Celestia from MLP Emojis & Text

Copy & Paste Celestia from MLP Emojis & Symbols 🎠👑📚🖋️🪄✨☀️🪻🌸🦋🌿🔭 | ⋆⁺₊⋆ ☀️ the holy sister

🎠👑📚🖋️🪄✨☀️🪻🌸🦋🌿🔭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠙⠢⡄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣴⠟⢠⣻⠀⢀⡤⠂⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠈⠳⣿⡆⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⣾⠏⠀⣼⣇⡔⠋⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡘⢗⠀⠀⠀⠻⣧⠀⠘⢦⣤⣄⠀⠀⠀⠀⠀⠀⣀⣀⠤⣄⣲⡾⠊⢣⠤⢥⣤⣼⢾⠇⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠈⠛⣿⣦⠀⠀⠈⠃⠀⢻⢻⠈⢦⠀⠀⢀⣔⠟⠀⢫⢡⡏⣾⢂⣎⢸⡎⢣⢔⣃⢀⠝⢿⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡦⡀⠈⠛⢵⡄⠀⠀⠀⠀⠻⠀⠈⣆⣾⡝⢡⠀⠀⣸⠎⠀⠎⢸⣿⢲⡗⠯⢠⠞⠉⠀⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢧⣄⠀⠀⠈⠀⠀⠀⣠⣀⠀⠀⡝⡱⡀⢸⣠⠞⡁⠀⠀⢀⣠⢽⠙⣒⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣍⠉⠻⣷⡄⠀⠀⠀⠀⢻⠀⠳⣼⠸⡀⢓⣯⣼⡔⠒⢢⠉⠉⠈⠑⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⠈⠙⠢⠀⠘⣏⠑⢧⠀⡞⠀⠉⠉⡏⡿⢷⣤⣀⠱⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⣌⢻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠘⢆⠀⠀⢣⠀⠀⡴⠀⢷⣠⣿⡿⡇⠀⠉⠒⠢⣤⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠑⠟⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣲⠶⠶⠯⣍⠓⢤⠀⠻⣅⠃⠀⠸⡀⠀⠳⠷⠈⠻⢞⣸⠋⠀⠀⠀⣴⡏⡇⠀⠀⠀⠀⠀⠀⠙⡈⠉⠒⠤⡀⠀⠀⢰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢊⠕⠊⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠈⠓⣄⠀⠳⡀⠀⡜⢄⠀⠀⠀⠀⠀⠀⠀⣧⠞⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢳⢄⠈⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⡔⠁⠈⠋⠀⡠⠚⠉⠀⠀⠈⠑⢞⠢⠀⠻⣄⠀⠀⠑⣄⢸⠀⠈⠓⢢⡀⡀⠀⠀⠟⡆⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⡎⠀⠃⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⡞⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⢀⣈⡳⣄⠀⠀⡑⠀⠀⠈⠻⡆⠀⠀⠀⠙⠓⠄⠒⠊⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⡴⠁⠀⢀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⢸⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡰⠁⠀⠘⢆⠑⠖⠕⠀⠀⠀⡞⣇⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⡦⠊⠀⠀⠀⡸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠘⡀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣨⡞⠉⠦⡀⠀⢠⠁⠸⠀⠀⠀⠀⠀⢸⢡⠀⠀⠀⠀⠀⢀⠞⠀⠀⢀⡤⠊⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢳⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⢰⡟⢲⢴⠧⣠⠀⢸⠄⠀⢣⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⢀⡆⠀⢀⠔⠁⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣼⡏⣿⣧⣰⡵⠆⠘⠀⢀⠀⠱⡄⠀⠀⡸⠀⢁⠀⠀⠀⢸⠀⡠⠋⠀⠀⠀⢀⣴⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠛⠉⠃⠀⠀⢷⠈⠂⠀⠈⠢⣠⠃⠀⡎⠀⠀⠀⠀⠟⠁⠀⠀⠀⡰⠋⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⣀⡴⠁⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠀⠀⠀⠈⢧⡀⠀⠐⢀⣯⠠⣱⠃⠀⠐⠒⢢⠀⠀⠀⠀⣴⠁⢀⡜⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠁⠀⠞⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢀⡿⣟⠢⣠⠀⠀⡱⡄⠀⢿⣿⢳⠃⠀⠀⠀⠀⢘⡆⠀⠀⠀⠘⣄⠉⠁⢙⡀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡏⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀⠀⠀⠀⠀⢠⠖⠋⠀⢀⡾⢡⠟⠀⠸⠀⠀⠱⠌⠷⡄⡱⣏⠁⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠙⠚⠉⠀⠀⠟⠻⢦⣄⠀⠀ ⠀⠀⠀⠀⢹⡄⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠏⠀⢀⡴⠋⠀⠀⡷⠀⠀⠀⠀⢠⡆⠀⣸⠃⠀⠀⢹⠀⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⠙⢷⡄ ⠀⠀⠀⠀⠈⠻⣦⣀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠏⠀⠀⡾⠁⠀⠀⣴⢷⡀⡆⠀⠀⠀⣇⣼⠃⠀⠀⠀⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⢰⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⣷ ⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠁⢢⠀⠀⠀⠀⢀⠆⠀⢰⠏⠀⠀⠀⠁⠀⣠⡾⠋⠘⡃⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⡎⠀⠀⠀⣴⠃⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟ ⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢀⠀⠀⠀⢀⠎⠀⢰⠏⠀⠀⠀⠀⠀⣰⢿⠖⡉⠙⠳⡆⠀⠀⠀⢿⠀⠀⠀⡀⣸⠁⠀⢀⠎⢸⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠁ ⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⡠⠋⠀⠀⢀⠎⠀⢠⠏⠀⢀⡀⠀⠀⠀⢿⡈⠉⢹⡆⢸⠀⠀⠀⠀⡇⠀⠀⡜⢡⡏⠀⣔⠚⠀⠸⠀⠀⡠⠊⠀⠀⠀⣀⣤⡴⠶⠚⠋⠉⠀⠀⠀ ⠀⠀⠀⢀⣴⠞⠉⠀⠀⢀⡤⠊⠀⠀⠀⠀⢸⠀⢠⡟⠀⡠⠊⡇⢀⠇⠀⠈⠛⠛⠛⠀⡇⠀⠀⠀⠀⡇⡀⠈⠀⡾⣄⠀⡗⠁⠀⡆⢀⠞⠁⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⠟⠁⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠈⢆⣾⠒⠺⠀⠀⠡⣼⠄⠀⠀⠀⠀⠀⠂⡏⠀⠀⠀⠀⣸⡰⡄⠀⠐⣄⠙⠚⠂⢠⡳⠃⠀⠀⣴⠏⠀⠀⠀⣠⣄⠶⠶⣤⡄⠀⠀⠀ ⢠⡟⠁⠀⠀⠀⠀⠋⠀⠀⣠⣶⣿⠯⣭⣉⠛⡗⣟⡇⠇⠀⠀⢶⡺⠀⠀⠀⠀⠀⠀⣀⣷⠀⠀⠀⠀⢹⠱⣇⠀⠀⠈⠓⢤⣠⡾⠁⠀⠀⠀⣿⡀⠀⠀⣮⠭⢦⡄⠀⠀⢻⡄⠀⠀ ⢾⠁⠀⠀⠀⠀⠀⢢⡀⠀⢿⡥⣤⡿⠀⢹⡆⢣⠘⠃⠀⠀⠀⠔⣧⡤⠤⢤⣤⡴⠟⡏⠉⣤⠀⢰⠚⠃⠀⡹⡄⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠷⣤⣀⣀⣠⣾⠃⠀⠀⣸⠇⠀⠀ ⠸⣧⡀⠀⠀⠀⠀⠀⠈⠉⠒⠉⠀⠀⢀⣼⠃⠘⢆⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⡇⣟⠀⠘⡡⠷⠀⢓⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢀⣴⠏⠀⠀⠀ ⠀⠈⠛⠶⣦⣤⠀⣀⣀⡀⠀⣠⣴⠶⠛⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠒⠤⠬⠀⠀⠘⠋⡷⢦⣄⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⢀⣀⠀⢀⣠⠃⠀⠉⠉⠛⠦⠶⢟⠶⠤⠤⠤⣖⠶⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀
⋆⁺₊⋆ ☀️ the holy sister of thy sun 👑 ⋆⁺₊⋆

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