Gym Dot Art

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⣿⣿⣿⣿⠏⠌⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠃⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠃⠀⠀⣾⣿⣿⣿⣿⣿⣦⠀⠈⠻⣿⣿⣿⣿ ⣿⠀⠀⠀⣿⣿⣿⠟⠉⠉⠉⢃⣤⠀⠈⢿⣿⣿ ⣿⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⢹⣿⣧⠀⠀⠙⣿ ⣿⡆⠀⠀⠈⠻⡅⠀⠀⠀⠀⣸⣿⠿⠇⠀⠀⢸ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠁⠀⠀⠀⣠⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿ ⣿⣿⡇⠀We Go Jim ⣠⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿ ⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿ ⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀ (\ __ /) (UwU) _ノ ヽ ノ\_ / `/ ⌒Y⌒ Y  \ (  (三ヽ人  /   | | ノ⌒\  ̄ ̄ヽ  ノ ヽ___>、__/ |( 王 ノ〈 /ミ`ー―彡\ |╰ ╯ | | /\ | | / \ | | / \ |
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣆⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣼⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠋⠻⠶⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⢻⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⡛⠛⢿⣶⣶⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣼⠤⡘⠣⠤⢊⣿⣿⡄⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡃⠀⠐⠀⠀⢸⡇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣼⣿⣿⣟⠀⠀⠀⠀⠀⠘⣦⡀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⡀⠀⠰⣤⣼⡇⢀⠀⠀⠀⣶⣾⣶⣷⣶⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣷⣌⢷⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣷⡄⠙⠟⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢨⣿⣿⡷⣄⣽⡖ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⢣⡀⠀⠀⠀⠀⠀⣰⠀⠉⠐⢿⡏⣽⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠠⢩⣁⣴⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⠁⠀⠀⠀⠀⠀⠙⠀⠀⡀⢀⣼⣿⣿⢯⠄⠀⣠⣀⣴⣿⣦⣖⣶⣿⣿⣿⡟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠉⠡⠀⢀⢰⣽⠟⣻⣿⣵⣿⣿⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⣾⣾⣿⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣟⣶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠁⡀⠀⢶⣄⣼⠷⡀⠀⠀⠿⣿⡿⣿⣿⣟⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⡏⠉⠂⠀⠉⠀⠀⠐⠂⢀⣠⣾⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣹⣶⠞⠂⠀⡞⡆⠰⠶⣬⣿⣯⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣦⣼⣧⣦⣤⣠⣼⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣯⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⣉⡘⠿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣾⠿⣡⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀ (\__/)⠀⠀⠀⠀⠀ ⠀⠀⠀⠀ (•ㅅ•)⠀⠀my gf telling the waitress ⠀_ ノヽ⠀ノ\_⠀⠀my food is wrong /⠀️⠀Y⠀⌒Y⌒⠀Y⠀️ヽ (⠀️⠀️⠀️(三ヽ人⠀⠀/⠀ ⠀| |⠀️⠀️⠀️ノ⠀¯¯\⠀ ̄ ̄ヽ ノ ヽ___⠀⠀>、__/ ⠀⠀⠀|(⠀王⠀)〈⠀⠀ (\__/) ⠀⠀⠀/⠀ミ`——彡⠀\ (•ㅅ•) me
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡄⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⣧⣼⣿⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⣿⠿⢿⠻⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⠿⠢⠄⠁⠀⣬⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢀⠠⠧⠄⠈⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⠀⠀⣀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠉⠠⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠉⠑⠀⠲⣤⠤⠘⠉⡁⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⡀⠀⡄⠀⠰⠀⠀⠀⢹⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢲⢧⣠⣀⣀⠴⢄⣀⣤⣆⠘⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠎⡾⣄⣀⣀⣴⠒⢄⣀⣿⠀⢺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢰⣷⣖⠁⠁⢈⡀⠣⣾⢻⣄⡜⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⢳⢉⡏⠃⠠⡀⠀⡏⠉⣼⠸⠙⡀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢰⠟⣄⢰⠈⢹⠉⢰⣿⣆⡆⠱⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡤⡔⠊⠉⡱⢆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡞⠀⠈⠳⡶⢼⠤⡿⠁⠘⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀ ⢀⡔⢺⠁⠀⡇⠀⠀⢷⠈⢣⠀⠀⠀⠀⠀⢀⣼⢦⣼⣁⣀⠤⠤⠷⠤⠼⠥⠤⢤⣻⣟⣻⡀⠀⠀⠀⠀⠀⡴⠋⠀⢸⠈⠹⠒⢄⡀⠀⠀ ⢻⠀⢸⠀⠀⢧⠀⠀⠸⣷⡞⢧⢀⡠⠤⠒⠛⣿⡓⣛⣧⣤⠒⡶⢶⣲⡶⠒⠶⣶⠏⠨⣹⣗⠒⠢⠤⣀⡎⠀⠀⠀⡘⠀⢠⠀⠈⡏⢳⡄ ⢸⠀⠀⡆⠀⠸⡄⠀⠀⢣⣤⠊⢁⡠⠤⠒⠉⠻⢿⡿⠋⠋⠐⡅⠀⣿⠀⠀⠰⠉⠚⣿⠋⠀⠉⠑⠢⡤⣉⣲⠀⢠⠃⠀⡜⠀⢠⠀⠸⢸ ⠀⡆⠀⢹⡀⠀⢳⠀⠀⠈⢏⠋⢳⠀⠀⠀⠀⠀⠸⣇⢄⡖⠀⢸⢸⢿⠰⠀⠀⡟⢰⠇⠀⠀⠀⠀⣸⠀⠀⠀⣰⠏⠀⣰⠃⢀⡎⢀⠇⡸ ⡀⠹⡄⠀⢷⠀⠀⢧⠀⠀⠈⡆⠀⡇⠀⠀⠀⠀⠀⢹⡟⠑⢤⣾⠋⠀⢳⣀⠘⠙⠇⠀⠀⠀⠀⠀⡟⠀⢀⣼⠋⠀⡰⠃⠀⡜⠀⡜⢀⠃ ⢣⡀⢹⣆⡀⢳⣀⠀⠳⣄⡀⠘⢦⡕⠀⠀⠀⠀⠀⢸⡇⠀⠀⢳⠀⠀⣼⠉⠀⢸⡆⠀⠀⠀⠀⠀⠺⣶⡚⠁⣠⠖⠁⣠⠎⢀⡜⣠⠊⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡖⠺⠉⠓⠢⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢞⣿⣿⣭⣟⣯⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣅⠉⠀⢻⣦⠀⡀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣿⡿⣿⣿⣿⢟⣿⣿⠟⢿⡀⠀⠀⠀⠀⠀⠀⠀⢟⣿⣾⣿⣿⣿⣇⠀⢡⠘⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣿⣻⡿⠁⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠁⢻⠈⡆⢳⡈⢳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣽⣿⡏⠀⠐⠾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠟⢰⡥⠀⢝⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡘⠃⠀⠀⠀⠀⠙⢁⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢣⠞⣀⢇⠈⠱⠚⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣻⣿⣿⣿⡅⠀⠀⠀⢦⣬⡇⠀⠀⠀⠀⠀⠀⠀⢠⠚⡏⠉⠑⢺⡄⠀⠀⠙⣧⡀⠇⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣷⠈⠉⠙⠛⠿⢿⣷⣦⣄⢰⣾⠖⣊⣉⡩⠍⢉⠓⠶⣿⢁⠜⢇⠁⢀⣹⣷⣤⣤⣈⣇⠀⣸⢧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢛⡇⠉⠀⠀⡀⢀⡀⠀⠀⠉⢙⡏⠁⠀⢹⣇⡀⠙⣏⠢⡌⡉⠉⣒⡷⠚⠉⠉⢻⣿⣿⣿⣵⣾⣷⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⢀⣼⠋⣿⡅⠀⠀⠀⠀⠈⠉⠓⣦⡨⠀⡀⠀⠀⢈⣉⡒⠒⣶⡶⠂⠉⠀⠠⣤⣴⣶⣾⣿⣿⠿⠛⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠙⠋⠉⢸⣥⡤⠜⠋⢤⣦⢤⣤⣴⡾⠟⠁⠀⠙⢒⣫⣥⣴⣶⣿⣏⠀⠉⠛⠿⢿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡤⠚⠙⣷⣿⣦⡀⠀⢨⡏⠀⠀⠀⠀⠀⠀⠀⣩⠀⠀⠀⠉⠉⠉⢉⡛⢻⣿⣿⣿⣷⣶⣶⣶⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠏⢀⠀⠀⣖⠈⠁⠉⠙⢻⣷⣄⣀⣤⣤⡴⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⢰⡟⠀⠀⣿⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣴⠟⠁⢿⣄⣀⡀⠀⣀⣤⣶⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠀⢸⡁⠀⠀⠸⣿⣄⠀⡀⣿⠀⠀⡠⣶⡷⠋⡀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠃⠈⠑⡿⢸⣯⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠇⠀⠘⣿⣦⣤⣤⣿⡟⠛⠓⢿⣞⠻⠟⣔⠲⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⣾⣺⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⣿⣿⠉⠛⠿⢦⣄⡠⠘⡆⣀⣤⠀⠀⠀⢐⣮⠗⠃⠋⠛⠛⠛⠛⠛⢻⣿⡿⡍⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠭⠌⣧⢾⣧⣤⣾⣦⠥⢠⣀⣀⢄⣠⣦⣶⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⣀⣴⣿⣿⣿⣿⣦⡂⠀⠀⠀⣾⣙⡇⠀⠀⠀⠀⠀⠀⠁⠀⣡⣿⣿⣿⣿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡿⢋⣡⣾⣿⣿⣟⣻⠿⣿⠷⣤⣿⣿⣇⠀⠀⠀⠀⠀⠠⣀⣿⣿⣿⠛⠛⠻⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡟⣻⣿⣿⣿⣿⣿⣼⡏⠀⠈⠑⢤⣹⡿⣿⣯⠻⢿⣿⣿⣿⣽⠿⢟⣃⣀⣀⡨⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣾⠁⠀⠈⢹⣿⣿⠟⠀⠀⠀⠀⠀⠈⠛⢾⣿⡆⣶⣿⣿⠗⠒⢉⣉⣉⣙⣛⢿⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⠀⠀⢷⡀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣿⣿⣷⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠿⣄⠀⣸⣿⣄⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⣉⣉⣉⣉⣿⣏⣉⣉⣉⣉⣉⣉⣙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢷⣌⠧⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣟⣏⣿⣷⡇⢸⣿⣿⣿⣿⣿⠆⣿⠀⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠏⠌⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠃⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠃⠀⠀⣾⣿⣿⣿⣿⣿⣦⠀⠈⠻⣿⣿⣿⣿ ⣿⠀⠀⠀⣿⣿⣿⠟⠉⠉⠉⢃⣤⠀⠈⢿⣿⣿ ⣿⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⢹⣿⣧⠀⠀⠙⣿ ⣿⡆⠀⠀⠈⠻⡅⠀⠀⠀⠀⣸⣿⠿⠇⠀⠀⢸ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠁⠀⠀⠀⣠⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿ ⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿ ⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
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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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