Dynamite Emoji Combos

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢸⣿⣷⣄⠀⢿⣿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣄⠙⢿⣿⣧⠈⠻⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠻⣿⣿⣷⣄⡉⠋⢀⣀⡈⠙⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣦⡀⠈⠙⠛⠋⢀⣤⠈⢿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡷⠂⠀⠀⢻⣿⣷⣄⠙⠿⣿⣶⣄⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣴⣿⡄⠈⠻⣿⣿⣷⣦⠄⠀⠹⣧⠀ ⠀⠀⣀⡄⠀⠻⣿⣿⣿⣿⣿⡿⠋⢀⣴⣿⣿⣿⣿⣦⡀⠀⠉⠛⠁⠀⠀⢠⡿⠀ ⠀⣼⣿⣿⣦⡀⠈⠙⠻⠿⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣴⠟⠁⠀ ⠀⠘⢿⣿⣿⣿⣦⡤⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠙⠿⠿⠋⢀⣴⡄⠀⠹⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣄⠀⠈⠛⠿⠋⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠶⠶⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡇⠀⠈⠻⣿⡀⠀⠉⠻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠻⣦⡀⠀⠘⣷⣄⠀⠀⠙⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣄⠀⠀⠈⠻⢶⣴⡿⠿⢷⣦⣴⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠙⢿⣷⣦⣤⣴⡿⠛⣷⡀⠀⠈⠻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⡄⠀⠈⠻⣦⣀⠀⠉⠻⣿⣿ ⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⢻⣷⣄⠀⠀⠈⠙⣻⣿⣆⠘⣿ ⣿⣿⠿⢻⣿⣄⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠙⢿⣿⣶⣤⣾⣿⣿⡟⢀⣿ ⣿⠃⠀⠀⠙⢿⣷⣦⣄⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠋⣠⣾⣿ ⣿⣧⡀⠀⠀⠀⠙⢛⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⢁⣴⣿⣿⣿⣿ ⣿⣿⣿⣦⣀⣀⣴⡿⠋⢻⣿⣆⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠁⣴⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠻⣿⣷⣤⣀⣴⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣉⣉⣉⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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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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