕⠋⢸⠯⡇⠀⠀⣿⠀⡸⢿ ⡇⠀⠸⣿⣿⡟⠿⣅⡞⠀⠐⠁⠀⠀⠀⠀⠀⡠⠚⣡⣤⣶⣶⣶⣶⣦⣼⣷⣾⣿⡇⠀⠀⠀⠘⠋⠉⠁⠀⠀⠀⢻⡆⡇⠀⠀⡇⢁⠁⠀ ⢻⡄⠀⠹⡿⣿⡀⠀⠉⠋⠀⡀⠀⠀⠈⢷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣾⡇⡇⠀⠀⡇⠘⡄⠀ ⠀⣿⠦⣀⠙⢿⣷⡀⠀⠀⡀⡇⠀⠀⠀⠀⠻⣿⣿⠟⠙⢿⣿⡿⠛⠉⠁⢹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⠀⠀⡇⠀⠱⡀ ⣾⣿⠀⠈⢑⣦⣉⣻⢤⣀⣉⣡⠄⠀⠀⠀⠀⢻⡟⠀⠀⢸⡟⠀⠠⢰⠀⣿⡇⠀⠀⠀⠀⠀⠀⠓⠃⠀⣠⣿⣿⣿⡟⣿⠀⠀⡇⠀⠀⠱ ⡿⠃⠀⣠⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢸⠇⠀⠀⡸⢶⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣧⣼⢇⣴⡷⣀⠀⠀ ⠙⠲⢿⣿⣭⣭⣽⣯⣹⡗⠀⢹⣦⣄⠀⠀⠀⠸⡀⠀⠀⣼⠀⠀⠀⠁⡸⢧⡽⠀⠀⠀⠀⢀⣴⣿⣿⣿⣏⣻⣿⣿⣿⡿⢸⣿⣧⡻⣷⣄ ⠀⠀⠀⠈⠙⠿⣿⣿⣿⠇⢠⣿⣿⣿⣷⣦⣀⠀⣇⠀⠀⠙⠀⠀⡠⠞⠁⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⣿⣿⠏⣷⡈⠉ ⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⡿⣿⣿⣿⣿⣿⣿⣷⣾⡄⠀⠀⢠⡞⠀⠀⠀⠀⣠⡴⠛⣛⣻⡿⠿⠟⠛⠉⠉⠀⠀⠀⠀⣸⣿⡟⠃⠈⢿⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠉⠙⠻⠟⠛⠻⠟⠛⢆⠀⠘⣅⣠⣤⣶⣿⠷⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠂⠀⠀⠀⡙ ⠀⠀⠐⠤⡤⠀⠀⠀⠀⠀⠀⠀⠐⣦⣀⠀⡀⠀⠀⠀⠈⣧⠀⣟⠋⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠄⠠⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⡇⡴⠶⠒⠒⠛⠛⠛⠛⠛⣛⣒⣲⣶⣶⣤⣄⣀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⣻⣿⣿⣿⡇⣀⡠⠴⠖⠋⢉⡉⢉⠉⢈⣓⡲⣄⠙⠉⠺⢯⣹⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠀⢠⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠈⠉⠳⡄⠀⠙⠊⠛⠢⠤⢄⣿⣿⣿⡿⣟⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⣿⣿⣿⡇⠈⠳⣌⡛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⣰⠎⣽⣿⡿⣛⡯⠵⠒⠒⢤⠀⠀⠀⠔⠒⠒⠒⢀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠈⠛⣄⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢀⠞⠁⠀⣫⠵⠋⠁⣀⣤⠴⠖⠲⠶⢮⡹⢭⣶⣄⡀⠀⠈⠉⠲⣄⠀⣸⣿⣿⣿⣿⡈⢧⠀⠀⠀⠈⢳⡀⠙⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⣰⠃⠀⡠⠎⠁⠀⠐⠋⡁⡠⠊⠀⠀⠀⠈⠳⡄⢀⠙⠿⣲⣄⠀⠀⠈⢗⢌⠻⣿⣿⣿⡇⠈⢧⠀⠀⠀⠀⠹⣄⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⡼⠁⣠⠞⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⡞⠀⠀⠀⢻⣦⠙⢦⡈⠙⢧⡀⠀⠸⣦⠳⡌⢿⣿⡁⠀⠈⠧⠀⠀⠀⠀⠘⣆⠀⠘⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⡼⢁⡴⠁⢀⠀⠀⠀⢠⡾⠃⠀⠀⠀⢸⠇⠀⠀⠀⠀⢻⣇⠀⢻⢦⡀⠑⠄⠀⣿⡆⠘⢆⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠈⢿⡄⠀⠀⠀⠀ ⠀⠀⣸⠟⠀⠀⠀⠀⠀⢰⢁⠎⠀⣰⡞⠀⠀⢠⣿⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢿⠀⠘⣇⠙⢆⠀⠀⠘⣴⠀⠘⢧⢧⠀⠀⠀⡄⠀⠀⠀⠀⠸⡾⡀⠀⠈⣿⡀⠀⠀⠀ ⠀⢠⡟⠀⠀⠀⠀⠀⢠⡏⡞⠀⣠⡟⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡆⠀⢸⡀⢨⢣⡀⠀⡏⡆⠀⠈⡞⡇⠀⠀⣷⠀⠀⠀⠀⠀⢳⢧⠀⠀⠸⣷⠀⠀⠀ ⠀⣿⠁⠀⠀⠀⠀⠀⣾⢹⠁⠀⣿⠁⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠻⠀⠀⡇⠀⢧⠱⡄⠀⢿⠀⠀⠸⡼⡀⠀⢸⠀⠀⠀⠀⠀⢸⢸⡆⠀⠀⢻⡇⠀⠀ ⢰⡟⠀⠀⠀⠀⠀⢸⣏⡏⠀⢸⡏⠀⣠⡟⢹⣹⢱⠀⠀⠀⠀⠀⠈⣧⠀⠀⢶⠀⠀⠀⠀⠀⠀⢸⠀⠈⢇⠘⢄⢸⠀⠀⠀⢳⢧⠀⠘⢰⠀⠀⠀⠀⠈⡇⢣⠀⠀⠈⣿⠀⠀ ⢸⠃⠀⠀⠀⠀⢀⡟⢿⠃⠀⣿⠀⣰⡟⠁⠸⣾⢸⠀⠀⠀⠀⠀⠀⢹⠀⠀⣻⣣⠀⠀⠀⠀⠀⠸⡇⠀⠘⡆⢸⠀⡆⠀⠀⠘⢾⡄⠀⡜⠀⠀⠀⠀⠀⡇⢸⡀⠀⠀⢿⡇⠀ ⢸⠀⠀⠀⠀⠀⢸⠏⡟⠀⠀⡏⣴⠏⠀⣄⠀⣿⡞⡆⠀⠀⠀⠀⠀⢸⡇⠀⢹⢿⣷⡀⠀⠀⠀⠀⢇⠀⠀⠹⡜⠀⣷⡀⠀⠀⠀⢇⠀⡆⡄⠀⠀⠀⠀⡇⠀⣇⠀⠀⢸⡇⠀ ⣿⠀⠀⠀⠀⠀⡟⠀⡇⠀⢰⣿⠋⢀⠀⠈⢳⣿⣧⢻⠀⠀⠀⠀⠀⠈⣇⠀⠈⠀⠙⣷⡀⠀⠀⠠⣾⠀⠀⠀⢹⠀⡏⢷⡀⠀⠀⢸⡰⡄⡇⠀⠀⠀⠀⡇⠀⣿⠀⠀⢸⡇⠀ ⢸⠀⠀⠀⠀⢸⠇⠀⠃⠀⣾⠿⣾⠟⠛⣿⣿⣟⡏⣎⢇⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠈⠳⡀⠀⠀⠘⡆⠀⠀⠈⣇⡇⠈⢷⡀⠀⠸⣷⢇⡄⠀⠀⠀⠀⣧⠀⢹⠀⠀⢸⡇⠀ ⢸⡀⠀⠀⠀⢸⠀⠀⠀⠀⢻⢿⣧⠀⢸⣸⢳⡿⣿⠘⡼⡄⠀⠀⠀⠀⢸⣇⢀⠀⠀⢀⠀⠘⠢⡀⠀⢿⢆⠀⠀⡟⣿⣄⠈⢳⡀⠀⣿⣮⡷⠀⠀⠀⠀⠿⡆⠘⡄⠀⣸⠃⠀ ⢸⣧⠀⠀⠀⣸⠀⢰⠀⠀⢸⠰⠟⢦⡀⠻⣿⣾⠿⣧⠰⡹⡄⠀⠀⠀⠀⣼⢽⢉⣉⣉⣉⣍⠉⠙⢦⣘⡾⣷⣄⡇⠘⢿⠆⠀⣷⡄⣿⡿⢭⠀⠀⠀⢀⠀⣇⠀⡇⠀⡟⠀⠀ ⠀⣿⡀⠀⠀⡏⠀⠸⠀⠀⠸⠂⠀⠈⠉⠁⠒⠂⠀⠘⣆⠳⠹⡄⠀⠀⠀⠸⣼⣴⠶⠛⣻⢯⡟⡷⣾⣝⣷⡬⡙⡇⢀⣈⠳⣦⣽⣿⣿⣶⠈⣧⠀⠀⢸⠀⣿⠀⣇⣰⡇⠀⠀ ⠀⠸⣧⠀⠀⡇⠀⢰⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣠⡟⣦⠀⠉⠀⠀⠀⠀⢻⡇⠀⠀⣯⢯⣹⠓⣾⣿⢿⣿⣝⠃⠸⠒⢻⣿⣎⠀⢼⢻⡇⣼⠀⠀⢸⡀⡏⡆⣼⡿⠀⠀⠀ ⠀⠀⢻⣆⢸⣧⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⡿⠀⠈⢇⠠⠀⠀⠀⠀⠀⡇⠐⢦⣈⠳⠭⠯⠟⣁⣀⠈⠛⠧⠤⠴⠟⠛⣻⠇⣾⣴⢿⠏⠀⠀⡞⠇⠇⢳⣿⠀⠀⠀⠀ ⠀⠀⠀⠿⢸⣿⡀⢸⡆⠀⠀⣧⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠈⢧⢣⡀⠀⠀⠀⢹⠀⠀⠈⠛⠶⠖⠞⠋⠉⠀⠀⠀⠀⠀⠰⠋⡁⠚⢉⣡⡿⠀⠀⢰⣷⠀⢠⡜⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣞⣧⢸⡇⠀⠀⡟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣱⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢰⠆⠒⠋⣡⡴⡟⣿⡇⠀⠀⢸⣿⠀⠈⠃⣟⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⡿⠟⣻⣧⠀⠀⡏⠙⣆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢣⣇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣨⣠⣶⣿⣡⣿⢡⡟⡇⠀⠀⣸⡈⡇⠀⠀⢸⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣞⢹⣸⠀⠀⡇⠤⠜⣦⠀⠀⢻⣧⢤⣀⣀⠀⠀⠀⠈⣾⡆⠀⡀⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⠳⢹⢀⠀⡏⠘⢻⣟⣼⣿⠃⠀⠀⣇⡇⠀⢸⠀⠈⣿⡄⠀⠀ ⠀⠀⠀⠀⢠⡟⠛⢻⢹⠀⠀⡇⠀⠀⠈⣧⠀⢸⡇⠀⡴⠈⠉⣿⢲⣤⣿⣇⢀⣿⠀⠀⠀⠀⠀⣠⡴⣿⡟⢹⠀⢸⢸⢸⠁⠀⢸⣿⠟⢿⠆⠀⢀⣿⣿⠀⢸⠀⠀⢻⣇⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⢸⢸⡀⠀⡇⠀⠀⢸⣿⣳⣸⡇⠀⠀⢀⣴⠟⠋⠁⠘⣿⠾⠏⠀⣀⣠⣤⢾⣋⣷⠋⠈⠘⠀⢸⢸⣼⠀⠀⣿⢿⠀⢸⠀⠀⢸⣼⠈⣇⢸⠀⠀⠈⣿⡆⠀ ⠀⠀⠀⠀⠸⡇⠀⢸⠘⡇⠀⢇⠀⠀⡾⡝⡇⢳⡓⣤⡴⠋⠀⠀⠀⠀⢈⣡⡤⡖⣚⡏⡛⣁⣼⡏⠁⠀⠀⠀⠀⢸⢸⠇⠀⢸⣿⣾⢀⣸⠀⠀⢸⣿⡷⣼⣾⠀⠀⠀⠸⣇⠀ ⠀⠀⠀⠀⠀⠹⡀⢸⠀⡇⠀⣾⠀⠀⣯⠻⣿⠈⠳⢤⣀⣠⣤⣶⣶⣿⡟⠁⠀⠁⠘⣇⡷⡏⠁⡇⠀⡀⡄⡄⠀⢸⠸⠀⠀⣸⣹⠋⢨⡏⠀⠀⣸⢿⡀⠘⢻⣦⠀⠀⠀⢻⠀ ⠀⠀⠀⠀⠀⠀⢳⡸⠀⠁⠀⣿⠀⠀⣿⠀⠹⡄⠀⠀⠀⣠⠏⢹⣿⡷⡀⠀⠤⣠⠟⣇⠀⠀⡄⠁⡄⠁⡇⠃⢠⢿⠀⠀⢈⣿⡟⣀⡼⡇⠀⢠⡏⠀⠹⣄⠀⣿⢷⣄⠀⠈⡁ ⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡿⠀⠰⢿⠀⠀⢳⡀⢀⣠⣿⣀⢀⣟⠀⡗⢰⢛⣅⡈⠛⠒⡖⠂⠀⠀⠀⠀⠀⡞⢸⠀⣀⣼⣿⡛⠁⢠⠃⢀⣞⠀⠀⠀⠸⢻⡌⠇⠙⢣⣄⢙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠷⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣠⣀⣤⣴⣶⣶⣾⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠟⠛⠛⠉⠉⠉⠙⠛⠛⠻⣧⡀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢀⣠⣴⣾⠿⠟⠛⠛⠋⠉⠉⠙⠋⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⢳⢒⣛⡶⣤⣄⡈⠷⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢀⡾⠛⠉⠀⢤⢶⣶⣲⣖⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⣹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣾⢣⣴⣶⣶⣿⣿⣿⣿⣿⠛⣿⣿⠳⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢩⡿⠙⢿⣿⣿⣿⣿⣿⣟⢻⣿⡆⢿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢺⣟⣿⣿⣿⣿⣿⣿⣁⣿⡿⠀⠈⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣈⠻⢿⣿⣿⣿⣿⡿⢠⡇⠈⡇⠰⣚⣿⣿⣷ ⠀⣀⣀⠀⢸⣿⡟⢿⣿⣿⣿⣿⣿⠟⢁⣤⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠾⠾⠭⠭⠴⠿⠁⠀⠙⠞⠁⠀⣼⠁ ⢸⡗⠮⣍⣻⡏⢿⣬⣛⣛⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀ ⠈⣧⠀⠀⠉⠁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀ ⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀ ⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀ ⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣻⡀⠀⠀ ⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⡀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⢀⣨⡵⠛⣷⠀⠀ ⠀⠀⠀⢀⡼⡃⡂⠀⠀⠀⠀⠀⢰⣴⣶⡈⠀⠀⣀⡀⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣵⡶⠟⠋⠀⠀⠀⠀⠀⠀⢀⡟⠉⠀⠠⣿⠀⠀ ⠀⠀⠀⣾⡏⡉⠋⠳⡆⠀⠀⠀⠈⠁⠉⠛⠿⢿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⡾⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣀⠀⠀⣿⠀⠀ ⠀⠀⠀⢿⡇⣇⠀⠀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠰⢦⣤⡿⠋⠀⠀ ⠀⠀⠀⠘⢷⣉⠃⢀⣿⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬜⬛⬜⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟥🟥🟥⬜⬜⬜⬜⬜ ⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜ ⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜ ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬛⬛🏻⬛🏻⬛🏻⬛🏻⬛⬛⬛ ⬛⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛⬛ 🏻⬛🏻⬛🏻🏻🏻🏻🏻⬛🏻⬛🏻 🏻⬛🏻⬛🏻🏻🏻🏻🏻⬛🏻⬛🏻 🏻⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛🏻 ⬜🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬜ ⬜⬜🏻🏻🏻🏻🏻🏻🏻🏻🏻⬜⬜ ⬜🟨🟨🟦🟨🟨🟨🟨🟨🟦🟨🟨⬜ ⬜🟩🟩🟦🟩🟩🟩🟩🟩🟦🟩🟩⬜ ⬜🟨🟨🟦🟨🟨🟨🟨🟨🟦🟨🟨⬜ ⬜🟦🟦🟥🟦🟦🟦🟦🟦🟥🟦🟦⬜ ⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜ ⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜ ⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜ ⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜ ⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠁⠢⡠⠒⠈⠉⠉⠉⠰⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⣀⠤⠀⠀⠐⠂⠤⡇⠀⠀⠀⠀⠀⠀⠜⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⠀⠀⠈⠀⠀⢀⣠⠔⠒⠀⠘⠂⣄⠀⠀⠀⠀⠀⢐⣓⢦⡀⠀ ⠀⠀⠀⢀⠖⡇⠀⠀⠀⢀⠤⠦⠛⠁⣀⣠⣤⡄⠀⠬⣏⠀⠤⢠⣤⣶⣆⠸⢵⠄ ⠀⠀⢠⠁⠀⠀⠀⠀⠀⠈⠁⡢⢍⣉⣾⢽⡋⣿⣄⣴⢅⣀⣀⣿⣺⣭⡿⢤⡔⠀ ⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠚⠛⢋⡢⠞⠁⠰⢄⣀⠀⠀⡤⠔⠁⠀⠀ ⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀ ⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⠀⠀ ⠘⡄⠀⠀⠀⠀⠀⢀⠀⣎⠀⠒⠒⠒⠒⠠⠌⣉⣉⣀⣐⡒⣒⣀⣉⣉⣡⠞⠀⠀ ⠀⠐⢄⠀⠀⠀⠀⠈⠢⠀⠈⠉⠉⠉⠁⠒⠒⠒⠀⠀⠤⠤⠤⠤⣤⠔⠋⠀⠀⠀ ⠀⢰⢣⠙⠢⢒⡂⠤⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠊⠀⠀⠀⠀⠀⠀ ⠀⢸⠘⠀⠀⠀⠀⠉⠑⠒⠂⠤⠤⠄⣀⡀⠤⠤⠔⠊⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⠤⠤⠤⠤⠤⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⣀⣀⣀⣀⣀⣄⣑⣄⠀⠀⠀⠀⠀

⠀⢠⡟⣁⠀⠀⠀⢹⡆⠀⠀⢀⣬⢭⡙⠳⣿⣤⣟⠀⣴⠏⠉⣿⠀⠀⠀⠀⠀ ⠀⣿⠀⠛⠀⠿⠀⣼⠁⠀⠀⡟⢷⢆⡿⠀⢁⠘⠙⢻⣧⣀⡼⠃⠀⠀⠀⠀⠀ ⠀⢿⡀⠀⠀⢀⣼⠃⠀⠀⠀⠙⠓⠛⠁⡼⢫⡿⣦⠀⠸⠻⣧⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⡶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢧⣬⣵⠏⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠷⣤⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⣿⠓⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠉⠳⡀⢠⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡏⠀⣧⠀⠀⠀⣀⠀⠀⢸⡀⠀⠀⠀⢠⠇⣸⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⠀⠈⠳⠶⠞⠋⠀⠀⠈⠣⣀⣀⡴⠋⣰⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⣄⠀⠀⠀⠀⠀ ⢀⣸⣷⣤⣶⠶⣿⠃⠈⠙⠷⢶⣤⣤⣄⣠⣤⣤⡶⠞⠋⠀⢤⣿⣆⡀⠀⢀⣀ ⠈⠉⣿⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠻⣿⣥ ⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⡟⠁⣠⣶⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣀⣀⣀⣀⣀⣀⣿⣤⡶⠟⠉⠻⣦⣿⣾⣃⣤ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⡏⠉⠉⠉⠉⠉⠉⣿⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠤⠤⠤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢴⣲⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠔⠋⢓⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⢢⡀⠀⠘⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠊⠕⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢠⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⡀⠈⠢⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠘⡆⡀⠀⠀⠈⣧⡛⠀⠀⠀⠀⠀⠑⠀⠀⠈⠢⣄⠀⠙⢦⡀⠀⠀⠀⠀⢠⠈⢷⠀⠀⠀⠙⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠸⣆⠀⠀⢷⠈⠀⠀⠀⠏⣷⣄⠀⠀⠀⠀⠀⣄⠀⠀⠀⢻⡑⠦⣄⠙⢦⡀⠀⠀⠀⠱⡌⣷⡀⠀⠀⠹⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠹⡄⠀⠘⢦⠀⠀⠁⠀⠘⡎⠳⣄⡀⠀⣀⣈⣳⣄⠀⠀⠱⡄⠈⠙⠦⢍⡲⣄⠀⠀⠙⠘⣟⢦⠀⠀⠸⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠹⣄⠀⠈⢷⡀⠀⠀⠀⠸⡄⠈⠙⠷⣄⡀⠀⠈⠳⢧⡀⠹⡄⠀⠀⠀⠀⠀⠡⡀⠀⠀⢹⡀⠱⡄⠀⠹⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣸⠁⠀⣀⡤⠤⠽⢦⠀⠀⠻⣆⡀⠀⠀⠙⡄⠀⠀⠀⠉⠓⠤⣄⣀⠙⠢⣝⡄⠀⠀⠀⠀⠀⢳⠀⠀⠀⢧⠀⠘⢦⠀⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣧⠴⠋⠁⠀⠀⠀⠈⠳⣄⠀⠘⢷⣄⠀⠀⠙⣄⠀⠀⢀⡤⢀⣤⣽⣽⣶⣾⡟⠲⢤⡀⠀⠀⠈⣷⠀⠀⠸⡆⠀⠈⢷⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠻⣷⣄⠀⠈⢦⣨⣴⣾⠟⠛⠋⠉⠉⠃⢸⠀⠀⠉⢃⠀⠀⠙⡆⠀⠀⢳⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠇⠀⠀⢸⠁⠀⠀⣠⣴⣶⣶⠤⢄⡀⠀⠈⠓⢦⡈⠂⠙⠦⣀⣻⡟⠛⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠘⣆⠀⠀⢿⠀⠀⠸⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡇⠀⠀⢰⠀⠀⣾⢀⣠⣶⣿⠿⠿⠿⢿⣿⡟⠁⠀⠀⠀⠙⠲⢴⣀⠈⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⡄⠀⢸⣇⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⡇⢀⠀⢺⡀⠀⣿⠹⠿⠋⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠘⣧⠀⢸⣿⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⢀⡀⣸⠃⡇⢸⠀⢸⣧⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⡿⡄⠈⡟⡄⠀⢸⠀⠀⠀⠀ ⠀⠀⣸⢠⠇⢠⠁⢸⠀⠀⣯⡆⣿⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⡇⠀⠀⠀⡇⢷⠀⡇⡇⠀⢸⡇⠀⠀⠀ ⠀⠀⣧⡎⠀⢸⠀⣿⡀⠀⠘⡾⣿⡣⣄⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⡇⠀⠀⠀⡇⠘⡀⡇⡇⠀⢸⡇⠀⠀⠀ ⠀⣼⠏⠀⠀⡼⢸⠁⣧⠀⠀⢻⡼⠙⠺⡟⠲⠬⣝⣢⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⣰⠟⢠⣿⠀⠀⠀⡇⠀⠇⠀⢸⠀⢸⡇⠀⠀⠀ ⠐⠃⠀⠀⢰⢇⡇⠀⢹⡄⠀⠀⣷⡄⠀⠙⣆⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⣤⠶⠒⠒⠚⣉⡽⠏⠀⠀⠀⡠⠞⠁⣠⠋⢸⠀⠀⠀⡇⠀⢰⠀⢸⠀⢸⠃⠀⠀⠀ ⠀⠀⠀⠀⡞⡜⠀⠀⠀⢣⠀⠀⠹⡹⣄⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⣠⡞⠁⣠⢸⠀⠀⢰⠃⠀⢸⡆⢸⠀⡼⠀⠀⠀⠀ ⠀⠀⠀⣼⠟⠀⠀⠀⠀⠈⣆⠀⠀⢧⠘⢦⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢏⠀⢀⡇⢸⠀⠀⣼⠀⠀⢸⡇⢸⢠⠇⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⣆⠀⠘⣇⠈⢳⡀⠀⠘⡄⠉⢻⡶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠏⣾⠀⠀⣸⠀⢸⠀⢀⡏⠀⠀⢸⡇⣟⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠘⡄⠀⠙⣄⠀⢹⠀⠀⣟⣾⡏⠛⠷⢤⣤⣄⣀⣠⣴⡿⠻⠁⠀⢸⠀⢠⠇⠘⢸⠀⣸⠀⠀⠀⣼⢡⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦⠀⠘⣆⠀⠈⢦⠈⣧⠀⢸⠹⡇⠀⠀⠀⠀⠉⠉⠉⠁⠈⠀⠀⠀⠘⡆⡈⢰⠁⡈⢠⠇⠀⠀⢀⣧⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠈⢦⡀⠀⠑⣿⠀⡼⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣸⠀⣧⡟⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠽⢦⡀⢿⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠲⢾⣹⠾⠋⠉⠙⠶⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠤⠤⠔⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡞⠛⠓⠦⢄⣀⠀⠀⠈⠛⢭⡉⣻⡿⠛⠒⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡫⠤⣄⡀⠀⠀⠈⠛⠲⢤⣄⣀⣙⣧⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠈⠉⠉⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠋⢙⣦⡈⣷⡄⠀⠀⠀ ⠀⣀⠶⠁⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠿⢿⡟⣌⢿⠀⠀⠀ ⣠⡿⠀⢠⣜⠉⠀⠀⠙⢷⢄⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠘⡆⢧⡀⠀ ⣯⠃⠀⢾⣿⠗⠀⠀⠀⠀⡽⠀⠀⠀⠈⠳⢄⣀⠀⠀⠀⡰⠃⠘⣵⡄ ⡏⠀⠀⠘⡄⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢱⡇ ⡅⠀⠀⠀⠙⠒⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡗ ⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣇ ⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣤⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀⣸ ⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇ ⠀⠀⢇⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀ ⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡶⠿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣶⣄⡀⠀⠀⣀⣤⡶⠛⢛⠛⠛⢿⣿⣿⠁⢠⠊⡭⠛⠶⣄⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⣿⣿⣷⣾⡟⣡⠊⣁⠤⠬⢍⡲⢌⠻⣇⢸⠸⠀⡎⡩⠽⣿⣆⠀⠀⠀ ⠀⠈⣿⣿⣿⣿⣿⡟⠀⠃⡘⢁⡔⠒⠂⢬⡳⡵⡜⢎⣆⢃⢣⢱⢻⣟⢻⢧⡀⠀ ⠀⠀⢹⣿⣿⣿⣿⣇⠀⠀⢃⠘⡄⢰⠉⣵⣿⣜⡜⡎⢿⣎⢢⡱⣕⠠⠴⢸⢳⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⠀⢇⠘⡄⠳⡈⢣⡣⣉⢿⢸⢸⠈⡝⢷⣝⠢⢍⣒⣋⢼⡇ ⠀⠀⢸⣿⣿⣿⣿⣿⣧⠈⢆⠈⢆⠙⢤⡉⠒⠋⡸⢸⠀⠇⠀⠈⢛⣶⣶⣄⠂⣧ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⡈⠳⣄⠑⠤⣈⣉⣉⡤⠃⡜⠀⠀⣰⣿⣿⣿⣿⡇⣽ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡉⠒⠠⠤⠄⣲⠜⠀⠀⠀⢻⣿⣿⣿⠿⠁⡇ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠀⣰⠋⠀ ⠀⠀⠘⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⢀⡼⠃⠀⠀ ⠀⠀⠀⠀⠀⠲⠿⠿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠊⣠⠶⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣦⣤⣀⣀⣀⣀⣀⣤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣠⣤⣤⣤⣤⣀⣀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡥⢤⡀⠀⠀⠀⠉⠻⡟⠛⠛⠛⠛⠿⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠈⠳⣄⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣳⡀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀ ⠀⣽⢷⡱⣄⠀⠪⡉⠓⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡀⠀⠀⠀ ⠀⣿⠀⠀⠀⠉⠒⠁⠀⣾⠿⠛⠙⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡛⠷⣦⡀ ⠀⣿⡀⠀⠀⠀⠠⣀⣀⠁⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣤⣤⣄⡀⢸⡇⠀⢸⡇ ⠀⢸⣇⠀⠀⠀⠀⣀⡈⠙⠂⢀⡴⠶⢦⣄⠀⠀⠀⠀⠀⠋⠉⠙⣷⢘⡇⣠⠟⠀ ⠀⢀⣿⠿⠛⢷⣄⣈⡉⠑⠂⢾⠀⢠⠀⠹⡆⠐⢯⣉⡷⠀⠀⠀⠋⢸⡟⠋⠀⠀ ⢀⡿⠁⠀⠀⠈⣿⠉⠛⠷⣄⠈⠳⢬⣦⣀⣙⣤⣿⠁⠀⡄⠀⠀⢀⣾⡁⠀⠀⠀ ⢸⡇⠀⠀⢀⡼⠋⠀⠀⠀⠈⢷⡀⠀⠀⠈⠉⠀⠙⠒⠊⠀⠀⣤⣾⠁⠀⠀⠀⠀ ⠸⣇⠀⠀⠙⠷⣶⡶⠇⠀⠀⠀⠳⠤⢀⣀⣀⣀⣀⣀⣠⠼⢾⡉⠈⠃⠀⠀⠀⠀ ⠀⠹⣦⡀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠓⠒⠒⠚⠻⣦⡀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣄⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⣄⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠙⣿⣿⣿⡿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣆⠹⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣷⠀⣟⣿⣿⣿⣧⠘⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⠈⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣧⣿⡹⡽⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡈⣇⠀⠀⠀⠀ ⠀⠀⠀⢸⡟⣿⣿⣿⣷⡙⣌⠻⠉⢩⣩⣉⣁⠈⠙⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡱⡸⡄⠀⠀⠀ ⠀⠀⠀⢸⡇⣿⣿⣍⠋⠁⠀⠀⠀⠹⢿⣿⡏⠓⢶⡂⠹⣿⣿⣿⣿⣿⣏⢭⡉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣧⠀⠀⠀ ⠀⠀⠀⢸⡇⠸⡟⣯⣷⣄⠀⠀⠀⠀⠈⣷⣹⠀⠀⠃⠀⣿⣿⣿⣿⣿⣿⠱⡈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⡀⠀⠀ ⠀⠀⠀⠀⢿⠂⠹⣿⠘⣿⡇⠀⠀⠀⠀⠘⣾⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⢡⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡇⠀⠀ ⠀⠀⠀⠀⠘⣷⠀⣿⣳⡘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣿⣿⣿⡗⠁⣴⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣷⠀⠀ ⣄⡀⠀⠀⠀⠘⣦⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣧⣾⣿⣿⣷⣿⠋⣼⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⣿⣿⣿⣓⠒⠀⠘⣧⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣏⠹⣿⣿⣿⡏⠀⡿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡅⠀ ⣿⣿⣿⣿⣿⡄⠀⡇⢻⣿⣿⣧⡠⣶⠋⢱⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⢀⡿⢿⣿⠀⢰⣧⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀ ⣿⡿⠿⠿⣿⣇⠀⢳⡼⠻⢿⣇⠙⢎⠒⠃⠀⠀⠀⠀⠀⣽⣤⣾⣿⣿⡏⣿⠈⣷⣾⡿⠀⠘⣯⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⡿⠿⣶⣄⠈⢿⡰⠋⣀⣠⣀⡈⣆⠀⠳⡀⠀⣀⣤⣔⣯⣿⡏⡏⢸⣿⠃⣿⠀⢻⣿⣷⣦⣄⢻⡇⠀⢹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⡄⠀⠹⠀⢸⠀⢀⣀⡀⠤⢼⠃⡇⠀⢉⣩⣴⣿⣿⣿⣿⠠⠇⣼⣿⠀⣿⠀⠈⣿⣿⣿⣿⣌⣷⠀⡾⢠⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⠀ ⣿⣿⡄⠀⠀⢸⠀⠁⠀⠀⣀⣸⣤⣷⣾⣿⣿⣿⠿⠛⠉⣿⠀⠀⣿⣿⢠⡟⠀⣠⣿⣿⣿⣯⣿⣿⣿⣯⣭⣛⢿⣿⣿⣿⣿⣿⣿⠀⣿⡄ ⠹⣿⡇⠀⢀⡾⠀⠐⠚⠉⠀⣷⣿⣿⣿⣿⡿⡁⠀⠀⡰⠃⡀⣶⣿⣿⢸⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⣿⣿⣿⣿⣿⠀⢹⡇ ⠐⠉⠀⢰⣿⡇⠀⠀⠐⠙⣇⣼⣿⣿⣿⣿⣧⡀⠉⠉⠁⠐⢷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⠀⢸⡇ ⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⣻⡿⣿⣿⣿⡿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇ ⠀⠀⣸⣿⣿⡇⠀⠀⠀⣠⠏⠀⣿⡿⣿⠀⠈⠉⣩⠿⠛⠟⠛⣿⣿⣿⠇⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠁

⠀⢀⡀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⡀⠀ ⢠⡿⠋⠉⠉⠉⢻⡋⢻⠗⠲⠀⠀⠀⢸⡷⠖⠛⠉⠉⠉⢹⡋⢻⠗⠲⢿⡄ ⣾⠇⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠸⠷⣤⠀⠀⠀⠀⠈⠉⠉⠀⠀⢸⣷ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟ ⠘⣷⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃ ⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀

⁣   😶😶😶😶😶     😶😶😶😶😶😶  😶😶😶😶😶😶😶 😶😶😶💣💣😶😶😶 💣💣💣💿💿💣💣💣 💣💣💣💿💿💣💣💣 😶😶😶💣💣😶😶😶 😶😶😶😶😶😶😶😶 😶😶💣😶😶💣😶😶 😶😶⁣😶💣💣😶😶😶 👖😶😶😶😶😶😶👖 😶👖👖👖👖👖👖😶 😶👖👖👖👖👖👖😶 👖👖👖👖👖👖👖👖 👖👖👖👖👖👖👖👖 👖👖👖    👖👖👖 👖👖👖    👖👖👖   👞        👞

➖➖🟥🟥🟥 ➖🟥🟥🟥🟥🟥 🟥🟥🟥🟦🟦🟦 🟥🟥🟥🟦🟦🟦 🟥🟥🟥🟥🟥🟥 🟥🟥🟥🟥🟥🟥 ➖🟥🟥🟥🟥🟥 ➖🟥🟥➖🟥🟥 ➖🟥🟥➖🟥🟥

⣿⣿⣿⣹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢑⡂⣰⠀⠈⠳⣦⠈⠙⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⣿⣿⣟⡀⠄⠛⠉⠀⣠⠔⠚⠛⠮⡉⢫⠉⠐⠪⣇⣠⠸⣿⣿⣿⣿⣿ ⣿⣿⣿⢿⠃⠀⡠⠐⠂⠀⢀⣼⠏⢀⣤⠀⠀⠈⢞⠀⠀⣔⣉⠪⠿⢌⡉⢹⣿⣿ ⣧⣼⣿⣿⢀⡠⠔⢈⣄⢞⣟⣇⡆⠀⠀⠀⠀⠀⢸⠀⣰⡟⠁⠀⢀⡀⠘⣼⣿⣿ ⣿⣿⠏⠹⡅⠀⣴⠞⢅⣮⡁⠛⢿⡢⠄⣰⣠⡵⠃⠀⢏⢇⠀⠀⠈⠁⠀⣟⢿⣿ ⣿⣿⡄⠀⢳⣊⣕⣠⡌⠀⢙⣋⣈⣈⠟⠛⠃⠠⠄⣀⠈⠦⣓⣢⡤⢦⡾⠁⣰⣿ ⣿⣿⣯⣥⣤⠸⡀⡁⠁⠀⠀⠀⠀⣼⣶⣶⣶⣤⣤⣀⣈⣙⠈⢭⣉⣇⣀⣴⣿⣿ ⠋⠉⣿⡋⢁⠠⠐⢌⠢⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣞⠑⠢⣸⠙⡀⣹⣿⣿ ⣧⣤⣾⣄⣁⣠⡴⠀⡽⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣆⣰⣟⡉⣿⣿ ⣿⣿⣿⣿⠛⣿⠁⢤⠇⢡⠀⣼⠿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣼⣿⣿⣶⣧⢻⣿ ⣿⣟⢙⣿⡄⢘⢧⡾⠀⠀⢳⡗⠉⠀⠀⠀⠉⠻⣿⣿⠁⢀⣼⣿⣿⣿⣿⣇⠀⣿ ⣿⣿⣿⣿⣻⣸⠞⠃⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠙⣏⣴⣿⣿⣿⣿⣿⣿⣿⠄⣿ ⣿⣿⣿⣿⣧⣿⣦⣶⣶⣶⣤⡄⠀⠉⠒⠒⠒⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿ ⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣶⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⠧⠚⠹⡀⣿⣿⣿⣿⣿⣿⣥⣤⣤⣼⣿⣷⣯⠻⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⢿⣿⡀⢿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀ ⠀⠀⣼⣮⣻⣿⣮⣿⡿⠛⠋⠉⢉⣽⢻⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠙⠂ ⠀⠀⢻⣿⣿⠏⠁⠀⠀⠀⠀⠀⢀⠏⠈⢷⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢾⣅⣀⠔⠂⣻⠿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣧⡀ ⡀⢨⣟⣿⠀⠀⠀⡀⠀⠀⠀⠥⠬⠤⠤⠜⠀⠮⠥⢀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⠉⢻⡆⠉⢉⣨⢦⡀⠀⠀⣎⢤⣶⠟⠾⢦⡄⠀⠀⣼⣿⣿⡿⣿⣿⣿⠙⠛ ⠀⠀⠀⢀⣷⡰⢋⣭⣝⠵⠀⠀⠈⠈⢱⣿⢿⡆⠙⡆⢠⣿⣿⣿⠇⠈⣻⣿⡆⠀ ⠀⠀⠀⣼⡾⢷⠈⢿⣿⠇⠀⢴⣤⣀⠪⠻⠛⠡⠐⣥⡿⠟⡿⢃⠴⡪⢣⠈⠁⠀ ⠀⠀⠀⠀⠠⠋⣃⠉⠈⠅⠀⠄⠫⡛⠁⠒⢄⠀⢸⠃⠀⠈⣠⣼⣴⣧⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⡆⠈⠁⠘⠀⠒⠐⠵⣄⢀⠵⡌⠀⢀⢾⣯⡿⣯⣩⡤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢃⢂⢀⠀⠒⠒⡢⠤⠔⠒⠊⠀⠘⠄⢁⡼⣿⡀⣿⣿⣿⣦⣤⣄ ⠀⠀⠀⠀⢠⠇⢨⡈⣄⢌⠐⠀⢜⠀⠀⠀⠀⠀⠀⢘⣿⣯⡎⠈⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠁⠀⣆⠣⠀⢰⣌⠐⡄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⡄⠀⣠⡤⡲⢟⠢⣀⡄⡇⠈⣾⣷⣤⣤⣶⣾⣿⡿⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿ ⣼⣿⣿⣾⣿⣿⣾⣿⣿⣿⣷⣶⣿⣿⠿⢛⠭⡫⠋⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⠶⠶⠶⠦⣤⣄⡀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠶⠶⢶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⣶⣤⠀⠀⠀⠈⠙⠻⢦⣴⠶⠟⠋⠁⠀⠀⠀⣠⣴⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣤⡶⠞⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠶⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣙⣷⣄⠀⠀⠀⠀ ⠠⣿⣥⣤⣤⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣦⡀⠀⠀ ⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀ ⠀⣾⣏⣀⣀⣀⣀⡄⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠀ ⠀⠉⠉⠉⣩⡿⠋⠁⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠲⠿⣯⣄⡀⠀⠀ ⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢸⣷⢾⡇⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀ ⠀⢀⡿⠁⠀⣀⣀⣴⠄⠀⢸⡧⠖⠒⠛⠂⠀⣠⠀⠀⠀⠀⠀⠉⠉⠙⠢⡀⠈⠁⢸⣧⣀⣀⠀⠀⢀⣤⡶⠟⠉⠀ ⠀⢸⠷⠞⢛⣿⠟⠁⠀⠀⢸⡇⠀⣶⡦⠀⠀⡏⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠘⢿⠋⢻⣇⠀⠈⠻⣦⡀⠀⠀ ⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⢸⡇⠀⠉⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⢙⣾⡿⢀⡀⠀⠈⢷⣄⠀ ⠀⠀⠀⣸⡇⠀⢀⣠⠀⠀⢸⡇⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣸⡇⠀⢿⣶⣤⣀⢿⡆ ⠀⠀⠀⣿⣤⡶⢿⡏⠀⠀⢸⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⢻⣏⠙⠻⠗ ⠀⠀⠀⠙⠉⠀⢸⡇⠀⢀⣸⡇⠀⠀⣠⠞⠉⠓⠒⠒⠒⠲⢄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⢻⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⠾⠛⠉⣷⠀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣸⡿⠁⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠉⢻⣤⡀⢀⡀⠀⢀⡀⠀⣀⡇⠀⠀⠀⢠⣿⠁⠀⠘⢿⣿⠶⢦⣤⣀⣼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠙⠉⠙⠶⠋⠉⠛⠁⠀⠀⠀⠀⣿⣿⣷⣶⣤⣄⣿⡀⠀⠀⠉⠙⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⢀⣀⣤⡶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣏⠛⠷⠶⠶⠟⢛⡿⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣦⣴⣶⣤⣴⠋⠀⢠⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⣿⣿⣿⣿⣿⠟⠲⠎⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⠀⠀⠻⠿⣿⣧⠀⠀⠾⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡏⠁⠈⠉⠙⠓⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⡀⢠⣄⠀⠀⠀⠀⠀⠈⠉⠛⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣮⡙⠁⠀⠀⠺⣷⡄⠀⠀⠀⠀⠈⠉⠛⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠲⣤⣀⠀⠀⠀⠀⠀⣰⡇⣤⠀⠀⠀⠀⠉⠛⠶⣤⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣎⡉⠀⠀⠀⢀⡿⢿⡟⠀⢀⣀⣤⣀⡀⠀⠀⠉⠛⠷⣦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⡶⠶⠎⠁⠺⢡⠞⠉⠀⠀⠀⠙⡖⡆⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⣟⠛⣂⡤⢤⣟⠀⠀⢀⣀⣀⡼⠷⡧⢾⣏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡞⠁⠀⠀⠈⣦⡠⠼⠿⠋⢀⡼⠃⣼⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⣤⣀⣠⠟⢲⠿⠗⠚⠉⠀⣰⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣒⡛⠋⠁⣠⠞⠀⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣫⠉⣁⣠⣤⣶⣿⣿⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠸⡏⠙⠛⠛⠛⠛⠩⠤⠴⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⡴⠊⠉⠀⠀⠈⠉⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡞⠁⠀⠀⠀⠀⣀⣀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡤⣄⠀⠀⢰⣿⣿⠈⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠦⡀⠀⠀⠀⠀ ⣼⣿⠇⣸⠞⠀⠙⠯⠥⠖⣁⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⠀⠀⠀⠀ ⠘⡟⠉⠻⠬⣝⣡⠤⠞⠋⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⡾⠀⠠⢸⠀⠀⠀⠀ ⠀⣧⠴⠒⠋⠁⠀⠀⠀⠀⡀⢀⠀⠹⡄⠀⠀⢀⣀⡤⣤⠇⠀⢠⣏⢴⣦⠀⠀ ⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⡆⠀⢹⣤⠖⢩⣀⡠⠾⠤⠤⠥⣁⠓⠚⠲⡄ ⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢇⢹⡀⠀⠹⠄⢰⠋⠁⢀⠀⠀⠀⠈⢧⠦⠟⠁ ⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠘⡌⣇⣀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⣸⠀⠀⠀ ⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⢠⢧⡰⡮⠝⠂⠀⠀⠐⢆⠀⠀⠀⢠⠇⠀⠀⠀ ⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠘⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⢁⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢻⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⡶⡖⠲⠒⢛⣉⣀⣳⠸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠈⠓⠦⣈⡀⣳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡑⢲⠇⡇⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀

⣀⣀⣠⣴⣶⣿⣿⠿⠟⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣶⣿⣷⣄⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠉⢹⡏⠀⡀⢈⣉⣿⡿⠿⠷⢾⣭⣲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄ ⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠿⠚⠋⠉⠉⠙⢛⣾⠭⠤⠄⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡿⠛⠛⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⣀⣤⠄⠒⠂⣀⠀⠀⠈⠙⠛⠒⠪⢤⣭⡙⠓⠶⣤⣄⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⢀⡀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⣠⣤⡤⠤⠔⠒⠠⡶⠞⠁⠀⠀⠀⠀⠈⠉⠓⠢⣄⠀⠀⠀⠀⠀⠉⠙⠦⣤⡈⠉⠛⢷⣶⠛⠁⠀⠀⠀⠀⠀⠀⠈⠃⢄⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⢀⡠⠴⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠶⢿⡟⠛⠒⠶⣌⣑⢦⡀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡠⠖⠉⠀⢀⣀⣴⠶⠖⠓⠀⣀⠀⣀⡀⠀⠀⠈⣿⣦⠀⠀⠀⠀⠀⠀⠀⠉⢳⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡈⠳⣄⠀⠀⠀⠀⠀⠀⠸⠙ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡴⠋⠁⠀⢀⣴⡿⠋⠀⠀⢀⣠⠞⡟⠀⡇⢱⡀⠀⠀⢹⡝⣦⠀⠀⠀⠀⠀⠀⠲⢄⡹⣆⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠁⠀⣴⠋⠀⠀⠀⣰⡿⠋⠀⠀⢀⡴⠋⠀⠀⡇⠀⢸⠘⡇⠀⠀⠀⢷⢊⣷⠀⠀⠀⠀⠀⠀⠀⠑⢼⣆⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠘⣆⠀⠠⠂⠀⠀ ⠀⠀⣠⡴⠋⠀⣠⠚⠀⠀⠀⠀⡰⣿⠃⠀⡀⣠⠋⠀⠀⠀⠀⣇⠀⢸⡆⡇⠀⠀⠀⠈⢿⢪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠘⣷⡔⠀⠀⠀ ⠹⢿⠟⠁⠀⣴⠃⠀⠀⠀⠀⣰⢳⠇⠀⢰⡿⠁⠀⠀⠀⠀⠀⣽⠀⠈⡇⡇⠀⠀⠀⠀⠀⡇⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⣄⠘⣇⠀⠀⠀ ⢀⠎⠀⢀⡾⠀⠀⠀⠀⠀⢰⣇⡎⠀⠀⣼⠁⠀⠀⠀⠀⠀⣰⢿⠀⠀⠇⡇⠀⠀⠀⠀⠀⡇⠀⣿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣧⠹⡄⢹⡄⠀⠀ ⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠞⢸⠇⠀⢸⠇⠀⠀⠀⠀⠀⣴⠃⢸⡆⠀⢀⡇⠀⠀⠀⠀⢰⠃⠀⢿⠄⠙⠷⣄⠀⠀⠀⠀⠀⠀⢻⣧⢸⡾⣆⠀⠀⠀⠀⠀⠀⠀⠘⣦⢻⠀⢣⠀⢀ ⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡎⠀⠀⠀⠀⠀⡴⠁⠀⢸⡇⠀⢸⠃⠀⠀⠀⠀⢸⠀⠀⢸⡄⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣿⣦⢇⠘⣆⠀⠀⠀⠀⠀⠀⠀⣿⡆⢧⠘⣧⠊ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⣼⠁⠀⠀⣼⡇⠀⢾⠀⠀⠀⠀⠀⢺⠀⠀⣸⠛⢦⡀⠀⠀⠈⠣⠀⠀⠀⠀⠙⢿⣾⠀⠸⡆⠀⠀⠀⠀⠀⠀⢹⢹⢸⡆⢹⣧ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣰⠃⠀⠀⣼⠏⡇⠀⣞⠀⠀⠀⠀⣸⣿⠀⠀⣿⡄⠐⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠐⢻⡇⠀⢹⡄⠀⠀⠀⠀⠀⠀⡇⠀⢱⠸⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡟⠀⠀⠀⢠⠏⠀⠀⣴⠋⠀⢸⢠⣿⠀⠀⠀⢠⠟⡟⠀⢴⡟⠁⠀⠀⠀⠀⠙⢶⣤⠀⠀⠀⣄⠀⠈⣷⡄⠀⢿⡄⠀⠀⠀⠀⠀⣧⢰⠈⡇⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⡇⠀⠀⠀⡾⠀⠀⡼⠛⠁⢀⣸⡟⣿⠀⠀⠀⠈⠀⡧⢼⣿⣲⠤⣤⣄⣀⣀⣀⣀⣀⣹⣦⣄⡈⢳⡀⢸⣧⠀⠸⣿⡀⠀⠀⠀⠀⢿⠘⡆⢸⡘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⡇⠀⠀⣸⠁⠀⣼⠗⠀⣴⠿⢻⣇⣿⡇⠀⠀⠀⢀⡧⠀⡟⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⣿⣿⡄⠀⢹⡇⠀⠀⠀⠀⢸⠀⡇⠈⣏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠇⠀⢠⡏⢀⡼⠁⣀⠶⠁⠀⠈⣇⡿⡇⠀⠀⠀⣼⣿⣼⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢺⣿⡇⠀⠘⣿⠀⠀⠀⠀⠸⠀⣷⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⢀⣴⡟⢀⣾⠶⠚⠉⠀⠀⠀⠀⣿⡇⡇⠀⠀⢀⡟⡿⡟⠀⠀⠈⠁⠀⠀⣠⣀⡴⣶⣶⣶⠿⣶⣶⣶⣦⣹⣾⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣟⣽⢷⡿⠁⠀⠀⠀⠀⠀⠀⠀⢿⠁⢱⠀⠀⣸⠁⣿⠁⠀⠀⠀⠀⠀⢸⠟⣡⡾⢋⣁⣀⣀⠀⠀⠉⠛⢿⣿⣇⣀⢸⡇⠀⠀⠀⠀⠀⠈⡆⠀ ⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢇⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⡀⢠⡿⠀⣿⠀⠀⠀⠀⠀⠀⢋⣼⡟⠁⡿⠛⢉⠛⣷⠀⠀⠀⠘⣿⡇⠉⢸⢿⠀⠀⠀⠀⠀⠀⡃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠟⠀⠀⠀⠀⠀⠀⠤⠤⢴⣶⡀⠀⠸⡇⣾⠇⠀⣿⠀⠀⠀⠀⠀⠰⠛⣸⡇⠘⡇⣾⣿⣿⣿⣧⠀⠀⠀⠙⢷⠀⠀⢿⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⢀⣠⣾⠟⠛⠛⠛⠻⢿⣶⣬⣗⠀⣧⣿⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢿⡛⠉⡤⠀⣿⠀⣠⣤⣶⢾⡀⢈⠈⠀⠀⠀⠀⢨⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣰⣿⠟⠀⠀⣴⡿⠿⢦⣄⠈⠳⢤⣁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠤⣞⣡⠼⠟⣫⠤⠿⡇⢸⠀⠀⠀⠀⠀⢸⢸⡇⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⠃⠀⠀⠀⣿⣀⣠⣴⣿⡆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠈⡂⠃⠀ ⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢿⣿⡟⠛⡁⢹⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠀⠀⠀⠀⠀⠀⡃⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡄⡄⠀⠀⠀⢹⣻⡟⢦⣀⠀⠀⠈⠳⣍⣉⡱⠎⢀⢀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⠀⠀⠀⠀⠀⣀⡇⠀⠀ ⠀⢸⣧⡀⠀⠀⣿⢳⢳⠀⠀⠀⢸⠃⢧⠀⢨⠷⣾⣿⣦⣤⣤⢀⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⠀⠀⠀⠀⠀⡿⠁⠐⠀ ⠀⠀⢯⣇⠀⠀⣿⣯⣿⠀⠀⠀⠘⡇⢸⣧⠀⠀⠀⠔⢋⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣸⢹⡇⠀⠀⠀⢸⠈⠁⠀⠀ ⠀⢠⣾⡿⡄⠀⢸⢹⣎⣇⠀⠀⠀⡇⠘⣯⣧⡀⠀⣰⣿⠟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢖⣛⣻⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢁⣿⡇⠀⠀⠀⣿⠀⢂⠀⢠ ⡀⢸⠇⢻⣻⠀⠀⠇⣿⣿⡀⠀⠀⢠⠀⢻⣿⢿⣆⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⢀⣿⠀⠈⡇⠈ ⡇⢸⠀⠀⣷⢤⠀⠀⢹⡼⣧⠀⠀⠀⠀⠸⣿⣆⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠛⠋⠋⠻⣄⠀⠀⠀⠀⠀⠀⢀⣼⡇⣿⡇⠀⠀⡿⣿⠀⠀⠘⢆ ⡳⠿⣄⠀⠘⣯⠀⠀⠀⣷⣿⣧⠀⠀⠀⠀⢿⣏⠳⣄⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠉⠉⠉⠉⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢀⣾⠛⡇⢻⣇⠀⢰⠛⢿⠀⠀⡰⠛ ⠉⠲⣎⡳⣄⠘⣆⠀⠀⢹⣇⠹⣇⠀⠀⠀⠈⣿⣳⡾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣴⣿⣧⠀⢠⠐⢿⠀⣾⠀⢘⢠⣾⣷⣦ ⠀⠀⠈⠃⠙⣆⠘⣧⠀⠀⢿⡄⢹⣆⠀⠀⠀⠘⣧⡇⠈⣿⣦⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⣠⣿⡿⡿⣿⠀⢸⡀⢾⡀⣿⡇⠼⢻⣿⣿⡿ ⠀⠀⠀⠈⢣⠙⡄⠈⣷⡀⠸⣿⣦⣿⣆⠀⠀⠀⠹⡇⠀⠋⠈⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⠈⠳⢤⣤⡤⠤⠖⠚⠛⠉⠁⠀⠀⣠⣼⣿⣿⣧⣻⢽⡆⠘⣇⠘⣇⣿⡟⠀⣾⡛⠋⠐ ⠀⠀⠀⠀⠀⠀⢻⡀⠈⣷⡄⢻⡄⠘⠻⣦⠀⠀⠀⢿⠀⢱⠀⠀⠀⠘⡏⠻⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⣟⠈⠉⠛⠻⢦⣿⣄⣻⡛⡄⠀⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⣧⠀⠻⡟⢞⢷⠀⠀⠈⠣⣀⠀⠘⣆⢸⡀⠀⠀⠀⠀⢀⣻⣿⣿⣿⡿⠿⣿⣷⣶⣶⣤⣄⣀⣀⣤⣾⣿⣿⣿⢿⠃⢹⣷⡄⠀⠀⠀⠈⠙⢯⣇⠹⡄⢻⣿⣿⡗ ⠀⠀⠀⠈⠀⠀⠀⠙⡄⠀⢹⡜⢯⣧⠀⠀⠀⠉⠶⣀⣹⣾⣧⠀⠀⡼⠞⠉⠉⠀⢀⡄⣻⡄⠀⠉⠙⢿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢸⣿⣿⣦⡀⠀⠀⠀⠀⠙⢧⡙⡄⢹⣿⣟

⠋⠉⠉⠉⠉⠁⠀⠀⣽⡏⠉⣿⣿⠏⠀⠀⠀⠀⣴⠟⠉⣁⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⢘⣿⡏⠉⣽⣿⣿⠍⠉⠉⢉⣍⠁⠁⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⣿⡏⠀⠀⠀⢀⣸⡃⣠⡏⠁⢈⣻⣆⣠⣤⣤⣤⣤⠤⢾⣿⣿⡇⢠⣿⠹⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⢀⠈ ⠃⠀⠀⠀⠀⠀⠀⣿⡟⠃⢸⣿⠟⠛⠛⠛⢻⣿⣏⠙⠿⠽⠟⢩⡟⠀⠀⠀⠀⠀⢠⡟⢀⣿⣇⣿⠇⠐⣿⡇⠀⠀⣾⣿⡇⠀⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠁⠀⡸⣧⣈⣷⣦⡴⠖⠋⠀⠀⠀⠀⠀⠀⣾⠁⢸⣿⣿⡏⠀⠀⣿⡇⠀⢀⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠠⠄⠀⠀⣿⡏⠀⠀⣻⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⢀⣾⣿⣿⣤⣶⣾⣿⣿⠀⢸⣿⣿⣿⠀⠀⠀⠀⢰ ⠀⠀⢀⠀⠀⢸⣿⣷⣤⣤⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⣿⣿⢀⣿⣿⣿⣿⡀⠀⠀⠀⣸ ⠀⠀⠈⠀⠀⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠿⢿⠿⠿⠛⠛⢋⣩⡿⢻⣿⡧⠶⠚⠛⠚⣿⣿⣾⣿⣿⣿⣿⡇⠀⠀⢠⣿ ⠀⢀⣷⠀⢰⣿⡇⠀⠀⠀⠈⣿⣈⣙⠷⢦⣄⣀⠀⠀⢸⠀⠀⠸⣄⢀⣤⠶⢋⣉⣴⣿⣿⣷⣶⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿ ⠀⢸⣿⠀⣼⣿⣧⠀⢿⡿⠛⠻⣉⣩⣭⣗⢮⣙⣛⠛⠋⠀⠀⠀⠈⢓⡆⢀⣿⡟⠁⠻⣿⣿⣿⡟⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿ ⠀⣿⣿⡄⣿⣿⣿⡀⠈⢷⠀⠀⣿⣿⣿⣿⠆⠙⡗⠀⠀⠤⠖⠒⠒⡾⡦⠈⠙⠀⠀⠀⠈⠉⠉⣀⣠⢾⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿ ⠀⣿⣿⣷⣿⣿⣿⡇⠀⠈⣷⣄⠈⠛⠛⠋⣀⣀⣈⣐⣄⠙⠂⠉⠀⢹⠧⣤⣈⠙⠛⠛⠻⠿⠭⠉⠁⢸⣿⡟⢹⣿⣿⣿⣿⣿⣼⣿⣿⡿ ⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠉⠉⠉⠛⠛⠉⠉⢉⠝⠀⣀⠀⠀⠀⠀⠀⠀⠲⢍⡉⠀⠀⠀⠀⠀⠀⣾⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⠤⠊⠉⣿⠑⢦⡀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⢠⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢀ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣦⣄⡀⠀⠊⠀⠙⠠⣤⣾⡏⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠑⠤⢀⡼⠋⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⢿⡏⢓⠂⠀⠀⠀⠘⢿⡇⠀⣈⠉⠉⠓⠦⡀⠀⠀⣀⡤⢶⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⢷⠘⣷⣄⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠈⠁⢋⡅⠀⡿⠁⠀⠀⡀⠀⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠘⠄⠘⢮⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⢻⠃⣸⠃⠀⠀⡄⠀⢸⡟⢻⣯⠀⠀⢀⣦⣤⣐⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣧⠀⠀⡀⠀⠀⠀⢱⡘⣷⣖⠲⠤⠤⠤⢺⡿⢉⡴⠒⠁⠀⠃⡔⢀⣾⡇⠀⢸⣧⠀⢿⣇⡀⠀⠹⠉⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⢷⡀⢣⠀⠀⠀⠀⢳⡘⢏⣉⣒⣒⣉⠟⢠⠎⠀⠀⠀⠀⣰⢃⡾⠋⠀⠀⣾⣿⡄⢸⣿⣟⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⢻⣿⠀⠀⠈⢷⡈⡆⠀⠀⠀⠀⢳⣄⠀⠀⠀⣀⣴⠏⠀⠀⠀⠀⢸⡿⠘⠀⠀⢀⡄⣿⣿⣇⠀⢿⣿⣦⠀⠀⠀⠀ ⣿⠃⠀⢹⣿⣿⣿⣿⢸⣿⠀⠀⢠⡏⢳⢸⡀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⢠⣿⡇⠀⠀⣠⢏⣼⣿⣿⣿⠀⢸⣿⣿⣄⠀⠀⠀ ⣿⠀⠀⠀⢿⣿⣿⣿⠀⣿⠀⠀⢸⠀⠘⣯⣇⠀⠀⠀⠀⠤⠄⠀⠀⠀⠠⠀⠀⠀⠀⣾⡟⠀⢀⣴⡷⠋⣼⣿⣿⡿⡇⢈⣿⣿⣿⣿⡇⠀ ⣿⡆⠀⠀⠸⣿⣿⣿⠀⢹⡆⠀⠸⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣹⠁⣰⡿⠋⠀⢀⣿⣿⡿⠀⣿⣾⣿⣿⣿⣿⣧⣶ ⡟⣷⡀⠀⠀⢹⣿⣿⠀⠾⡇⠀⢸⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠞⠉⠀⠀⠀⢸⣿⡿⠁⠀⣹⣿⣿⣿⣿⣿⣿⣿ ⠁⠘⣧⡀⠀⠀⢻⣿⡄⠀⠑⠀⢸⣷⡄⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⣹⣀⣿⣇⠉⠁⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⢁⡤⠀⠀⢀⠔⠉⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠊⢀⠔⠉⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠋⢀⡴⠋⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠲⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠞⠁⡰⠋⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⡀⠀⢣⠀⠀⡤⠒⠢⠤⠤⣀⠀⣠⣚⡁⠀⣀⣀⠼⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⢀⡞⠁⠀⠀⠀⣴⢻⢁⠀⠀⠀⠀⠀⠀⡙⢦⡈⢣⡀⡇⠀⠀⢀⣠⣤⣯⣀⠀⠉⠻⡖⠒⣒⣻⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⢾⠟⠀⠀⠀⠀⣼⠏⠈⡹⡒⠤⠀⠀⠀⢠⠃⠀⡝⢱⡟⢻⢴⡮⢛⡫⠭⠛⢺⡶⠀⠀⠹⡍⠀⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⢃⠏⠀⠀⠀⠀⢠⠿⣶⣦⡇⢳⡀⠀⠀⠀⢸⣀⠞⠠⠬⣧⣈⢿⡊⠁⠀⠀⠀⡸⡇⠀⠀⠀⢹⣀⣀⣿⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⡞⠀⠀⠀⢠⠀⢸⢰⣿⡿⣿⡝⢳⡄⠀⠀⢺⣁⡀⠀⢀⣿⣇⠙⠓⢤⡀⣠⠜⠁⣧⠀⠀⠀⠀⣇⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠃⡄⠀⠀⠘⢦⢸⠸⣄⠛⠝⠀⠀⠙⠢⢄⡸⡖⢛⣿⣾⣦⣿⡄⠀⠀⢏⠁⠀⠀⢸⡀⠀⠀⠀⡟⣆⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡀⡇⠀⠀⠀⠈⡟⠲⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠿⠿⣿⣿⡿⢦⠀⢸⡀⠀⠀⠀⢧⠀⠀⠀⢹⣌⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⣟⣄⠀⠸⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣜⣀⠉⠹⠿⡇⠀⠉⠀⢻⠀⠀⢸⠈⢆⠀⠀⢸⢎⣷⠚⠙⠒⠒⠂ ⠀⠀⠀⠀⠀⠙⢎⢑⡤⣘⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣟⣿⣿⣶⣾⠁⠀⠀⠀⠀⠇⠀⣾⠀⠘⣆⠀⢸⠈⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⢧⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠙⢋⠇⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠈⢇⠀⢧⠀⠱⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠀⠀⢀⡜⠀⢷⠀⠀⠀⠀⡳⠄⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣾⠀⠀⡇⢸⠀⠀⠈⢦⠘⢷⡄⠀⠉⠀⠀ ⠀⠀⠀⠀⠔⠁⣠⠂⢠⠞⠀⠀⠀⢳⣄⣀⣀⣀⣀⣀⣀⣀⡤⢴⡞⠀⠀⠀⠀⠀⢰⢻⠀⠀⣧⢸⠀⠀⠀⡏⢧⠈⠳⣄⠀⠀⠀ ⠀⠀⠀⠀⢠⠞⠁⢠⠏⠀⠀⠀⠀⣼⣿⣿⣯⣿⣿⣿⠀⢀⣠⠊⠀⡄⠀⠀⠀⠀⡞⠈⡆⠀⢻⠸⡄⠀⣼⠁⢸⡇⠀⠀⠙⡆⠀ ⠀⢀⡠⠚⠁⠀⡠⠃⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠞⢉⠁⠀⢠⡇⠀⠀⠀⡼⠁⠀⢱⠀⠀⢣⡱⢾⡇⢀⣟⡇⠀⠀⠀⠈⠄ ⠰⠃⠀⠀⠀⡴⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⡜⠀⠀⢀⡼⣇⠀⠀⠀⢣⡀⠀⣼⣿⢁⡞⠘⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⡴⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⣠⠎⠀⠀⣠⢮⡀⠘⡆⠀⠀⠀⠙⢢⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠃ ⠀⠀⡄⢠⠇⢠⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣚⣋⣉⠉⠉⠉⢳⠚⠁⠀⠈⢢⣹⡀⠀⠠⢤⣚⣁⣀⠤⠆⠀⠀⠀⠀⠀⠀⠀ ⠈⠂⠜⢸⡀⠸⣷⡀⠀⠀⠘⣿⣿⡿⣿⣿⡷⣄⠀⠀⠉⠙⠳⢤⡟⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⢷⡀⢻⣷⣦⣀⣀⣙⣿⣷⣿⡿⣇⠈⠙⢦⣄⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⣿⣿⣧⠀⠀⢢⠀⠀⠀⠀⢸⣦ ⠀⢠⢻⣿⠀⢿⣶⣽⣿⣿⣿⣿⡿⢡⢿⡇⠹⡄⠀⠀⠙⣧⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢿⣿⣿⣷⡄⠈⢇⠀⠀⠀⢸⣿ ⠀⡈⢸⣇⠀⠘⣿⡿⣿⣿⣿⡿⢠⡟⢸⠀⠀⠈⢱⡒⠛⠉⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⠈⢷⡀⠘⣿⣿⣿⣿⡅⢸⠀⠀⠀⣸⣿ ⠀⠀⠘⣿⣄⠀⢻⣧⠀⠙⣿⠃⣿⠁⣿⠀⠀⠀⣾⢧⠀⠀⠀⢠⠀⠀⠀⠀⠀⠣⣤⠇⠀⢈⣿⣦⣬⣙⣻⣿⣿⣼⠀⠀⣰⣿⣿

🟥 🟥🟥 🟥⬛️ 🟥🟥 🟥⬛️ 🟥🔳⬜⬜⬜⬜ 🟥⬛️ ⬜🟥⬛️⬛️⬛️🟥🟥 ⬜⬜🟥🟥🟥🟥🟥🟥 ➖➖➖⬜⬛️ ➖➖➖⬜ ➖➖➖⬜ ➖🔳⬜🔳⬜🔳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⢶⣶⣶⣤⡀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢛⣽⠶⣛⣭⣭⣭⣽⣿⣦⣴⣿⣿⣟⣓⠺⠯⣽⣳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢟⣥⣾⠿⠞⣹⠟⠉⠁⠀⠀⠀⠀⠉⠀⠀⠉⠉⠛⢷⣶⣍⡳⣯⡳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣷⠟⠋⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⠙⠷⣿⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠶⠛⠓⠶⠦⢤⣤⣈⠀⠀⠈⠻⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠟⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠛⠉⠀⢀⣤⣤⣶⡶⣶⣶⣤⣌⡉⠓⢶⡆⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄⠙⣆⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠘⣧⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⡇⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⣷⠀⢹⣧⠸⣷⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣶⣾⣿⣿⣿⣿⣟⣿⣏⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣴⣿⠀⠀⣿⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⣿⠀⣼⠋⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⠉⠉⠉⠉⠉⠉⠉⠙⠾⢿⣆⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⡏⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢀⡾⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⣠⠞⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣄⠈⠉⠛⠓⠒⠶⠒⠒⠛⠉⢀⣴⠞⠋⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠲⠶⢶⣶⠶⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣤⣀⣀⠀⠀⠀⠀⣀⣀⡤⠞⠋⠀⠀⠀⠀⠀⢀⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⢺⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡃⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⡟⢻⡄⠀⠀⠀ ⠀⠀⠀⣹⣿⣿⣿⣿⣿⣦⣤⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣟⠉⢹⣿⠏⢰⠀⢻⡄⠀⠀ ⠀⠀⢠⡏⠀⠙⠿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠁⠀⠈⣧⠀⢿⡀⠀ ⠀⢀⡿⠀⠀⢀⠀⠈⠙⠻⣿⣦⣠⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣯⡭⣿⣭⣴⣾⠛⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⠀⠈⣷⠀ ⠀⣼⠁⠀⢀⡟⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠋⣀⣈⣛⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣿⣤⡀⠸⣇ ⢸⡇⠀⠀⣾⡅⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣅⠀⢿⡿⢉⣽⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣦⢿ ⣼⠁⠀⢰⣿⣧⣀⣀⣀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡻⢿⣷⣦⣰⣾⠿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠟ ⣿⠀⠙⠛⠻⣿⣟⣛⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀ ⠸⢷⣄⡀⢠⢿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⠛⢾⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⢙⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠿⠿⠛⠛⠛⠋⠁⠀⠀⠀⠻⠿⠿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⡞⠉⠉⢠⡾⢷⡀⠉⠙⢳⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⣴⠏⠻⢷⣦⣤⣾⣀⣀⣧⣤⣴⡾⠟⢹⣆⠀⠀⠀ ⠀⠀⠀⣿⡀⠀⠀⠈⠉⣿⠉⠉⣿⠉⠁⠀⠀⢠⣿⠀⠀⠀ ⠀⠀⠀⠘⢷⣄⠀⠀⠀⢻⣄⣠⡟⠀⠀⠀⣠⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠲⠤⠬⢿⡿⠥⠤⠖⠋⠁⠀⠀⠀⠀⠀ ⣤⣀⣀⠀⣠⣤⡀⢠⡀⢀⡠⢀⣤⣄⡀⣄⣀⣀⠀⣀⡀⠀ ⠀⣿⠀⢸⡇⠀⣹⠄⢻⡞⠁⣿⠀⢈⡷⠀⣿⠀⢰⣏⣿⡀ ⠀⠛⠀⠀⠙⠛⠋⠀⠘⠃⠀⠈⠛⠛⠁⠀⠛⠀⠛⠀⠈⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⠴⠈⠿⡿⠿⢟⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⡿⠶⠈⠙⠻⠟⠑⠛⠀⣠⣄⣀⠐⠛⢻⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⡷⠀⡠⡔⣨⡍⠐⣒⠪⠭⠀⠀⠠⠤⠤⠀⠀⡜⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣷⠭⠞⢉⣀⣀⣀⠘⠀⠀⠀⠍⠀⠈⠡⠀⠀⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⣨⡤⢒⣾⣃⡒⠰⠽⢻⠿⠬⣹⠆⠀⠤⡷⠿⠿⠗⠐⠐⡾⣦⠀⠀⠀⠀⠀ ⠀⢰⠃⢰⠋⢀⢆⣉⠒⠒⠁⠀⣀⣀⠀⠀⠀⢧⡀⠰⠴⢊⡉⢚⢸⡇⠀⠀⠀⠀ ⠀⠘⣦⣎⡎⠉⣆⣈⢱⠲⠤⢀⣸⡴⠒⠂⣀⡴⠛⠒⢄⣼⡇⠔⡞⠁⠀⠀⠀⠀ ⠀⠀⠈⠳⡀⠀⠘⢯⢹⠷⢦⣤⣏⡉⠉⡖⠒⣖⠒⢸⣉⣯⣧⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠱⡀⠀⠀⠻⢤⡀⣸⠉⠛⢻⠿⠿⣿⠻⣿⡿⣿⡏⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢢⣐⠠⢢⠍⡓⠲⠤⠼⠤⠠⠁⠽⠧⢁⡻⢀⠀⡄⢀⣤⣤⣀⠀ ⠀⠀⠀⠀⢀⣴⣿⠀⠁⠲⢍⡘⠓⠶⠆⢤⣤⡤⠤⠤⠐⣉⠖⠷⣷⣿⣿⣿⣿⠀ ⠀⢀⣠⣾⣿⣿⣿⣇⠳⡑⢄⠈⠑⠢⠴⠤⣀⡀⠀⠀⠀⠀⣀⠜⠉⠙⠻⠿⠋⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⡄⣹⢶⢕⢄⡀⠀⠀⠀⠈⠉⠉⡉⣭⣅⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⣿⣿⣿⣿⣿⣿⡌⠲⡗⢕⠯⡂⢀⡔⠀⠲⡔⢅⢸⣿⣷⣦⣀⠀⠀⠀⠀ ⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡑⢌⡢⣑⢠⡏⢳⡀⠀⣇⠈⢸⣿⣿⣿⣿⠿⢶⣤⡀ ⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⡐⠁⡀⢸⠃⠀⡿⣇⠻⡧⢸⣿⣿⣿⣿⠃⠀⠈⠁ ⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣄⠱⠃⠀⢠⠃⠉⠀⠙⣾⣿⣿⢿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠻⣿⣿⣿⣦⡀⠀⢸⠀⠀⠀⠀⢸⠻⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣦⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄⠀⠀⠀⠀ ⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⠀⠀⠀⠀⠀⠤⠶⠶⠒⠲⠦⣄⡆⠀⠀ ⠀⠀⢀⡖⠋⣭⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡎⡇⠀⠀ ⠀⠀⢺⣾⣿⣿⣽⢉⡷⠁⠀⠀⠀⠀⠀⠀⠻⢌⣿⣿⠿⡹⢡⡰⢶ ⢰⠃⠼⠫⠿⠿⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎ ⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁ ⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣐⠼⡀ ⠀⢠⣞⠢⡄⠀⠛⠲⠴⠤⠤⠤⠤⠤⠤⠴⠒⠋⠁⠀⠀⠠⠅⢀⠇ ⠀⠀⠫⠂⠗⡄⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⠁⠀ ⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀ ⢀⣰⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⣿⣿⡿⠿⠟⠋⠉⠁⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠙⡟⢀⣀⣀⠄⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⢿⣷⠀⠀⠀ ⠀⢇⣵⠿⡆⠛⠛⠷⠶⢶⣤⠀⠀⢹⣿⠟⢑⡁⠈⡆⠀⠀ ⠀⡿⢋⣒⣧⠰⠰⣛⡓⠞⠛⠁⠀⠈⠉⠀⢨⢀⡼⡇⠀⠀ ⠀⠑⠿⢒⠾⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡔⠁⠀⠀ ⠀⠘⠀⡣⣇⠠⠀⠐⠀⠑⢄⡀⡄⠀⠀⠀⢸⢸⠁⠀⠀⠀ ⠀⠈⢄⡅⣤⣲⠾⣿⣛⣓⡾⡇⡇⠀⠀⠀⠈⡼⠀⠀⠀⠀ ⠀⠀⠈⠪⡺⣟⠿⠏⣛⠍⠁⡶⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠚⠃⠀⠀⠀⠔⠁⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠡⣀⣀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠸⡢⡀⠀ ⠀⠀⠀⠀⠀⡐⠑⡌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠈⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠟⠋⠉⠁⠀⠉⠉⠻⢿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⠀⠀⠀⢠⣶⣶⠿⠿⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢀⣀⣠⣴⡾⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠉⠙⠿⣿⣿ ⣿⣿⣶⣀⠀⠀⠀⠀⣤⣶⣾⠿⠟⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⡉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣻ ⣿⣿⣿⣿⠀⠀⠀⣰⠿⢿⡖⠛⣿⣿⣿⡖⢦⡀⠀⠀⠀⠀⣠⠾⢻⣿⣿⣿⠄⠉⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠜⠁⠀⠈⢇⠀⠻⠿⠿⠁⠀⠗⠀⠀⠀⠀⠻⣄⠀⠛⠿⠛⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡄⢠⠀⡄⠀⢤⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠒⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⠀⠀⠹⣄⠀⠙⡦⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾ ⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⡶⣄⠀⣀⠀⠈⠁⠀⠀⠀⣠⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣤⣴⡾⢿⣿ ⣿⣿⣿⣿⣿⣿⡄⠀⢀⣀⣀⣀⠀⠈⠀⠈⠓⠦⣤⣭⣭⣭⠽⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠁⠀⠈⠓⣿ ⣿⣿⣿⣿⣿⣿⣿⠾⠟⠋⠉⠉⠙⠓⠶⣤⣀⠀⠀⠲⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⠀⠀⠀⠀⠀⡈ ⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠏⠀⠀⠀⠀⣰⡀⣷ ⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣶⣧⣤⣰⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧⣄⣀⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⡀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣦⣶⣦⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠋⠙⠛⠋⠉⠑⠾⠿⡆⠈⠛⠋⠈⠟⠉⠁⠈⠛⠛⠋⠉⠙⢿⠁⠉⠉⠽⢿⠛⠉⠉⠉⠛⠙⣿⡿⠋⡡⠄⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠿⢆⠀⠘⢁⡞⢡⠀⠀⠀⢀⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠐⣦⣄⡀⠀⠀⢺⠁⡾⠀⡰⠀⠊⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠛⠀⠀⢸⢀⠉⠴⠠⢖⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠸⢈⠀⡀⠀⠈⠉⠓⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣦⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠛⠛⡉⣉⣉⡀⠀⢤⡉⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⣀⣤⣾⡿⢋⣴⣖⡟⠛⢻⣿⣿⣽⣆⠙⢦⡙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠒⠻⠻⠶⣦⣄⠀ ⠉⣿⢸⠁⣸⣥⣹⠧⡠⣾⣿⣿⣿⣿⣧⡈⢷⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⣿⣿⣶⣦⣈⠈⠻⣤ ⠀⢹⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣫⠀⠙⣿⣿⣿⣿⣷⡄⣽ ⠀⠀⠳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠭⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣼⠉⠓⢦⠀⠀⠉⠩⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡊⠙⠉⠉⠉⠓⠲⠤⡀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠏ ⠀⠀⠀⠈⢦⡀⠈⡇⠀⠀⡠⠒⠛⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣦⣴⣿⣶⣶⠀⠠⠀⣰⣤⣿⣦⠀⠀⠀⠀⠉⠙⠛⠻⠛⠁⠀ ⠀⠀⠀⠀⠀⡇⠀⢧⡴⠋⠀⣀⡀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⠃⢀⣄⠀⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⡇⠀⠉⠀⣰⠋⢱⠃⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠟⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉ ⠀⠀⠀⠀⠀⢇⠀⣰⡿⠋⠀⠘⢦⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠋⠁⣀⡤⠎ ⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⡀⠀⠀⢀⣀⣠⣴⡿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠉⠉⠉⠉⠉⠑⠋⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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➖➖➖🟩🟩➖🟩🟩 ➖🟩🟩🟩🟩🟩🟩🟩🟩 🔲⬛⬜🟩🔲⬛⬜🟩🟩 ⬛🔲⬜🟩⬛🔲⬜🟩🟩 ➖🟩🟩🟩🟩🟩🟩🟩🟩 🟧🟧🟧🟧🟧🟧🟩🟩🟩 ➖🟥🟥🟥🟥🟧🟧🟩🟩 ➖🟥🟥🟥🟥🟧🟩🟩🟩 ➖🟥🟥🟥🟧🟧🟩🟩🟩 ➖🟧🟧🟧🟩🟩🟩🟩

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠛⠛⠛⠉⠉⠉⠛⠛⢷⣤⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⡟⢠⣴⠾⠛⢋⣉⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣻⣯⣭⣭⣽⣶⣦⠙⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡞⣠⣤⣼⣿⣿⣿⡿⣿⡦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢻⡿⣿⣿⣿⣿⣿⡿⣿⡅⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣻⣿⣿⣿⣿⣿⣭⣿⠇⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣌⣻⢿⣿⣿⣷⢏⡇⠘⡄⢒⣿⣷⠄ ⢠⣤⠄⣽⢿⡹⣿⣿⣿⣿⣫⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠒⠚⠁⠀⠙⠁⢀⡏⠀ ⢻⡈⠑⠺⠈⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀ ⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀ ⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀ ⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢢⡼⣆⠀⠀ ⠀⠀⢀⣽⣀⠀⠀⠀⠀⢠⣤⣄⠀⢀⡀⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⠀⠀⠀⠀⢀⡞⠁⠀⣿⠀⠀ ⠀⠀⣾⣧⠈⠙⡆⠀⠀⠀⠀⠉⠛⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⡼⢧⠀⢀⡿⠀⠀ ⠀⠀⢹⡟⠦⠀⡿⢆⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠈⠙⠋⠀⠀⠀ ⠀⠀⠀⠈⠓⠚⠁⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⡴⡶⢄⠀⠀⠀⠀⠀⠀⠀⢀⣾⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⢽⣤⡈⢦⡀⣄⢀⣀⣀⠠⠾⢇⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣼⣿⣟⣿⡞⠀⠀⠀⠢⡀⠀⠀⠩⡃⠤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⡘⣃⣾⡟⠛⠁⠀⠀⠀⠀⠱⣄⢂⢀⣐⡀⠈⢦⠀⠀⠀⠀ ⠀⠀⢀⠃⠟⡓⠀⠀⠀⠀⣤⣶⡲⣦⠈⠀⠙⠻⠟⠀⠘⡆⡀⠀⠀ ⠀⠀⢸⠁⢰⠁⠀⠀⠀⠈⠪⠍⠈⠙⠀⠀⢀⣠⣤⣄⠀⢩⣀⣀⠄ ⠀⠀⢇⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣿⣿⣿⠀⢀⣖⡤⠀ ⠀⡘⠈⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⣌⣈⣆⣡⣿⣿⡟⠀⢸⠘⠐⠀ ⠀⠃⠀⢢⡀⠈⡄⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠛⠋⠀⠀⠌⠀⠀⠀ ⠀⡀⠅⡘⢿⣦⡎⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⡄⠀⠀⠀ ⢸⣷⠀⠀⠈⠓⠦⠀⠀⠀⠙⠡⢒⡀⠀⠀⠀⢐⠎⠊⠀⠇⠀⠀⠀ ⠸⠼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠇⠀⠀⠀⠰⠀⠀⠀

⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀ ⠀⣸⣿⣧⣶⣶⠿⠿⠿⠿⢿⣿⢿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⣿⡇⣀⣠⣤⣶⣶⡿⠿⠿⠿⢿⣿⢿⣶⣶⣤⣄⡘⣿⡆⠀ ⢸⣿⡏⠁⠀⠀⠀⠀⠀⠀⢻⣧⡀⣠⣿⠉⠙⠛⠀⠀⠀⠀⠀⠀⣿⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⢺⣯⡀⣠⣿⠉⠙⠛⢻⣿⡄ ⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⣿⣧ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿ ⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣤⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏ ⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁ ⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠶⠶⠶⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⣶⣶⡶⠶⠶⠾⠿⠿⠿⠿⠿⣿⣿⣛⠛⠛⠒⠛⠿⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡞⣋⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⡀⠀⠀⠀⠀⠀⠉⠙⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠛⠛⠓⠒⠛⠉⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠶⠶⠶⠶⠶⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⡿⣿⣶⡄⠀⠀⠀⠀ ⠀⢠⣿⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡟⠉⢧⠈⠻⣧⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠀⠠⠤⣶⣶⣶⣶⣶⣶⣦⣤⣤⣬⣷⣶⣶⣶⣶⣤⣠⣤⣶⣿⣿⡿⢿⡏⠉⠀⠀⠸⣿⡿⠟⠁⠀⣼⠀⠀⠹⣷⡀⠀⠀ ⠀⣸⡇⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠋⢉⣽⣿⣿⣿⠛⠛⠛⠛⡏⠉⠉⣉⣉⣍⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢻⣿⡄⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⣾⡁⠀⠀⠀⠺⠿⣿⡿⠟⠀⠀⠀⢰⡇⠀⠀⠈⠛⠛⠂⠀⠠⣝⣓⣶⠤⣤⣤⣤⣶⠿⠋⠀⠀⠀⠀⠘⣯⢿⡀ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⢻⡌⣇ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⠤⠤⣤⣤⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢹ ⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠀⠀⠀⠀⢧⢸ ⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⠀⠀⠀⠀⠀⢸⣘ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⣼⡟ ⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠋⠉⠁⠀⠈⠉⠙⢿⡇⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⣿⠇ ⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀ ⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀ ⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀ ⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠻⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣵⠏⠀⠀⠀⠀⠀⠀ ⠀⢸⣥⣄⣀⣉⣉⡉⣉⣉⣉⣵⠀⠀⠀⠀⠉⠙⠛⠲⠶⠤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢋⡽⠋⠉⠉⠹⣏⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠿⠉⢉⣉⣀⣶⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣰⠟⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⢜⡃⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣾⢟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⠟⠉⠉⠉⠻⠻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠏⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢀⣠⣤⠀⢠⣷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡟⠀⠀⠀⣿⣣⠶⠚⢀⣀⣀⣀⠀⠀⢄⠈⠂⠻⢿⣿⣿⣧⣴⣿⠻⡏⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⢀⡀⠀⢸⣷⣶⠛⠋⠉⢙⣿⣿⣦⣸⣇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣇⡀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⠀⣇⠀⣼⣿⣷⣀⡀⠀⣼⣿⣿⣿⣿⣿⡆⠀⠀⠙⠿⢿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡁⠀⠇⢰⣿⣿⣿⣿⣿⠛⠋⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣀⣀⣀⣸⡇⠀⠀⣼⣿⣿⣿⣿⣿⣾⣿⣿⡿⢿⣿⡾⢿⣏⠀⠀⠀⠀⠀⠀⢀⣴⠟⠿⠿⢿⣿⣄⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⡆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⠃⠀⣹⣧⣄⠀⠀⢀⣤⠾⠉⠀⠀⠀⠀⠈⠻⣄⠀⠀⠹⡦⣄⡀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠉⠛⣿⠃⠀⠀⠉⠻⣿⡿⠿⠿⠛⠉⢸⣿⡇⣦⣴⣿⣿⣿⣿⣿⠟⠁⣀⠀⠀⠀⠀⠀⣸⠗⠘⠆⠀⠐⣿⡀⠉⠒⠤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡶⠀⠀⠀⠀⠹⣧⣄⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠹⣧⠀⠀⣠⣴⢿⠀⠀⠀⠀⠀⢻⠙⠲⢤⣀⠀⠉⣳⠤ ⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡿⢁⠃⠈⠀⠀⠀⢀⠀⠀⠀⠀⣸⣶⣾⠿⠃⡋⠀⠀⠀⠀⠀⠈⡆⠀⠀⠈⠙⠋⢉⡄ ⠀⠀⠀⠀⠀⢀⡾⣧⠀⠀⠀⠀⠀⠀⣰⣿⣿⣟⠀⠈⠀⠀⠀⠀⣀⣸⣷⣤⣶⣿⣿⠿⠁⢀⠞⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⡠⢃⣤⠏⠀ ⠀⠀⠀⠀⢀⠞⠀⡼⣿⠀⠀⠀⢀⣼⣿⣿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢁⣠⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⣇⡠⠎⣠⠟⠁⠀⠀ ⠀⠀⠀⢠⠎⢀⡼⠁⠘⣧⠀⠀⠀⠙⠛⠛⠀⠈⡿⠿⢿⣿⣿⢿⣟⣋⣉⣤⣤⣾⡛⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠇⢠⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⣿⡒⠻⢄⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠈⠀⠀⠀⠀⠀⠀⢀⣼⡤⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠦⣀⠑⢦⡀⠈⢳⣖⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⢤⡈⠉⠉⠙⢷⣵⡂⡀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⠟⠏⠁⠀⠀⠀⠀⠀⢀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⣹⡿⠿⣷⣶⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣠⣴⣶⣿⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠋⢩⠇⠀⢠⠏⠈⠉⠙⠛⠿⢷⣶⣶⣶⣾⣿⣿⣿⠿⠟⠋⠁⢻⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⡖⠒⠚⠁⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠈⠑⠒⠒⠒⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣄⡀⣸⣡⣏⠀⠀⠤⠤⠴⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠤⠤⢤⣤⠀⠀⠀⠀⠀⢦⡀⣀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⡄⠀⣤⠀⠀⠈⠳⣦⣄⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣧⣿⣿⣿⣷⣿⣿⠃⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⢀⣀⣶⢤⣼⣿⣦⣀⣀⡀⠈⠻⣷⡀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠃⢀⣠⠴⠛⠉⠀⠀⠀⠀⣠⡶⠟⠛⠛⠛⢆⠀⠀⢹⡄⠀⠉⠙⠲⢬⣇⢀⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣾⠋⠉⠉⠉⠋⠉⣀⠀⠀⠀⠀⠀⣰⣾⠇⠀⠀⠀⠀⠀⠀⠙⠢⣈⡇⠀⠀⠀⢀⣸⠟⢛⠓⣤⡼⠙⠛⠿⠿⣿⣿⣿⣿ ⣿⡿⣿⣿⣿⢻⣿⠀⠀⠀⣠⠏⠁⠀⠀⠀⠀⢀⣼⣿⠟⠀⠀⣶⣶⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⣼⣁⡤⠤⠟⠒⠒⠦⣄⠀⠁⣿⣿⣿⣿ ⣿⣀⣹⣿⣿⣿⣿⠀⠀⠁⣀⠤⠒⡁⠀⡠⢾⣿⣿⠈⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠈⢳⡀⣿⣿⣿⣿ ⣿⣿⣿⣿⣾⣿⣧⡤⠖⠋⠁⠀⣠⣾⠞⢁⣾⣗⢛⣟⡳⣄⠀⠀⠀⠀⠀⠀⢀⠀⣰⠇⠀⢸⣿⡏⠀⠀⠀⠀⢰⣶⡆⠀⠀⢻⣿⣿⣿⣿ ⣿⣿⣿⣿⠁⠀⢿⠀⠀⠀⢠⣾⠿⠣⠀⣾⢽⠀⠋⠹⣿⡏⠳⢄⣀⠀⣆⣀⣤⡿⠋⠀⠀⠸⡇⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⣿⣿⣿ ⣿⣿⣿⡇⠀⠀⢸⡆⣠⡴⢟⡁⠀⠀⠸⠉⠫⣗⣷⢶⡺⠟⠓⠶⣬⣿⣿⠛⠋⠀⠀⠀⠀⠀⢻⡀⠳⣖⡀⠀⠀⠀⡠⢀⣾⡟⠁⠈⣿⣿ ⣿⣿⣿⣿⠀⠀⢀⣛⣉⣀⡼⠤⠤⢿⠤⠤⠤⠤⠤⠤⠤⣀⣀⡞⠉⠀⠈⠉⠉⠒⠲⠤⢄⣀⡀⠛⠾⣄⣉⣷⣶⠖⢳⣿⡟⠀⠀⣴⣿⣿ ⣿⣿⣿⣿⡏⠉⠉⠀⠀⢸⠀⠀⠃⡜⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣦⣤⣤⣤⣄⣀⡀⠀⠀⠀⠉⠙⢶⠀⠛⣟⠛⠓⡿⠀⠀⣠⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠟⠈⢦⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⢠⣾⡀⠈⠻⢷⣶⣧⡦⠾⣿⣿⣿⣿⣿ ⡟⠉⠈⢹⡿⢋⡉⠀⢀⡤⠀⠳⣄⠈⠂⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠉⠓⢤⣀⡟⠈⢇⢀⠘⣿⣿⣿⣿ ⣆⠀⠀⢈⣿⡉⠠⠚⠁⠀⢀⣤⠈⠳⣦⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢸⠁⠀⣸⣼⡟⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣄⣀⣤⣶⣿⠃⠀⢰⠿⡄⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢀⣇⣀⣾⣿⣽⡇⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠹⣿⡿⠋⡠⢀⣼⠀⢹⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣼⣿⣿⣿⣷⣤⣧⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠀⠸⣿⡄⠀⢡⡇⠀⠀⢳⡀⢸⠟⣫⡵⠞⠛⠛⠻⠶⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠇⠘⣿⣿ ⣿⣿⡟⠉⠙⣿⣯⠀⠀⢝⣿⣶⣿⠁⠀⠀⠀⢻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡏⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠰⠀⣿⣿ ⣿⣿⣿⣶⣾⣿⣿⣷⡄⣾⣠⣿⡟⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿ ⣿⣿⣿⣿⣿⣿⣯⣼⣇⣽⡏⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⠃⢻⣿ ⣿⣿⣿⣿⣿⣿⣿⣇⣿⣼⣄⣀⣤⣤⣤⣤⣤⣀⣀⠀⠀⠉⠛⠲⠦⠤⠤⠤⠤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣿⣿⣿⣾⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿ ⣿⣿⡿⢙⣿⠟⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣯⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸ ⣿⡿⠟⠋⠁⠀⢳⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠈⠉⠉⠀⠉⠉⠉⠉⠒⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀ ⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀ ⠀⢀⡟⠀⠀⠀⠀⠀⠀⠠⢤⣀⣀⠀⠀⠤⠤⠤⠤⠤⠤⠀⠀⣀⠀⠀⠀⠈⣇⠀ ⠀⢸⠃⠀⠀⠀⠀⠀⢠⣄⣀⣀⣤⣀⢨⣿⡒⠒⠒⢒⣀⣤⣀⣀⡀⠀⠀⠀⠸⡄ ⢀⡟⠀⠀⠀⠀⠀⠙⠛⣿⠟⠛⠛⢛⣿⡟⠁⠀⡄⠈⣻⡿⠛⠛⠛⢟⠂⠀⠀⣧ ⢸⡇⠀⠀⠀⠀⣀⣈⣿⣿⣳⣣⣤⣐⣿⡂⠀⢸⡇⠀⢹⣧⣄⣤⣿⣼⠀⠀⠀⡇ ⢸⠁⠀⢠⠚⣕⠢⠀⠈⠻⣿⣅⣀⣀⠈⢙⠀⢰⣷⡄⠈⣻⠿⠶⠴⢚⡟⠙⢠⠇ ⢸⠀⠀⠸⡀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠰⣯⣶⣿⡿⣿⣷⠾⠀⣀⣤⠎⠀⠀⢸⠀ ⠈⣧⠀⠀⠀⠀⠀⠈⠻⣿⣶⣶⣷⣷⣟⣋⣩⡽⢷⡿⢿⣟⡿⣻⠋⠀⠀⠀⣼⠀ ⠀⠘⢦⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣼⢿⠧⠮⣑⣦⣯⣟⣿⠟⠃⠀⠀⠀⢠⠇⠀ ⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⠿⠟⣏⠁⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀ ⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⣀⡔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣤⠾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠤⠤⠤⠤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛🟥🟥🟥🟥🟥⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜ ⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜ ⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜ ⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥⬛⬛🟥🟥🟥⬛⬜⬜⬜⬜⬜ ⬜⬛🟥🟥🟥🟥🟥🟥⬛⬛⬜⬛🟥🟥🟥⬛⬜⬜⬜⬜⬜ ⬜⬛🟥🟥🟥🟥🟥⬛⬜⬜⬜⬛🟥🟥⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟥🟥🟥⬛⬜⬜⬜⬛🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟥🟥⬛⬜⬜⬜⬛🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟥🟥🟥⬛⬛⬛🟥🟥🟥⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥⬛🟥⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟥🟥🟥🟥⬛⬛🟥🟥⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬛🟥⬛🟥🟥🟥🟥⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜ ⬜⬜⬛🟥⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜ ⬜⬜⬛⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟦🟥🟥🟥🟥⬛⬜⬜ ⬜⬜⬛⬛⬛🟥⬛🟥⬛⬛🟥🟦🟦🟦🟦🟦🟥🟥🟥⬛⬜ ⬜⬛🟥⬛🟥⬛⬛⬛🟥🟥🟥🟦🟦🟦🟦🟦🟦🟥🟥⬛⬜ ⬜⬛🟥⬛⬛🟥⬛🟥⬛⬛🟦🟦🟦⬛⬛🟦🟦🟦🟥⬛⬜ ⬜⬛🟥⬛🟥⬛⬛⬛🟥🟥🟦🟦⬛⬜⬜⬛🟦🟦🟦🟥⬛ ⬜⬛🟥⬛🟥🟥⬛🟥🟥🟦🟦⬛⬜⬜⬜⬛🟦🟦🟦🟥⬛ ⬜⬜⬛⬛🟥🟥🟥🟥🟦🟦🟦⬛⬜⬜⬜⬜⬛🟦🟦🟥⬛ ⬜⬛🟥⬛🟥🟥🟥🟥🟥🟦🟦⬛⬜⬜⬜⬜⬛🟦🟦🟥⬛ ⬜⬛🟥⬛⬛🟥🟥🟥🟥🟦🟦🟦⬛⬜⬜⬜⬛🟦🟦🟥⬛ ⬛🟥🟥⬛🟦⬛🟥🟥🟦🟦🟦🟦⬛⬜⬜⬛🟥🟦🟥🟥⬛ ⬛🟥⬛⬛🟦🟦⬛⬛🟦🟦🟦🟦🟦⬛⬛🟥🟥🟥🟥🟥⬛ ⬛🟥⬛🟦🟦🟦🟦⬛🟦🟦🟦🟦🟦🟦⬛🟥⬛🟥🟥🟥⬛ ⬛🟥⬛🟦🟦🟦🟦🟦⬛🟦🟦🟦🟦🟦⬛⬛⬛🟥🟥🟥⬛ ⬜⬛⬛🟦🟦🟦🟦🟦⬛🟦🟦🟦🟦🟦⬛⬛🟥🟥⬛⬛⬜ ⬜⬜⬛🟦🟦🟦🟦🟦⬛🟦🟦🟦🟦🟦🟦⬛⬛⬛⬜⬜⬜ ⬜⬜⬜⬛🟦🟦🟦⬛⬜⬛🟦🟦🟦🟦🟦⬛⬜⬜⬜⬜⬜ ⬜⬜⬛🟦🟦🟦🟦⬛⬜⬛🟦🟦🟦🟦⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛🟥🟥⬛⬜⬜⬜⬜ ⬜⬜⬛🟥🟥🟥🟥⬛⬜⬜⬛🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜ ⬜⬜⬛🟥🟥🟥🟥⬛⬜⬜⬜⬛🟥🟥🟥🟥⬛⬜⬜⬜⬜ ⬜⬜⬛🟥🟥🟥🟥⬛⬜⬜⬜⬛🟥🟥🟥🟥⬛⬜⬜⬜⬜ ⬜⬜⬛🟥🟥🟥🟥⬛⬜⬜⬜⬜⬛🟥🟥🟥🟥⬛⬜⬜⬜ ⬜⬜⬛🟥🟥🟥🟥⬛⬜⬜⬜⬜⬛🟥🟥🟥🟥⬛⬜⬜⬜ ⬜⬛🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥⬛⬜⬜ ⬛🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥⬛⬜⬜ ⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜

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

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🟩🟥🟥🟥🟩 🟥🟥🟥🟥🟥 ⬜⬛🟥⬜⬛ ⬛⬛🟩⬛⬛ 🟩🟧🟧🟧🟩 🟩🟩🟧🟩🟩

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⠀⠀⠀⠀⢸⢢⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⢠⠀⢸⠃⠀⠐⡄⠀⠉⠙⣿⣄⡠⢸⣿⣿ ⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠀⡠⠆⠁⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⣰⡗⠀⠀⠀⠀⢀⡎⠀⣸⠀⠀⠀⣝⡆⠀⠀⠈⢻⣇⢸⣿⣿ ⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⢀⡴⠋⠀⢠⠶⠁⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⣴⠏⠇⠀⠀⠀⠀⣸⠁⠀⡇⠀⡀⠀⠘⢿⡄⠀⠀⠀⠙⢾⣿⣿ ⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⢀⡴⠋⠀⢀⡴⠃⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⢠⣞⠁⢀⠀⠀⠀⠀⢠⠇⠀⣸⠁⠀⢧⠀⠀⠀⢻⡄⠀⠀⠀⠈⢿⣿ ⣿⠏⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢀⡜⠁⠀⠀⠀⢀⡴⠋⠀⠀⡴⠋⠀⠀⢀⣠⡴⠛⠀⠀⠀⠀⢀⡴⠛⠋⠒⢸⠀⠀⠀⢀⡞⠀⢀⡿⡆⠀⠸⡆⠀⠀⠈⢻⡀⠀⠀⠀⠈⢻ ⠙⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢠⠟⠀⠀⠀⠀⣠⠎⠀⠀⢠⠞⠀⢀⣤⠖⣿⠛⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⡀⡎⠀⠀⠀⡼⠀⠀⣸⠁⡇⠀⠀⢳⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⠋⠀⠀⠀⢀⡴⠁⠀⠀⣴⣋⡴⠞⠉⣠⠞⠁⠀⠀⠀⠀⣠⣞⣁⣀⣀⣀⡍⢰⠃⠀⠀⣸⠁⠀⢰⡇⠀⣼⠀⠀⠈⡆⠀⠀⠀⣽⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⢀⡞⠁⠀⢀⣼⣿⣭⣗⣶⠞⠁⠀⠀⠀⠀⣠⠞⠁⠀⠈⠁⠀⠀⠀⡟⠀⠀⣰⠃⠀⢀⡟⠀⣄⢹⡄⠀⠀⢱⡀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢠⠟⠀⠀⢀⡾⠉⠙⣿⠟⠁⠀⠀⠀⠀⣤⣞⡁⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢠⠇⠀⠀⡼⠀⠙⠛⢸⣧⠀⠀⠈⡇⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⠄⠀⠀⣠⠋⠀⠀⢠⣾⡇⣠⠞⠁⠀⠀⠀⢀⣤⣾⣿⣾⡽⢦⡀⠀⠀⠀⠀⢀⡏⠀⢠⠏⠀⠀⡼⠃⠀⠀⠀⠘⣿⡀⠀⠀⢸⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠛⠀⢠⠏⠀⡖⣰⠋⠀⠀⢠⡟⣸⠟⠁⠀⠀⠀⢀⡴⣿⡿⡟⢿⣿⣷⣤⣽⣶⠄⠀⠀⡾⠀⣠⠋⠀⠀⣰⠃⠀⠀⠀⠀⠀⢳⣇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡴⠋⠀⠀⣰⠏⢀⡜⡴⠁⠀⠀⢠⣯⡾⠁⠀⠀⠀⣠⠾⠋⠀⢿⠀⠳⠤⠽⣿⣿⣆⠈⠧⠀⡸⠁⣰⠋⠀⠀⣰⠃⠀⠀⠀⠀⠀⠠⣬⣼⡄⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀ ⢀⡤⠞⠉⠀⣀⡴⣾⡟⠀⣸⡝⠁⠀⠀⢀⡿⠃⠀⠀⢀⡴⠞⠁⠀⠀⠀⠈⠳⢤⣠⣶⠿⢻⠷⠀⠀⣰⠃⡴⠁⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣳⡀⠀⢸⡆⠀⡇⠀⠀⠀⠀ ⢁⠤⠠⠖⠿⠅⠀⢹⠁⢠⠏⠀⠀⣠⠎⣾⠞⢀⣠⣶⡏⣷⠟⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠣⠞⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡾⡆⠈⡇⢀⠃⠀⠀⠀⠀ ⠌⢀⠌⠀⠀⡀⢀⡟⡰⠋⠀⢀⡴⠃⢸⣣⣴⣻⣷⡿⡟⢆⢀⡀⠀⠉⣙⠒⠲⢦⣌⣲⡀⠀⠀⡴⠃⠀⠀⠀⣠⡞⠁⠀⠀⠈⠐⠒⠷⢤⣄⣀⠀⠀⠈⠹⡾⠀⢻⣸⠀⠀⠀⠀⠀ ⠀⠁⠀⠒⠒⠂⣸⠟⠁⠀⡠⠊⠀⢀⣿⣯⢀⡽⣧⠀⠀⠂⠳⣿⠌⠳⡜⢧⠀⢄⠈⢣⡙⢆⡼⠁⠀⠀⢀⡼⡗⠁⠀⠀⢀⣠⠤⣤⣤⣤⣤⣍⡙⢢⣀⡀⠹⡄⢸⡿⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⣀⠜⠁⢀⣠⠊⠀⠀⠀⣸⢁⠸⠋⠀⠈⠻⡧⠳⡵⣌⢳⣤⡙⢦⡱⢞⠡⡐⢯⡞⠀⠀⠀⣠⣞⠀⠀⠀⡆⠀⠈⢻⠟⡟⡿⡿⣿⣿⣿⣿⣯⣤⠄⢳⣸⠃⠀⠀⠀⠀⠈ ⣤⣤⣔⣋⣁⣤⠞⠉⡇⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠙⢿⡺⠷⡟⢦⡽⠋⠀⠀⣠⣾⡿⡳⣀⡀⠀⢷⡀⠀⠘⣦⣛⣿⣿⠿⠀⠈⠻⣿⣿⣤⣸⣿⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⢻⣿⠀⢸⠃⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠞⠁⠀⣠⣾⢿⠋⡳⣜⢿⢟⢦⡀⣿⣄⠀⠈⠙⠉⠁⠀⠀⠀⠀⢘⣿⣿⣿⡏⠀⠀⠀⠀⠀⠢ ⠳⡄⠀⢤⣸⡏⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣀⡴⠟⠛⠉⠄⠱⡝⢾⢦⡹⣿⣿⣿⡍⠳⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠁⠀⠀⠀⠀⢀⠆ ⠀⢹⣦⠀⢹⠁⠀⢸⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣡⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣝⢿⣿⢿⣂⠙⢷⠶⡶⢦⡴⠞⢉⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠀ ⠀⣾⡏⠱⣾⠀⠀⣾⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⣾⠏⠉⠉⠙⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡻⣷⡹⣷⣄⠹⣶⠶⠀⢀⣾⣿⡿⢻⠁⠀⠀⠀⠀⠀⠀⠀ ⢠⡿⠁⠀⡇⠀⢀⣿⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣀⠤⠖⠛⠉⠀⢰⣿⣍⣻⣤⡤⠤⡤⢤⣈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠙⠀⢹⣾⢫⢬⡈⠓⠀⣾⢿⣿⠃⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠃⠀⢰⠃⠀⢸⣿⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⣯⣽⠡⠆⠀⣄⣑⣀⣈⣛⣦⡄⢹⣦⠀⠀⠀⠀⠀⠀⠀⠉⠳⡻⣝⠢⠄⣿⣾⠇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⢀⡿⠀⠀⣼⡿⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣧⠀⣴⣽⣭⠶⠤⠶⠦⠝⣆⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⡼⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⠃⠀⢠⡟⣠⡇⠀⠀⢨⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠉⠀⠈⠉⠹⢶⣒⣒⠛⠲⢆⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⡇⠀⢸⠇⠀⠀⠀⠀⠀⠀ ⠀⠞⡜⠀⠀⣾⠞⠉⡇⠀⠀⢸⣯⢿⣆⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⢷⠀⠀⠀⠀⠈⡏⠉⠛⢻⣿⣁⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⠁⠀⢸⠀⠀⡜⠀⠀⠈⠀⠀⠀⠀ ⠎⠰⠁⠀⣸⠃⠀⠀⢹⠀⠀⢸⡿⢷⣿⣧⡄⠀⢀⣠⡶⠟⠁⠀⠀⠸⡄⠀⠀⠀⢠⡇⠀⠀⠈⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠇⠀⠀⡜⠀⢀⠇⠀⠀⠃⠀⠀⠀⠀ ⠐⠃⠀⢀⡏⠀⠀⠀⢸⡆⠀⢸⠀⠀⠉⠙⠛⣶⣯⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠋⠀⠀⠀⣼⣏⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⡾⠀⠀⢸⡇⠀⢸⠀⠀⠔⠀⠀⠀⠀⠀ ⡌⠀⠀⡞⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⣇⢸⣦⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣰⢃⣈⡁⠸⡄⠀⠀⠀⠀⠀⠀⢀⣴⠟⡟⢰⠃⠀⠀⣿⠃⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡈⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⣿⡞⢻⣿⣦⡀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠾⡟⠁⠀⠘⠆⢱⠀⠀⠀⢀⣠⣶⡟⡽⢹⠁⡼⠀⠀⣼⡜⠀⢠⠁⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⡐⠀⠀⠀⠀⠀⠀⠸⠁⠀⢸⠀⠀⠀⠀⠀⡈⡇⠀⠘⢿⣿⣦⣠⣞⠵⠛⠒⠒⡿⣣⠏⠀⠀⢀⣀⣧⠦⠴⠒⢻⠉⣿⣟⣀⡇⡼⢰⡇⠀⢠⠇⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣷⡇⠀⠀⠀⠈⣿⣿⣧⣤⣤⣴⣫⣒⡤⠴⠚⠛⠉⠀⠀⠀⠀⠀⣾⠀⢹⡏⠙⢧⡇⣼⠀⠀⡸⢀⡇⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⣻⣤⠀⠉⠑⠲⣤⠴⠚⠉⠁⣠⣼⡋⠀⠀⠀⠀⠀⠀ ⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠲⣄⠀⠀⠀ ⠯⢤⡤⠆⠀⠀⠀⠀⣀⡤⠤⠤⠤⣤⣀⡀⠀⠀⠀⠀⠈⠻⢧⡀⠀ ⣴⣋⣀⣀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠉⢳⠀⠀⠀⠀⢀⣠⠿⠀ ⠉⢩⠟⠉⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡀⠀⠐⠛⢦⡀⠀ ⢰⠋⣀⣀⠄⢰⡧⠐⠂⢀⠀⠀⠀⠒⠒⢄⠘⠉⣇⣀⠀⣀⡴⠛⠀ ⠘⢉⡽⠁⠀⢸⠀⠺⠂⠘⠀⠀⠀⠰⠆⠀⠀⠀⠫⣹⡆⠈⠳⡀⠀ ⠀⢸⠁⣀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⠀⢶⣤⣹⡄ ⠀⠸⠚⣿⠀⢸⡆⠀⡠⠣⠄⠀⢄⠀⠀⠀⠀⢀⡴⠁⠀⠈⢳⠈⠁ ⠀⠀⠀⠘⠞⠉⡇⢸⡀⠀⠀⠀⠀⠱⠀⠀⢀⡿⠁⣄⣀⠀⠈⡇⠀ ⠀⠀⠀⠀⠀⠀⢹⡀⠋⠒⠢⠔⠲⠒⠀⠀⣸⣧⣤⣘⡎⠉⠓⠃⠀ ⠀⠀⠀⠀⢀⣠⣾⣷⣇⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣶⣄⠀⠀ ⠀⣠⣴⣾⣿⣿⣿⣿⡟⡟⠶⠴⠒⡻⢉⣾⣿⣿⣿⣿⣿⣿⣿⠗⠀ ⠀⠙⠻⣿⣿⣿⣿⣿⡷⢼⣾⣷⣯⢄⢎⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠈⠙⠻⠿⣿⣇⠈⣿⣿⡇⠀⣾⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠴⠶⠖⠒⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠟⠙⠳⣦⡀⠈⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⢠⣷⣿⣷⣄⠹⣮⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⢸⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠸⣿⣿⣿⡟⢷⡈⢿⣇⠀⠀⠀⠀⠀ ⠀⠀⣿⡏⠀⠀⠀⢀⣤⠶⠚⠛⠛⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⢿⡔⢻⣆⠀⠀⠀⠀ ⣤⢸⣿⠇⠀⠀⣰⣿⣁⡀⠀⠀⠀⠀⠀⠹⣟⢳⡄⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣿⣆⠀⠀⠀ ⣿⢉⡟⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠈⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠸⣟⣧⡀⠀ ⣿⣾⠁⠀⠀⠘⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⢤⣤⣤⣤⣤⠶⠋⠀⠀⠀⢻⡿⣧⠀ ⣿⡏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀ ⣿⡇⠀⠀⠀⠀⠈⠻⣄⣀⠀⢀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⣷⡇⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄ ⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⢹⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠸⣧⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷ ⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣶⣶⣶⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿ ⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁ ⠀⠀⠀⢻⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀ ⠀⠀⠀⠈⣧⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀ ⠀⠀⠀⠀⠻⠂⠀⠉⠛⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣴⡻⠋⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡀⠀⡿⠦⣤⣤⡈⠳⡙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠛⢹⣅⣠⠤⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⡇⠀⠀⠙⠉⠛⠛⠀⠙⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⠀⠀⠀ ⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠤⠤⠤⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⣻⡟⠁⢰⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⣀⡾⢽⠗⢲⠏⠘⠋⠉⢛⠉⠉⠉⠉⠑⠲⣄⡀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⣼⠤⠖⡻⠃⠀⢸⠀⡜⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⡄⠈⢳⡀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠁ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⡤⠒⢩⠇⠀⡴⠁⠤⢀⣘⣸⡀⠀⢀⣧⢀⣿⣸⡀⠀⠀⢀⡇⠀⢀⠙⣆⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀ ⠈⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⢡⠀⢠⠋⣀⠞⠀⠀⠀⠀⢸⡏⠀⠀⠀⢇⢸⠙⣿⠀⠀⠀⡸⡇⠀⣾⠀⠈⢷⡀⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠿⡇⠀⠀⡇⠀⡏⢠⣏⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢠⠃⡇⣰⠀⡇⠀⢸⢳⡈⣧⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⢀⡼⠋⠀⡇⠀⢸⣇⡸⠀⠈⠛⢿⣶⣤⣄⣐⠠⠤⡀⠀⠀⠘⠁⠀⠏⠀⢀⠎⠀⣿⠷⣄⣣⠀⡎⠀⠹⣼⡄⠀⠀⠀⠀⡏ ⠀⠀⠀⠀⢠⠞⠀⠀⠀⠸⡄⢸⢻⡇⠀⠀⠀⢸⣇⠈⠉⠛⣿⡿⠇⠀⠀⠀⠀⠀⡇⣠⠋⠀⠘⠁⠀⠀⠙⢲⠇⠀⠀⢹⣧⠀⠀⠀⢠⠁ ⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⣿⡼⢼⠇⠀⠀⠀⠘⠿⣶⣴⡾⠋⠀⠀⠀⠀⠀⠀⢸⠟⠁⣷⣦⣤⠀⠀⠀⢰⢻⠀⠀⣰⠀⣿⠀⠀⢀⡞⠀ ⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⢸⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠷⣶⣦⣤⣼⡀⠀⡇⠀⣿⡀⠀⣼⠁⠀ ⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⡀⢀⣼⡿⠙⠀⣸⠃⢸⣿⠀⣼⠇⠀⠀ ⠀⣼⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠋⠀⡇⡰⠟⢀⡟⣿⣠⠏⠀⠀⠀ ⢠⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⢦⡁⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠞⢁⣧⠞⢀⣿⡏⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣿⠀⣷⡄⠀⠀⠀⠀⢸⠛⠛⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⢄⡾⢃⡴⣼⢻⠃⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⡄⢿⠙⣦⡀⠀⠀⠈⠦⣀⡀⠀⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣡⠏⢀⡞⣽⠃⣾⠀⠀⠀⠀⠀ ⠻⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣿⣷⣿⢠⠇⠙⢦⡀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⡄⠏⣠⣿⠞⠁⠀⣿⠀⠀⠀⠀⠀ ⠀⠹⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⡏⣸⠀⠀⠀⠉⠢⣄⣀⣀⣀⣀⣀⣀⣠⣤⣤⠴⠒⠚⢉⡴⠋⢸⣠⡾⠛⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⡀⠀⢹⡿⠁⠀⠀⠀⠀⠀⣾⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣥⣾⣿⡟⠀⠀⢀⡴⠋⠀⢀⣿⠋⠀⠀⣀⣀⣠⣤⡿⠀⠀⠀⠀⠀ ⠙⢦⣴⠃⠀⠀⠀⠀⠀⢸⠋⠉⠻⣿⡀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⢈⣹⠇⢀⡴⠋⠀⠀⠀⣼⣷⣶⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⣙⠀⠀⠀⠀⠀⠀⣏⣀⣀⡀⠙⠿⣦⣀⣤⢶⠋⠀⠀⣠⠶⠶⠚⠉⣹⣰⠞⠀⠀⠀⠀⢰⠏⠉⠉⠙⢻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⣸⡀⢿⠐⣆⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⣿⠃⠸⡄⠸⡄⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⡴⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠼⠁⠀⡰⣿⡟⠀⡄⣇⠀⢳⡄⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠠⣀⡴⠋⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠋⠀⢀⣼⠟⠁⡇⠀⣧⢸⡀⠀⠱⡄⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠁⢀⣠⣿⣯⡀⠀⡇⠀⢻⠘⣷⡀⠀⠹⣄⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠉⢦⡀⠀⠀⠀⣀⣽⠤⣄⡀⣆⢹⡄⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣧⠴⠊⠉⠀⠀⠈⢻⠀⡇⠀⠈⡇⢻⠳⡄⠀⠘⢦⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢦⡉⠲⣞⠉⠁⠀⠀⠈⢳⡘⢆⣷⠀⠀⠀⠀⠀⠀ ⢠⠾⠋⠀⠀⠀⠀⠀⠀⢀⡟⠀⡇⠀⡄⢳⠘⡆⠙⢦⡀⠀⠳⣄⠀⠀⠀⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡝⢦⠀⠀⠀⠙⢦⡈⠳⢄⡀⠀⠀⠀⡇⠘⣞⡆⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⡇⡀⢳⠘⡇⠹⡄⠀⠱⢦⡀⠈⠳⣄⢣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣑⣄⠀⠀⠀⠙⠲⣤⣍⠲⢤⣴⠃⠀⠘⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⢷⣣⠈⣿⡹⡀⠹⡄⣠⠏⠉⠳⠦⣈⡉⠺⣷⣦⣀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⡝⠳⢤⡀⠀⠀⠀⠙⠿⡓⠮⣝⣓⣶⢼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠘⣿⡄⠸⣧⣹⣦⡿⣇⠀⠀⠀⠀⠀⠉⠓⣶⠽⢻⢯⣳⣤⣀⠘⠦⡀⠀⠀⠀⠀⠀⠀⠙⣝⢦⡀⣉⠓⠦⢄⣀⠀⠈⠳⢶⡄⠀⠀⢻⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⣤⠖⢀⣹⣿⡐⢻⡍⢻⡷⣜⢦⡀⠀⠀⠀⠀⠀⢨⣷⡀⠀⠈⢿⢯⣍⠓⠛⠶⣦⣀⠀⠀⠀⠀⠀⠀⠹⣮⡳⣯⣦⣬⣄⣀⠀⠀⠙⠒⠤⣄⣷⡀⠀⠀ ⢀⠀⠀⠀⠀⠀⣠⣧⠾⠛⠊⠉⠀⠀⠘⢷⣄⢳⡄⢿⡞⣷⡙⢦⡀⠀⠀⠀⠈⢷⢻⡶⣄⠀⠀⠉⠙⣝⣶⣘⢾⡓⠦⣄⡀⠀⠀⢢⡈⢿⣿⡳⢦⣌⡉⠉⠱⡖⠒⢚⠻⣽⡇⠀⠀ ⠀⠑⣤⣀⣤⠾⠋⠀⠀⠐⣚⣛⣭⣷⣲⣤⠿⣷⣿⣄⠹⣌⣻⣦⡙⠦⡀⠀⠀⠈⢷⣷⡈⠳⣦⣤⣦⣴⣻⣿⣽⡻⢦⣀⠻⣄⡀⠀⠹⣗⠿⣧⣈⡒⠉⠲⠤⣽⡄⠈⠳⣿⣟⠀⠀ ⠀⠀⣷⡏⠀⠀⠀⣠⣴⡿⠛⠉⠁⢤⡉⠙⠛⠻⣖⠙⠣⣄⠙⢧⡙⠳⣝⣦⣄⡀⠀⢹⣿⠟⠉⠈⠓⢤⡀⠈⠙⠿⣦⣌⡛⢮⡻⣦⣄⣈⠳⣌⣧⠈⠉⠀⠀⠀⢻⡀⠀⢻⡿⡄⠀ ⠀⠀⢹⡇⠀⠀⣠⡿⠋⠀⠀⠀⢀⣴⣿⣿⣆⠀⠈⠀⠀⠈⠳⢶⡍⢦⡀⠉⠺⢯⣟⠻⠽⣦⣀⣴⣶⣷⣾⣧⠀⠀⠈⢿⡄⠀⠉⢸⠂⠈⢻⡉⠙⡦⠄⠀⠀⠀⠀⢣⠀⠘⣧⠈⠀ ⠀⠀⢸⡇⠀⢀⣿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠓⠶⠤⠈⠙⠲⣾⠿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣏⠀⠀⣸⠀⣀⡀⢳⡀⢿⠀⠀⠀⠀⠀⠸⡇⠀⠈⣦⢀ ⠀⠀⠀⣷⠀⠀⣿⠀⠀⠀⠼⣯⣿⠟⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⠛⠉⠙⣿⠟⠀⠀⠀⠀⠘⠃⢰⣿⡴⠋⠳⡌⢇⠈⡆⠀⠀⠀⠀⢰⣿⠀⠀⠀⡀ ⠀⠀⠀⢿⡀⠀⠁⠀⠀⠀⠀⠉⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⣦⠞⢩⣟⣤⠬⠀⠹⡾⡄⢃⠀⠀⠀⠀⠀⢳⣇⠀⠀⠱ ⠀⠀⠀⢈⣧⡠⠖⠉⣉⡴⢂⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠖⠩⢞⡭⢞⣁⣴⠏⠹⠀⠈⡳⠀⢹⢻⢸⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀ ⠀⢀⢀⡼⣿⡄⣀⠿⣡⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢀⣠⣖⡿⠛⣡⣶⢿⡷⣶⢦⣠⠟⢀⡸⠈⣾⡄⠀⠀⠀⠀⠀⡿⠀⠀⠀ ⣧⣈⠉⠙⠛⣿⡥⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠒⠒⠒⠲⣦⡀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⢈⡟⠛⠛⢉⣠⡴⣞⠁⠀⢇⡇⠀⠀⠀⠀⠀⣷⠀⠀⠀ ⡙⣌⠓⢤⣄⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⣿⣿⣿⢛⠛⠉⠋⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣤⠴⠋⠁⠀⣧⢸⣇⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠿⣦⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣡⠐⣢⠤⠿⠛⠓⠚⠳⠶⢝⣧⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⡾⠳⠆⡄⠀⠀⠀⠹⣸⡿⡀⢸⡇⠀⠀⠀⠀⢀⢿⠂⠀⠀ ⠀⠀⠈⠳⣄⣤⣀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠫⠕⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠐⠋⣠⠞⠀⠀⣧⡇⠀⠀⠀⠀⣿⡇⢻⣸⣷⠀⠀⠀⠀⣾⢀⠀⠀⠀ ⣒⣲⣶⠖⠚⠛⠺⢿⣶⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⢀⣿⣧⠀⠀⠀⢠⣿⠇⠀⣟⡟⠀⠀⠀⢰⡏⣾⠀⠀⡀ ⠀⠹⡾⠿⠶⢶⣶⠶⠛⣿⡿⠙⣶⣄⡀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⢀⣴⣾⡿⠙⢿⣄⠀⢸⠃⣿⠀⠀⠀⣸⣿⣦⣴⢃⡇⠀⠀⣼⣞⣧⠃⠀⢀⠇ ⠀⠈⠛⠶⣿⣏⣥⣤⠾⡟⠀⠀⢹⣷⠙⠳⢤⣀⠀⠀⠀⠙⠦⢄⣀⣀⣀⣀⣀⣠⠴⠁⢀⣠⡤⠚⢫⢋⡝⠁⠀⠘⣿⣿⣯⡀⢹⠀⠀⢠⡿⡿⣿⣫⡾⠁⢀⣼⣟⡼⠁⠀⢀⡞⠀ ⣦⣠⣀⠀⠉⠙⢒⣶⣿⠓⠂⠀⠀⠹⣄⠀⠀⠘⢻⣖⢤⣄⡴⣋⡵⠺⣯⡉⢙⣧⣴⣚⡿⠑⠀⢀⡴⠋⠀⠀⠀⠀⠸⡿⠃⠉⠳⢦⣤⣞⣾⣽⡟⣿⢃⣤⣺⢯⡞⠀⠀⠀⠋⠀⠀ ⠈⠉⠻⢯⡉⠉⠉⢁⡇⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠙⢶⣏⡴⠉⢀⣀⣴⠟⠉⠳⣝⣿⣛⣦⡴⠋⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠻⠛⣿⣼⡋⠉⠀⠁⠀⣍⠻⢗⣦⣀⠀⠀ ⠓⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⡿⠋⣠⠞⠉⠀⠙⣲⡤⣄⠀⢙⢿⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠙⠦⡉⠻⣟⡆ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣧⡶⠃⠀⢀⡼⠞⠉⡀⠈⠳⣼⣮⢳⣼⡄⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠈⠓⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢰⠋⢾⠶⢯⣤⡤⠞⠉⠀⠀⣀⣷⣄⠀⢸⣎⢻⠙⣷⡀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠐⠋⠀⠀⠀⣴⠚⠉⣻⢮⠉⠓⠛⠁⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⣳⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⡟⠷⠄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡋⡼⠀⠀⠀⠀⠀

⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⣌⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀ ⠀⠀⠀⡟⢃⠙⢌⠢⢄⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⣀⠔⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⡷⣑⡌⠇⠂⠀⠈⠈⠉⠙⢿⡽⠉⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⠃ ⠀⠀⠀⠸⣼⠱⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢠⠗⡀⠀⠀⠄⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⢠⣚⠚⠈⠄⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⡰⠟⠀⠀⠀⣼⢋⣥⣶⣮⡳⡄⠀⠀⠀⠀⠀⠀⢀⣴⣶⡒⢦⣀⠀⠀⠀⠸⠀ ⢀⠃⠀⠀⠀⠀⠈⠾⣿⣟⣿⢇⡇⢰⡀⠄⡀⠀⢰⡏⣿⣿⣿⣦⢻⠆⠀⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡑⣃⢀⡀⠈⠣⠸⠗⠛⠛⠛⠓⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡇⣀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢓⡖⢢⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠠⢠⡀⠀⠀⠀⠀⠀ ⢠⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣠⣤⢴⠟⠳⢤⣂⠀⠀⢤⣔⠷⠟⠘⠀⠀⠀⠀⠀ ⠈⢇⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡏⢧⣟⣋⠏⣏⢟⡻⠟⠛⠑⢄⠀⠀⠀⠀⠀⠀ ⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠫⣿⣗⣦⣾⣾⣿⠀⠀⠀⠀⠀⠀⠐⠄⡠⠊⠀⠀ ⠀⠀⠀⠀⠁⠐⠠⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀ ⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀ ⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀ ⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠟⠋⠉⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠛⠛⠃⠀⠀⠀⠀⠀⠀⠘⣧⠀ ⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⣤⣤⣄⣀⣠⣶⣺⣿⡏⠉⠉⠈⠉⢉⣶⣀⣄⣤⣤⣤⣤⣀⢀⡀⠀⠀⠀⠀⠹⡇ ⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⢻⣿⡿⠿⠿⢿⠿⣿⣿⣿⡿⠿⠃⠀⠀⢀⠀⠘⠻⣿⣿⠿⠟⠻⠛⠻⢿⡿⠒⠀⠀⠀⠀⣿ ⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⣟⣦⢦⠀⠀⠀⠈⠓⣿⡇⠀⠀⠀⢠⣇⠀⠀⢸⣿⣇⠀⠀⠀⠀⣠⣄⢱⠀⠀⠀⠀⠀⡟ ⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣿⣿⣧⣝⠋⠁⠀⠀⠄⢉⣿⣷⠀⠀⠀⣿⣿⠀⠀⠈⣿⣿⡆⠀⠀⠀⠙⣁⣾⡀⠀⠀⠀⠀⡇ ⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⣤⣬⣷⣶⡿⢋⠜⠀⠀⠀⢺⣿⡄⠀⠀⠘⢿⣿⣿⣶⣶⣿⡿⠉⠙⠆⠀⠀⢀⠇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⡄⠀⣀⢹⣿⣿⡦⣄⠀⢼⣿⣿⣿⣿⡿⠓⠁⠀⠀⠀⠀⢸⠀ ⠘⣷⠀⠀⠀⢀⡤⠔⠒⠒⠀⢄⠀⠀⠀⠈⠙⠿⣛⠟⠉⣠⣴⣾⣿⣤⣿⣿⣿⣿⡿⣿⣿⣿⡿⢃⡀⠀⠀⠀⠀⠒⠉⠓⢶⠀⢸⠀ ⠀⢻⡆⠀⢰⠏⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⡾⣿⣷⣾⣿⣿⣿⣿⣛⡛⠛⠿⢯⣥⣤⠼⠿⠾⠿⣿⣶⣦⣤⣀⣀⡀⠀⠀⠇⣾⠀ ⠀⠈⢿⡄⢻⠀⠀⠀⣴⣶⣾⡿⠿⠗⠺⠿⠛⠟⠙⠿⢿⣿⣿⣯⣉⣉⣉⣉⣿⣿⣯⣉⣉⣉⣉⣭⣩⡽⠟⠛⠛⠲⠿⣾⡇⢸⡇⠀ ⠀⠀⠈⢿⣄⠀⠀⠀⢿⣄⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠟⣻⣿⣯⣭⣿⡛⠽⣟⠋⠉⠀⠀⠀⠀⠀⣠⣤⠴⢃⡿⠀⠀ ⠀⠀⠀⠀⠹⣦⡀⠀⠀⠙⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⣉⣡⣤⣄⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⢠⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⠶⠶⠶⣤⣤⣤⡴⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⡿⠋⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠿⢿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⢣⣶⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣸⠃⠀⠈⠙⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⢿⠀⠀⠀⠀⠀⠈⠛⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⢸⣇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡌⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣿⣷⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢈⣿⣿⣷⡘⢿⣤⠀⠀⠀⠠⣖⠚⠛⠛⠛⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠙⠻⣷⣄⠙⢷⣤⡀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀ ⠀⣸⣿⠀⠀⠀⠈⠁⠀⠉⠻⠶⢦⣤⡾⠃⠀⠀⢀⣴⣾⣿⣿⣿⣿⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀ ⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠋⠀⠀⠀⠀⠈⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠈⠙⠿⢿⣿⣷⣄ ⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠉⣿⣿ ⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⣄⠀⠀⠀⢸⣿⡇⠀⠀⠀⢀⣿⡿ ⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⢿⣿⣷⡄⠀⢸⣿⡇⠀⠀⢀⣿⣿⠃ ⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠦⠀⠀⢀⣠⣶⣶⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠹⣿⣿⡄⠸⣿⡇⠀⢀⣾⣿⠁⠀ ⠀⠀⠈⣿⣿⣆⣀⣀⣀⣀⣀⠀⠠⠤⠶⠶⣶⣶⣤⣀⠀⠀⠀⢠⣾⡟⠉⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⢀⣠⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠇⢰⣿⣇⣠⣿⠟⠁⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⡿⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠉⠙⠓⠂⠀⢸⣿⠀⠀⠰⣦⠀⠀⠀⠹⣿⡆⠀⠀⢸⣿⡄⠀⠈⠙⣿⡄⠀⠀⠀⠀⠀⠀⠿⠋⠀⢸⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⣰⣿⡿⠋⠉⠀⠀⠀⠙⢿⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠸⣿⣄⠀⠀⢿⣆⠀⠀⠀⠙⣿⡄⠀⠀⠹⣿⣦⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠛⠻⠿⣿⣿⣦⡀⠀⠀⠙⢿⣷⣄⠘⢿⣄⠀⠀⠀⠙⢷⠀⢠⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠙⠿⣿⣦⡀⠀⠀⠉⠻⠿⣾⣿⣷⣤⣠⣤⣼⣿⡿⢿⣏⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣀⣤⣾⣿⣥⣀⡀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠉⠀⠘⣿⣦⣤⣤⡶⠟⠀⠀⠀⠀⠀⠀⣠⣿⡿⠉⠉⠉⠉⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠘⢲⣾⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠐⢾⣿⣭⡀⠀⠀⢀⣠⣼⣷⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣾⡿⠟⠙⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣆⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠘⢿⡶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⡿⢿⣯⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠙⠛⠻⠿⣿⡿⠿⠿⠿⠛⠛⠉⠉⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠻⢿⣷⣶⣶⣶⡶⠾⠛⠻⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⣀⡀⠀⢀⣀⣠⣶⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⠛⢗⠀⠀⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⣦⠐⣴⠀⠀⠀⠀⡜⠀⣀⠤⠐⢒⢾⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⢤⡓⠉⠣⡏⠇⠐⠒⠲⠚⠛⠀⡠⣾⡥⠀⠊⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣀⠘⠉⠀⠀⠀⠸⣰⠀⢰⠣⡠⠀⠂⠈⠈⢽⡦⠀⡇⠀⠀⠀ ⠀⠀⠀⢀⠔⠁⢀⢤⣀⠆⠿⠿⠷⣈⣀⢘⡱⢠⣤⣄⠀⠀⠘⢇⠀⡇⠀⠀⠀ ⠀⠀⡤⠥⠐⡂⠭⠙⣇⣠⠈⠀⢀⠨⣏⠁⠈⠍⣛⠛⠓⠠⠄⠀⠴⣇⠀⠀⠀ ⣀⡏⠀⠀⢀⠄⠊⠁⠈⠀⠉⠁⠀⠀⠀⠑⠠⠬⠷⠬⡽⡋⢄⠀⠀⠀⢧⠄⠀ ⠉⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠢⡑⠈⠂⠄⢺⠁⠀ ⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⡆⠀ ⠀⡀⠀⡀⠀⠑⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠀⠀⢳⠀ ⠀⢹⣆⣿⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠴⠤⠴⠛⠁⠀⠀⣸⡆ ⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠀⠀⠀⠉⠙⡇

⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠰⠶⢶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⠴⠶⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀ ⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣀⣀⣤⣤⣤⣤⣤⣤⣄⠛⣿⣶⣿⣟⡋⠉⠋⠁⠀⠀⠀⢉⣷⡚⠉⣍⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣗ ⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⣿ ⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⣿⣿⠿⠛⠻⠋⠉⠋⠛⠛⠿⢿⣿⣿⡉⠁⠀⠀⠀⢀⡾⠀⠀⠀⠀⣿⣿⣿⠿⠟⠋⠉⠋⠙⠙⠟⢿⡏⠉⠁⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣤⣤⣿⣿⢻⣶⠦⡄⠀⠀⠀⠀⠐⠂⣾⣿⡟⠃⠀⠀⠀⢀⣾⡧⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⢀⣤⣤⠈⣧⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⠿⠶⠏⠀⠀⠀⣀⠀⠒⢾⣿⣷⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⣿⣷⣿⣁⠀⠀⠀⠀⠘⠷⠿⢠⣿⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠟⢻⣿⣿⣿⣯⣧⣀⡄⠀⢠⣄⠈⣇⣠⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠹⣿⣿⣷⣄⠒⠀⢀⣀⣠⣶⣿⡷⣦⡄⠀⠀⠀⠀⠀⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⢛⣵⠃⠀⠀⠀⠀⢠⣿⣿⣧⢀⠀⠀⠀⠙⢿⣿⣿⣿⣾⣿⣿⣿⣿⡏⢀⠈⠓⠀⠀⠀⠀⢰⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠏⠀⣀⣠⡤⠀⠀⣠⣿⣿⣿⣿⣀⠀⠀⢀⠘⣿⣿⣿⣿⣿⣟⣿⣿⠗⠉⠀⠀⠀⠀⠀⠀⣼⠏ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣶⣿⢟⡿⠛⠁⢀⡀⣼⣿⡛⢡⣶⣾⣿⣿⣿⣿⣿⣭⣭⣽⣥⣶⣿⠋⠉⠛⠟⠛⠉⠁⠀⢀⣀⣄⣀⠀⠀⠀⣿⠀ ⡇⠀⠀⠀⠀⢠⣶⠾⠛⠉⠋⠛⠛⠒⠦⠀⠀⠀⠀⠀⠀⠉⠻⠤⠌⠉⠀⣠⣴⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⠋⣦⣀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠻⡄⠀⣿⠀ ⣿⡀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣍⣳⣌⣢⣠⣿⣿⣾⣿⣿⣿⣷⣴⣤⣀⣀⣀⣀⠀⠀⠀⢀⡇⣼⣿⠀ ⢹⣷⠀⠀⣿⠀⠀⠀⠀⠀⣀⣄⣠⣶⣾⣟⣿⣿⣯⣭⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⠿⠷⠦⠶⠤⢤⡬⢭⢭⣤⣤⣤⣤⠤⠴⠾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣤⡌⢸⣿⡇⠀ ⠀⢿⣧⡀⢿⠀⠀⠀⠀⣾⣿⣿⣾⣿⡯⠕⠚⠛⠋⠉⠉⠁⠈⠉⠉⠛⠿⢿⣿⣿⣿⣦⣴⣴⣦⣶⣷⣤⣴⣶⣶⣶⣤⣤⣤⣤⣶⣾⣿⡿⠿⠋⠉⠉⠁⠙⠻⣿⣷⢿⣷⢸⣿⠃⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⣿⡿⠟⢛⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⣩⠉⠉⢿⠀⢞⠉⠈⠳⠌⢿⣿⣿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢠⠋⢀⣤⢤⣄⠀⡞⠛⢶⡀⠀⠸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⢀⣿⣿⣿⡇⠀⢰⠏⠀⠀⢹⣾⡇⠀⠀⢷⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠸⣇⢠⣦⣤⡇⢷⣿⣷⣺⡇⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⠙⢯⣿⣿⣿⣼⣿⡿⠿⢧⣄⠋⠉⠉⠻⢿⣆⠀⠀⢀⡞⠉⠙⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠛⠻⡄⢠⡜⠋⢰⣿⣿⣿⣿⡇⠀⣬⣥⣤⣤⠀⠀⢹⡆⠀⣸⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⢀⡴⠋⠀⠀⢻⣿⣿⣿⣿⠇⠀⢠⠞⠀⠀⠀⢀⡾⠁⠀⡏⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠰⠟⠷⣤⣀⠀⠀⠈⠉⠉⣀⣠⣴⠋⠀⠀⣀⡴⠋⠀⠀⠀⢹⠀⠀⢀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⠀⠀⠉⠻⣿⣻⣿⣭⣭⣴⠏⣠⡴⠟⠁⣠⠴⢶⡟⠉⠹⣇⠀⢸⡗⢶⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡬⣽⠛⢛⣷⠦⣌⣙⣛⣛⣋⣥⠞⢯⠀⢀⡞⢡⣤⠀⠹⠆⢠⠋⠀⠀⠁⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠉⠉⢁⣠⣾⣃⣰⡿⠁⠀⠀⠀⠀⣹⡟⠀⠀⠈⢷⡾⣷⣼⠿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⡴⢋⣄⠉⠉⠉⠉⠓⠲⢤⣀⣼⠟⠀⠀⠀⠀⠈⢿⡞⠁⠀⠀⠀⢰⠄⢰⠀⡄⢠⡟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠎⣠⣾⣿⡇⠀⣠⣾⣿⡄⠀⠈⠙⢦⣸⠻⣆⠀⠀⡾⢷⡀⠀⠀⠠⣾⣠⢏⡼⣡⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠀⣿⣿⣿⠃⢰⣿⣿⣿⣿⠀⠀⠀⠀⠙⡆⢹⡀⠐⣧⠀⠙⢷⣤⡀⢀⣃⣯⠶⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠉⠁⠀⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⣹⠀⢧⠀⠈⠳⢦⣤⠼⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠈⠳⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣴⣋⣀⣀⣀⣀⣀⠀⠀⣀⣀⣠⣀⣀⣘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⣈⠉⠉⠙⣟⠉⠀⠀⠀⡇⠉⠉⠉⠑⠒⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠘⣇⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢹⡄⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣾⡇⠀⠀⣷⡀⠀⢀⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟⠉⢏⠙⢦⡀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢱⡀⠈⢦⠘⡄⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢀⣀⣠⣤⣶⣦⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⣤⣼⣿⡄⢀⣿⣷⠀⠀⠀⠀⠀⠀⡰⠁⠀⣀⠤⠒⠉⠉⠀⡠⠞⠿⢿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⡠⠿⠷⠍⠛⣄⣯⠙⡏⠑⠒⠓⠴⢲⠷⠾⠿⠃⠀⠀⣠⣴⣏⣀⡀⠀⠘⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢀⣤⡿⠃⠀⠀⠀⠀⢻⡆⢇⠀⠀⠀⢠⡎⡀⠀⡀⠀⡠⠊⠡⠒⠿⣷⡄⠀⠀⠈⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣄⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⠀⠀⠀⣿⢠⢁⠜⠁⠈⠀⠀⠀⠀⠘⢦⣽⠦⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⡠⢔⣿⣿⣿⣷⣌⠛⠀⠀⢠⡇⢣⣊⣀⣀⡀⠀⠀⠀⠀⠀⢩⣿⠄⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢀⣜⣛⣷⠦⣉⣉⣉⡉⠉⠉⠉⢶⣤⣤⣤⠴⣏⣡⣾⣿⣿⣷⣦⡀⠀⠀⠀⠙⠳⠀⢀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠧⡤⠔⠊⢉⡀⠤⠜⢳⣀⣀⡤⠀⠀⠀⠀⢀⣠⣿⠁⠀⠀⠀⢈⡉⠙⠛⠛⠻⠗⠀⠤⡀⠀⠀⠴⢾⣇⠀⠀⠀⠀⠀ ⠀⢀⡶⠋⠀⠀⠀⠀⠉⠀⣠⠔⠂⡩⠜⠋⠓⠒⠒⠒⠉⠁⠀⠈⠑⢦⡀⠀⠀⠑⢤⡉⠒⠲⢵⣶⠄⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀ ⣀⣼⡁⠀⠀⠀⠀⠠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠚⠻⡒⢇⠛⢬⡑⠢⢄⠀⠀⠀⠈⠹⣟⠂⠀⠀ ⠉⠉⠻⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠙⢦⡈⠑⠀⠉⠢⢄⠀⠠⣿⠁⠀⠀ ⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠁⠀⢻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢾⡄⠀ ⠀⠀⣄⠀⠐⣦⡀⠀⠀⠀⠙⠦⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⠆⠀⠀⠀⢨⣷⠀ ⠀⠀⢻⣼⡇⣿⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣴⣀⣤⣴⠿⠛⠁⠀⠀⠀⠀⢸⣿⡆ ⠀⠀⠈⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⠉⠁⠀⠀⠀⢉⡀⠀⠀⠀⣀⡤⠤⠿⣿⠃ ⠀⠀⠀⠀⠘⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⢘⡄

⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠛⠉⠉⠛⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣸⣏⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠁⠉⣹⣆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢹⣏⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠈⢃⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣩⡭⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠛⠛⠉⠚⠛⠛⠒⠲⠶⠤⠤⠤⠤⠛⠓⠒⠛⢁⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠿⠛⠉⠉⠙⠲⢭⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⠟⠉⠁⢀⡤⠖⠲⣄⠀⣠⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠹⡟⣄⣙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⣀⣴⡾⠟⠧⠴⠋⠀⠀⠀⠙⢦⡀⢀⣼⡞⠋⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣾⣿⡿⢷⢿⣤⡙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢠⣿⢿⣿⣿⣿⢷⣦⡀⠀⠀⠀⣀⣤⢿⣋⣠⣇⡤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣿⣿⠟⠛⠻⣿⡿⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⡇⢠⡿⠁⣨⡶⠿⣾⡿⠟⣷⣤⡴⠟⠋⠀⠈⣠⡾⠋⣰⡿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⢸⡇⠀⠀⠀⠘⣷⢹⣿⡿⣦⡀⠀⠀⠀⠀⠀ ⡇⣼⡇⣸⡏⠀⠀⠈⣿⡄⣸⡇⠀⠀⢀⣠⡾⠋⠀⣼⣏⣴⡾⣿⠻⢶⣤⣄⡀⠀⠀⠀⠀⠀⣿⠉⠛⠻⢶⣦⣤⣤⣤⣤⣴⣶⣿⣿⡈⣿⣄⠀⠀⣰⣿⢸⣿⣧⣹⣷⣦⣄⠀⠀⠀ ⡇⣿⡀⢿⣇⠀⠀⢀⣿⢡⡿⠁⢀⣴⣾⠁⠀⠀⣼⡟⠛⢿⣄⢿⣆⣠⡾⢽⠻⢷⣦⣤⣤⣤⣿⣤⣤⣄⣀⠀⠀⠉⣽⢟⡄⢹⣯⣹⣷⣬⣟⠛⠛⠛⠁⠈⣿⡹⣧⣿⠈⢻⣧⣤⡀ ⣇⣿⣷⠈⠻⠷⠶⠿⣣⡿⢁⣴⠟⢹⢸⣀⣀⣼⡟⠀⠀⠀⢻⡎⢉⢙⣿⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠹⣏⠛⢿⡿⠋⡆⣼⠟⠛⣿⡉⠻⣷⣄⠀⠀⠀⢸⡇⢹⣿⠀⢠⡇⠈⢿ ⣿⣿⣿⠀⠀⠀⢠⣾⠏⠀⢸⡇⣠⣾⠿⠋⠙⡿⠁⠀⠀⠀⣸⡧⣿⡾⡟⠛⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠘⣷⠀⠃⢻⣦⣄⡙⣷⡀⠈⣿⡄⠀⠀⠈⣿⡀⣿⣦⡿⢃⡴⣾ ⣿⣼⡏⠀⠀⢠⡿⠁⠀⢀⣼⠿⢿⣦⣄⣠⣾⣷⡄⠀⢀⣴⡿⢠⡿⠁⠘⠢⡀⠀⠉⠉⠛⠛⠶⣤⣀⠀⢠⠎⠀⢀⡿⠁⠀⢀⣷⠉⢿⣜⣿⡄⠈⢿⣆⡀⣀⣿⠇⣸⡇⠀⢫⣾⠟ ⣿⣿⠁⠀⢀⣿⠃⣠⡾⠿⣥⣤⠆⠈⠉⠉⠁⠙⣻⡶⢿⡛⠀⠘⣷⡀⠀⠀⠙⠢⣄⠀⠀⠀⠀⣼⠟⣶⣾⣀⣤⣿⠃⠀⣰⠟⠁⣴⡾⠛⠛⢿⣦⡈⠙⠛⠛⠁⣠⡿⢁⣴⣟⠁⠀ ⡇⣿⣷⣶⣿⣿⠿⢿⣦⣤⣄⣀⠀⠀⠀⢀⣠⣾⢿⡇⠈⢠⡘⣦⠘⣿⠀⢠⡤⠤⠼⠗⠚⢁⣼⠃⠀⣀⣿⢹⡇⣿⡀⠀⠀⠀⡀⢿⡰⠞⠋⠉⠉⠻⠷⣶⣶⠾⣋⣴⡿⠋⠘⢧⣴ ⣧⡿⠀⠀⣤⣀⠀⠀⠀⠈⠉⢙⠛⠛⠛⠛⠋⣠⡿⠡⠞⢸⡇⠘⠃⣿⣇⣀⣀⣤⣤⠶⠶⠻⣷⠛⠋⠉⠁⠀⠻⣿⣧⢸⡀⢸⡁⠘⣷⣄⣀⣀⣤⣤⣶⢶⡿⠟⠋⠁⠀⣀⣴⠿⠁ ⡿⣷⡀⠀⠙⠛⢷⣦⣀⠀⠰⠃⠀⠀⠀⣀⣴⣿⣷⠀⠀⢸⡇⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣟⣛⡟⠛⠷⣤⣿⡆⢇⠀⠳⠼⣮⠉⠉⠹⣷⡀⠀⠀⠻⡀⢀⣠⡾⠟⢁⡼⠀ ⣿⢻⣿⣶⣄⡀⠀⠈⢛⠻⠶⠶⠶⠶⠛⠛⣽⠏⠹⣇⠀⢸⡇⢀⣿⠁⠀⠀⠀⣀⡤⠤⠒⠚⠉⢉⣉⣹⣏⣙⠒⣮⡿⠁⢸⡇⠀⠀⢿⡀⠀⠀⢸⡻⢷⣦⠶⠾⢟⠉⠀⠀⠀⢉⣽ ⡇⢸⣯⠀⠙⠻⣶⣤⣼⣀⣀⣀⣀⣤⣴⡾⠋⡆⠀⣿⡄⣸⠇⣸⡇⢠⠤⠒⠋⣉⣤⠤⣒⣶⣭⡽⠿⢾⣯⣍⣿⠟⠀⢀⣼⠇⠀⠀⢸⡇⠀⠀⠀⢣⡈⢻⣦⡀⠈⠓⢀⣤⡾⠟⠁ ⣷⠈⠿⣦⣴⡶⠟⠉⣩⡍⠉⠉⠉⠉⠀⢠⠟⣧⢀⣿⠁⠻⠀⣿⠃⠠⢶⣚⣽⠷⠟⠋⠉⠀⠀⠀⢸⠀⠀⢹⡇⠰⠶⠋⠁⠀⠀⢀⡾⠁⠀⠀⠀⠈⣇⠀⠙⢿⡿⠟⠋⠉⠀⠀⠀ ⡿⣧⠀⠀⣆⠀⢀⣼⠟⠀⠀⣀⣴⠷⣰⢏⡼⢁⡜⠋⠀⠀⣸⠟⠴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⣧⠀⠀⠀⠀⠀⢀⣸⡃⠀⠀⠀⠀⠀⠘⢦⣀⠈⢿⡄⠀⠀⠀⠀⠀ ⡇⢻⡇⠀⢻⣆⣛⣡⣤⡶⣿⡛⠡⠞⢁⡞⣤⡿⠃⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⡟⠀⣀⣴⠟⠃⣀⠀⠀⠈⠷⣄⡀⠀⠀⠀⠈⢣⡘⢿⡶⣶⣤⡀⠀ ⡇⢸⣧⣤⠀⠉⠛⣩⠟⠋⠉⠀⠀⢠⢞⣿⠏⠀⣀⣤⡾⣿⠃⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣀⠀⠀⠉⠀⣠⡿⠁⣀⣉⣀⠀⢠⡟⢷⡄⠀⠀⠈⠻⣦⡀⠀⢠⠀⢱⠀⠀⠀⠙⣷⡄ ⡇⠀⢻⣮⡃⠀⠀⠙⠒⠒⠦⠤⠖⢠⣿⠃⠀⠊⢉⡞⠁⣿⠀⠀⢰⡞⠛⠋⠉⠉⠉⠀⠀⠉⢷⡄⢀⣴⣿⠑⠋⠉⢩⠏⣰⡟⠀⠀⠻⣦⡀⠀⠀⠈⠙⠓⠘⡆⠈⣷⠀⠀⠀⢸⣷ ⡇⠀⠀⠉⠻⢷⣦⣄⣀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣼⡶⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿⠉⢻⣦⡀⠀⡇⣴⠟⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⢱⡀⠘⡆⠀⢀⣾⠿ ⡇⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠶⠶⠾⣿⠀⠀⠀⠧⠇⢸⡿⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⡀⠀⠙⣷⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀⡀⠈⢁⣀⠸⡄⢸⣿⠀ ⡇⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣤⣿⠃⠀⠀⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⣼⡀⢸⣇⠀⠀⢹⡇⠀⠙⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⠀⠀⣸⡉⢣⡀⠘⣿⠀

⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠐⠒⠀⠒⠒⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⢤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠢⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠊⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⡀⠠⡀⠀⠀⠀⠀ ⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢄⠀⠀⠀⠀⠈⠂⠈⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⢣⠀⡆⠀⠸⡀⠀⠈⡀⠑⡤⡀⠀⠀⠠⢂⠀⢢⠀⠀ ⠀⠀⠀⠀⠀⠀⡈⠀⢂⠘⠄⠀⠩⠒⢔⡘⠢⡈⠄⠁⠑⢀⠉⡗⠄⢣⠀ ⠀⠀⠀⠀⠆⠀⠧⠂⠈⠑⠈⢢⡀⠡⡀⢈⣱⣦⡽⠠⢀⠈⡄⠰⠈⢂⠆ ⠀⠀⢰⠀⡃⢰⠀⣠⣤⣤⡈⠑⢝⡒⢼⡛⠁⠀⠀⡆⠀⡆⢰⠀⠇⠀⠀ ⠀⠀⢼⠀⢇⢸⠛⠁⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⣀⠀⢰⠀⡆⢰⠀⠀ ⢀⡜⠈⡆⠸⣼⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠁⢸⠀⠀ ⠜⠀⡦⠸⠀⢫⠙⢅⠓⠒⠀⠀⡠⠤⢄⡲⠀⠀⢜⠜⠀⠘⢠⠸⢸⠀⠀ ⠀⠰⠁⠀⢃⠈⡱⡈⠢⢄⡀⠀⠈⠉⠀⠀⠀⣠⠂⡖⠀⡄⠀⢰⡌⠀⠀ ⠀⠀⠀⠀⠀⢢⠐⡈⢄⢃⢸⡗⠂⠤⠤⠴⠋⢸⠠⡡⢠⠁⢸⠜⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠁⠐⢄⢸⣸⠄⠀⠀⠀⠀⠀⢀⣦⡸⠆⡀⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⣳⣉⠐⠠⢈⡙⢕⠂⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠲⣿⣿⢿⠻⣷⣶⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⣀⣠⣷⣷⣶⡾⣿⣶⣝⣿⣿⣆⠈⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡿⠭⠽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣴⡾⠟⠛⡋⣉⣽⣿⡿⠈⠻⣿⣿⣿⣿⣧⡟⢻⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡀⠀⠈⠻⠥⢌⡙⠻⠿⠟⠋⠀⣀⠀⠙⢿⣌⢿⣿⡇⢰⣿⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⢧⣼⣿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣻⣶⣾⡷⣦⣄⣁⣀⣤⣤⣴⣾⣿⣿⣾⣳⣽⠿⠻⠃⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⠈⣿⣉⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢰⣿⡟⠉⠀⠀⠀⠙⠊⠻⣿⠿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠘⢷⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⣿⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢀⣠⣾⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠈⢿⣿⠷⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠉⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠺⢿⣿⠀⠀⠀⠀⣀⣤⣶⣶⣤⣤⣄⡟⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⡄⠻⡗⠀⠠⠾⢛⣭⣿⣿⡿⣿⠿⠃⠀⠀⣿⣿⢟⣛⠛⠁⣼⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠏⠁⠈⡇⠀⠀⠀⠀⢻⠛⠛⠳⢦⠀⠀⠀⠀⢸⢿⣿⣶⡇⠀⠀⠀⠛⠛⠉⣉⡤⠟⠀⠸⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⣷⠀⠀⠀⠀⠸⣦⠀⠀⠘⣧⣤⣤⡀⠸⣿⢹⠀⠱⣆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⢸⡙⣦⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣷⠖⠲⠲⠏⠀⠀⠀⠈⢧⣿⠋⠛⠲⣾⣧⣠⣽⣧⠹⣞⢦⠘⡟⢦⡀⠀⠀⠀⠀⠀⢀⣄⠐⠂⠀⠈⣿⢙⣷⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡟⣿⠀⠀⠀⣾⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠁⠀⠉⠙⣷⠈⠳⣄⣹⠈⢳⡀⠀⠀⠀⣴⡟⠈⠱⣶⣤⣰⣿⣿⣿⣷⣄⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠏⠀⢹⣦⠀⣼⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢦⣄⡀⣼⠀⠀⠀⠈⣇⠀⠈⠢⡀⢸⣿⣁⠀⢀⣀⣈⣛⣿⡿⠿⣷⡿⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠯⠀⠀⢸⡇⣤⡀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢠⣿⠀⠀⠀⢀⣾⣆⠀⠀⢻⡄⠙⠻⣿⣍⣉⣁⣀⣀⣤⣴⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠀⠀⠀⢸⡇⠘⡇⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣽⠀⢀⣴⣿⣿⠙⢦⡀⠀⠁⠀⠀⠙⢿⣿⠿⠿⠟⣻⠟⣽⠇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⡄⠀⠀⣾⠃⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢿⣶⣿⣿⣿⣿⡄⠀⠓⣄⠀⠀⠀⠀⠀⢸⣍⣉⣩⣥⣾⠏⠀⠀⣼⠇⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀⠀⠈⠳⣤⡀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⣸⣿⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢸⠀⣄⠀⠀⠘⢷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠈⠙⠒⠒⠒⠺⣯⣡⣤⡀⣻⣿⣿⣿⣦⣤⣘⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠻⣍⠢⠀⠀⠀⠀⠀⣠⣾⠛⠉⢙⣿⣿⣾⡟⣷⠈⠻⠁⠙⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⢷⣄⠀⠀⢀⣴⡿⣿⣿⣿⣉⣀⣉⠙⠻⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢴⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠻⣿⣮⣿⠟⠀⠀⠈⠻⢿⡿⠿⠿⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣟⠗⠀⠀⠀⠀⠀⠛⠁⣤⡾⠋⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⠛⠁⠀⠀⠀⠀⠀⠀⠙⢶⡶⢶⣿⡀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠆⠀⠀⠀⣀⣤⠴⠛⠉⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⠟⢉⣽⣤⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣿⣿⣷⠶⠒⠋⠉⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⡟⢁⣴⣿⡿⠛⢦⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠋ ⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠉⠁⠀⠀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣷⣿⡿⠋⢀⣴⣿⣧⠀⠀⠀⣿⣿⡿⠟⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠁⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⡤⠤⠤⠚⠛⠿⣅⣰⣿⣿⠟⢉⣇⣀⠠⠛⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠁⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣾⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡛⠦⣀⢀⣀⠤⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣫⣶⣿⣿⣿⣿⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠙⠻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⢻⣿⣿⣿⣮⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠞⣱⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣹⣿⣿⣿⣧⡈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⡇⠀⣿⢿⣿⣿⣿⣿⡄⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⢿⣿⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⣿⣿⣿⣿⢸⣿⣼⣿⣿⣿⣿⣯⢆⠘⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⣿⣿⡈⢿⣿⡼⣿⣿⣿⣿⣿⣿⢿⣧⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣯⢣⠘⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣷⣿⣿⣧⣿⣧⢹⡙⣿⣿⣿⣿⣿⣎⣻⣷⡈⢻⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣇⢧⠸⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⢿⣿⣿⢿⣿⣇⠻⣌⠻⡟⠉⢄⣠⣭⠈⠙⠀⠉⠻⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢃⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢧⢻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⢸⣿⣿⡞⠿⠟⠃⠉⠀⠀⠠⢺⡯⣮⣽⡛⠦⣤⡤⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⢛⠋⠛⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣮⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠘⣧⢿⣷⣄⡀⠀⠀⠀⠀⠀⠋⠀⣿⡟⢷⠀⠈⢹⠂⠀⣿⣿⣿⣿⣿⣿⣿⣧⣍⠑⠄⠈⢿⣻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⠀⠸⡌⢻⠾⣿⣦⠀⠀⠀⠀⠀⠀⠹⣷⣸⡇⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠈⢳⠀⡀⠘⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡷⠀⠹⣾⠀⠸⣿⣣⠀⠀⠀⠀⠀⠀⠹⣾⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⡼⠁⣸⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡆⠀⢸⣷⡄⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢸⣿⣿⣿⣿⣿⡧⠴⠃⣰⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⠀⢾⣿⣿⣦⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⣿⣿⣿⣿⣿⡇⠀⣴⣿⣿⣿⢀⣇⡿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀⠀ ⣧⣤⣄⡀⠀⠀⠀⠘⣇⡏⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣯⣿⣺⣿⣿⣿⣿⣼⡿⠁⢸⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⠀⠀ ⣿⣿⣯⣭⡉⠙⠲⠀⠘⣿⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⡏⣿⠀⢿⣿⣿⣧⣿⠇⡄⣿⠃⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢸⡀⠀ ⣿⣿⣿⣿⣿⣿⣆⠀⠀⢻⢹⣿⣿⣿⡻⡀⢀⣴⡶⠒⡆⠀⠀⠀⠀⠀⠀⢸⣯⠀⣿⣿⣿⣿⣧⣿⡇⢸⣟⣾⣿⣇⠀⣧⣿⠀⠈⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡌⡇⠀ ⣿⣿⣿⣿⣿⣿⣽⡆⠀⢸⠈⣿⣿⣿⣿⠙⢦⠻⣄⣠⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⣻⣿⣿⣿⣿⢸⡇⢼⣇⣸⣿⡏⠀⠸⣿⠀⠀⢹⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡇⠀ ⣿⣭⣛⠻⠟⢿⣿⡇⠀⢸⡴⠋⠉⠻⢿⣆⠈⠳⣌⠉⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⠟⣿⣿⢸⢸⡇⢸⣮⣿⣿⠃⠀⠀⢿⣶⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡀⠀ ⣿⠿⢿⣷⣄⠀⠹⢇⡴⠋⠀⣀⣤⣄⣀⢹⣆⠀⠙⣆⠀⠀⢀⣠⡴⠚⣯⣽⣿⠏⣿⠀⣿⣿⠈⢸⡇⠀⢿⣿⣿⣷⡶⣄⢸⣯⠀⠀⢸⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡇⠀ ⣿⡆⠀⠈⠻⡄⠀⢸⠀⠉⠉⠁⢀⣀⣈⣿⠉⡇⠀⠈⠉⢉⣡⣶⣿⣿⣿⣿⡇⡇⡿⢸⣿⣿⠀⢸⡇⠀⠸⣿⣿⣿⣿⣿⡄⢻⡇⠀⣸⡅⣸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣇⠀ ⣿⢿⣆⠀⠀⠁⠀⡏⠠⠖⠒⠉⠉⠀⠀⡏⠀⣇⣀⣤⣾⣿⣿⣿⣿⣿⡿⢻⡇⠀⠁⢸⣿⡏⢀⢸⡇⠀⠀⣽⣿⣿⣿⡟⣿⣿⢿⣆⣿⠥⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⠀ ⣿⣿⣿⡀⠀⠀⠀⡇⠀⠀⠀⣀⣀⠤⢤⢹⣾⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⢸⡇⠰⠀⣿⣿⡇⢸⢸⠀⣠⣾⣯⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣤⡙⢿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀ ⠈⣿⣯⠇⠀⢀⣴⡇⠀⠐⠉⠉⠀⢀⢸⣽⣿⣿⣿⣿⣿⣟⣁⠀⠀⠀⣰⠏⢠⠀⣷⣿⣿⡇⢸⣿⣾⣿⣿⣿⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢻⣿⣿⣿⣿⣿⣿⠀⠈⣿⡄ ⠐⠛⠁⠀⢠⣿⣿⡇⠀⠀⠠⠖⠚⡏⢀⣿⣿⣿⣿⣿⣿⣇⠈⠙⠒⠒⠁⠀⢼⡶⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⠀⠀⢽⡇ ⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⡷⣿⣻⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣀⣀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⠀⠀⢸⡇ ⠀⠀⠀⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⢧⠿⢻⣿⣿⢻⡟⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⠛⠻⢿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⠀⠀⠂⡇ ⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⣴⠏⠀⢾⡟⡿⢾⡇⠀⠀⠀⢀⣴⠟⠛⠏⠛⠩⣿⣿⣿⣿⠃⠀⠀⠀⠹⣷⣮⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡆⠀⠀⠇

⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣒⡲⢶⣶⣶⣶⡶⠶⠶⣶⡶⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄ ⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⣶⣶⣶⣶⣾⣶⣶⣶⣬⣿⣿⣶⠀⠀⠀⠀⠀⢰⣾⣥⣴⣶⣶⣶⣶⣶⣤⣄⡄⠀⠀⠀⠀⠈⣿ ⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⣿⣿⠿⠿⠛⠟⠿⢿⣿⣿⡟⠛⠀⠀⠀⡴⠀⠈⠙⣿⣿⣿⠿⠻⠛⠛⢿⣿⡟⠓⠂⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣴⣿⣟⣦⢤⠀⠀⠀⠀⠂⣾⣿⠃⠀⠀⠀⣸⡇⠀⠀⢠⣿⢿⡀⠀⠀⠀⢀⡤⡈⡇⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⣿⣿⡛⠛⠁⠀⠠⢄⠈⣻⣿⠄⠀⠀⠀⣿⣇⠀⠀⠘⣿⣿⡥⠀⡀⠀⠘⠛⢡⡿⠀⠀⠀⠀⠀⢾ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣾⣤⣘⣧⣼⣾⡿⢻⠀⠀⠀⠀⣹⣿⡁⠀⠀⠸⣿⣿⣷⣅⣤⣶⣿⡿⠛⠳⡀⠀⠀⠀⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠁⣀⡀⠀⢀⣿⣿⣷⡂⠀⠀⠈⣿⣿⣿⣿⣿⣿⡧⠒⠀⠀⠀⠀⢰⡟ ⡇⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠙⠿⣿⢷⣾⣿⡟⠋⢁⣀⣾⣟⢡⣶⣿⣿⣿⣿⣮⣭⣽⣵⣿⠋⠙⠛⠛⠉⢀⣀⠤⢄⡀⠀⢸⡇ ⣇⠀⠀⢀⡴⠟⠉⠈⠈⠉⠉⠂⠀⠀⠀⠀⢀⢙⣒⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⡙⡛⠿⣿⣟⣃⣶⣄⠀⠀⠀⠀⠀⠀⠀⠙⡄⣼⠀ ⢿⡄⠀⡾⠁⠀⠀⠀⠀⢀⣠⣴⠦⠶⢖⣛⣻⣻⣿⣿⣿⣿⣿⣿⣯⣭⣭⣉⣉⣛⣳⣿⣚⣚⣙⣛⣛⣻⣿⣿⣿⣶⣶⣶⣀⢀⡐⢹⣿⠀ ⠘⣷⡀⢇⠀⠀⠀⣾⣿⣿⣿⠫⠝⠛⠛⠛⠋⠉⠛⠻⠿⣿⣿⣿⣅⣤⣤⣴⣆⣨⣷⣧⣭⣭⣩⣤⣴⣶⡿⠟⠛⠉⠙⠿⣿⡾⣧⢸⡏⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣟⣩⡽⠹⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣾⡿⡿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣾⣻⡻⢽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⣾⣿⣿⣿⣿⣷⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣫⣵⡥⠀⠀⣀⠠⠤⣠⠀⠒⣨⢄⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡿⠇⠀⠈⢠⠚⣉⣉⡙⠒⠉⠀⡰⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⣟⣩⣿⣿⡀⠀⠀⢠⡾⠛⠛⣛⠁⠀⠠⡷⢶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⡿⣿⣿⣿⣿⠀⠀⠀⠈⢀⣴⠛⣿⠇⢦⠀⠳⡝⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣷⠋⠶⣭⠉⠟⠁⠀⠀⠀⠀⠉⠉⠚⠁⠀⠀⠀⠽⣄⠘⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡶⡰⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢲⣆⣤⣀⠞⢰⠃⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠙⢷⣜⠉⠀⠀⠀⠀⡄⠀⢤⣤⡶⠃⠀⠀⠈⢋⡔⡏⠀⠀⠀⢀⡀⠀⢸⣿ ⠀⠀⠀⠀⠙⠦⠞⡄⠀⠀⠘⢄⠘⠛⠘⠒⠲⠯⢉⣩⣿⠉⠉⠉⠉⠛⠙⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠈⠂⠀⠀⠀⠀⠀⠀⠉⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⣀⡀⠀⠀⠀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⢉⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀