Don't Know Don't Care Emojis & Text

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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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