Hot Dog Face Emojis & Text

Copy & Paste Hot Dog Face Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⢀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⢀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠉⠈⠁⠂⠂⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⠀⠀⠀⠀⠀ ⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠇⠀⠐⢎⡅⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀ ⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⠂⠌⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⠳⠢⡀⠀ ⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠙⡄ ⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠹⡀⠀⠀⠀⡇ ⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡃⠀⠀⠀⡇ ⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⢳ ⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⡀⠀⠀⢸ ⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢣⠀⠀⢘ ⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⣇⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⡜ ⠀⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⣇⡧⣀⣀⣀⣀⣀⣀⣀⡠⠊⠀⠀⡅⠀⠀⡅ ⠀⠀⠀⠁⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⡀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢀⠜⠁ ⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠂⠤⢄⣈⡁⠉⠉⠈⠉⠉⢁⡄⠆⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠢⠄⢄⢀⡀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠁⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⢀⢀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡠⠂⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠁⠒⠄⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠈⡆⠀⠀⠀⠀ ⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡇⢀⠀⠀⢸⡏⡇⠁⠀⠀⠀⠈⡄⡀⠀⠀ ⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⣀⣀⣁⡇⡀⠀ ⢀⠇⠀⠀⠀⠀⠀⠀⡠⡒⠉⠉⠉⠉⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢐⠉⠱⡀ ⡏⠀⠀⠀⠀⠀⠀⡊⠀⢇⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⡎⠀⠀⢱ ⡇⠀⠀⠀⠀⠀⡊⠀⠀⠈⡆⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢀⡇⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠅⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠈⠓⠆⠤⠤⠤⠤⠏⠀⠀⠀⠀⠀⡎⠀⠀⠀⢸ ⡃⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢀⠎ ⠩⡀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠀⠀⠑⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠞⠁⠀⠀⠀⡠⢻⠁ ⠀⢇⡀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⡠⠊⠀⢸⠀ ⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠁⠃⢄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠊⠁⠀⢀⡇⠀ ⠀⠀⠀⠘⠤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢈⢦⣀⣀⣀⣀⣀⣀⣀⡄⠔⠊⠁⠀⠀⠀⡠⠋⠀⠀ ⠀⠀⠀⠀⠀⠉⠂⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠔⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠉⠈⠁⠁⠉⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

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⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠒⠒⠒⠒⠲⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠉⠛⠦⣄⠀⠀⠀⠀ ⠀⠀⣴⡯⠲⡀⠀⠀⠀⠀⡠⠒⠉⠁⠀⠀⠈⠉⠐⠢⣄⠀⠈⠳⣄⠀⠀ ⠀⣼⠋⠀⠀⠘⠦⣀⠀⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠘⣆⠀ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠸⡆ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡇ ⢸⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡇ ⠈⡇⠔⠉⠀⠀⠈⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢠⠇ ⠀⡇⢀⠔⠈⠀⠉⢂⠀⠀⠈⠂⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡜⠀ ⠀⡇⡾⢶⠤⣤⣄⣀⠆⠀⠀⠠⠋⣐⠂⠭⠅⡒⠄⠀⠀⠀⢸⠀⡼⠒⡄ ⢰⠃⠑⠄⢓⣽⠥⠞⠀⠀⠀⢋⡫⡻⠿⣟⠟⢺⠀⠀⠀⠀⠈⠌⡜⢁⡇ ⢸⡀⠀⠀⠀⠀⠀⡔⠒⠒⡄⠀⠈⠈⠛⠒⠂⠁⠀⠀⠀⠀⠀⠀⢌⡽⠁ ⠀⢷⠀⠀⠀⠀⠀⠀⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠉⠉⠀⠀ ⠀⠈⠳⣄⡀⠀⠀⠀⠤⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠓⠲⠤⣄⣀⣀⣀⣀⣀⣀⡠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆。˚˙✧˖°📷 ༘ ⋆。˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧。⋆🌻⋆。‧˚⛷🧚‍♀️🛖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠞⠻⢷⡿⣏⡛⠲⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠛⠉⠉⠉⠓⢤⡙⠆⠑⢀⣀⡬⠿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠥⠒⠚⠉⠉⠓⠲⢄⠑⠄⠀⣨⡶⠿⣿⡯⢿⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⢀⣀⠤⠤⢤⣀⠀⠀⠀⠃⢀⣾⣍⣉⠉⠲⢄⠐⢌⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢁⠴⠚⠁⠀⢀⣠⣤⣀⠙⢦⠀⠀⠈⠀⠀⠈⠑⠦⠀⠳⡀⠑⢄⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⡔⠁⠀⠀⢀⠔⣡⣾⣿⣉⣦⠀⢀⡈⠉⠑⠦⡀⠀⠀⠀⠀⠙⡄⠈⠣⡈⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠋⠀⠀⠀⡠⢃⡴⠋⠁⠀⠁⠉⠉⠉⠙⢣⡀⠀⠈⢳⣄⠀⠀⠀⠘⢆⠀⠑⡜⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⡴⢁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠙⣷⡀⠀⠀⠈⢆⠀⠘⣾⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⡜⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠈⢷⡀⠀⠀⠈⢆⠀⠸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⡼⠁⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠳⡀⠀⠀⠘⡆⠀⢻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⠁⢀⣿⢠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣦⠀⠀⠘⣄⠀⠀⠸⡀⠸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⠇⠀⡼⣿⠀⢀⣠⣤⣤⣭⠉⠛⠀⠀⠀⠀⠘⠋⢉⣥⣤⣬⢷⣄⠀⠈⣆⠀⠀⢇⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡼⠀⢠⠃⣿⠶⣿⡻⣿⣿⣿⠷⠀⢠⠀⠀⠀⠀⢸⣿⣿⣿⣟⣿⡿⢦⡀⠘⡄⠀⢸⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⠇⠀⡎⠀⣿⠄⠀⠉⠛⠛⠉⠁⠀⠘⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁⠀⠈⣷⡀⢱⠀⠀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⣸⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢳⠈⡆⠀⣷⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠇⢠⠇⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡇⠀⠀⡇⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⡞⠀⢰⣿⠃⣇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⢰⠃⡇⠀⠀⢸⠀⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣸⠁⢀⣾⡏⢸⣿⡀⠀⠀⠀⠀⠀⣠⠔⠢⠤⠒⢄⡀⠀⠀⠀⠀⠀⣼⡆⢇⠀⠀⢸⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⠃⠀⣼⣿⠀⣿⠁⣷⡀⠀⠀⠀⠺⡗⠈⠉⠉⠉⠘⡿⠀⠀⠀⠀⣼⡇⣧⢸⡀⠀⠸⡄⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⢡⠏⠀⡸⢹⠇⣸⡏⠀⡜⢿⢦⡀⠀⠀⠈⠒⢲⠶⠒⠋⠀⠀⠀⣠⣾⠁⡇⢸⣧⢳⡀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣷⠏⠀⢠⠃⣼⢠⣿⠀⠀⡇⣸⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⡏⠀⡇⠘⡏⢷⡷⡄⢻⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⡎⠀⣿⣾⠃⠀⢸⠁⣿⡆⠀⠀⠈⠓⠢⠤⠤⠴⠒⠉⠀⠀⢠⡇⠀⡇⠀⡇⠀⠻⡜⢾⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡟⠁⠀⠀⢸⠁⠀⣿⡏⠀⢀⠇⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⡇⠀⡇⠀⠀⠹⡎⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠟⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⡜⢀⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢹⡀⢳⠀⠀⠀⢻⡸⡇⠀⠀⠀⠀⠀ ⠀⠀⣰⢿⠀⠀⠀⠀⢀⣾⡇⠀⣿⠀⢰⠁⣸⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣧⡘⣆⠀⠀⠘⡇⢻⡄⠀⠀⠀⠀ ⠀⢰⡏⠈⣆⠀⠀⣠⡎⣹⢻⡄⠹⣦⡼⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠺⠦⢄⣸⣁⣀⣻⣄⡀⠀⠀ ⠀⡿⣄⠀⠈⢑⡸⠋⣰⡟⠋⠻⣦⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒ ⢸⠃⠀⠉⣉⣡⡤⠾⠋⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠤⠤⢀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡷⣦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠆⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠙⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠹⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⣤⣴⣶⣶⣾⣟⠟⠀⠀⠠⠃⢠⠎⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠑⣟⢿⣷⣶⣶⣶⣤⣤⣀⠀ ⠀⠸⣿⣿⣿⣿⣿⡿⢻⠋⠀⠀⠀⠁⡰⠃⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⡀⠀⠀⠀⠈⢺⠛⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⢿⣿⣿⣿⡿⢳⠃⢀⡀⠀⠀⡼⠁⠠⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠑⠄⠀⠳⡛⢿⣿⣿⣿⡟⠀ ⠀⠀⢸⣿⣿⣿⣤⡇⠃⠀⠀⠀⢰⠃⠀⢡⡎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡄⠀⠀⠀⠀⢱⢸⣿⣿⣿⠃⠀ ⠀⠀⠀⣿⣿⢫⡟⠸⠀⠀⠀⠀⡏⠀⠀⡎⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⣄⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⢦⠀⠀⢫⡹⣿⡟⠀⠀ ⠀⠀⠀⢸⣿⣿⠁⣏⠀⠀⠀⢸⠁⠀⡸⠀⠀⣼⠟⡇⠀⠀⠀⠀⠀⠀⠘⣼⡆⠀⠀⠈⣧⠀⠀⠀⠀⠀⠘⡆⠀⠀⢧⠀⠀⢻⣿⠃⠀⠀ ⠀⠀⠀⠀⣿⠇⠀⠮⠀⠀⠀⡏⠀⠀⡇⠀⡰⠧⠤⠼⡀⢰⠀⠀⠀⠀⠀⠸⣿⣦⠀⠀⠘⣧⡀⠀⠀⠀⠀⠹⡀⠀⠸⡄⠀⠈⢿⣄⠀⠀ ⠀⠀⠀⢠⡟⡄⠀⡳⠀⠀⢰⠇⠀⣼⠁⡰⢁⣀⣀⠀⠹⡄⢣⠀⠀⠀⠀⠀⠙⣌⠛⠦⡀⠱⡙⢦⡀⠀⢣⠀⢣⠀⠀⢇⠀⠈⢏⣏⠛⢖ ⠀⠀⢠⢳⠃⡇⠀⢑⠀⠀⢸⠀⡜⢉⣦⣯⡵⠶⢦⣌⠐⠜⢄⠳⣄⡀⠀⠀⠀⠈⢲⣈⣭⣵⣿⣑⠳⣄⠈⡇⠘⡆⠀⢸⠀⠀⢸⠘⡆⠀ ⠀⣠⠃⡞⠀⢱⠀⢸⠀⠀⢸⡜⢠⣿⠟⢁⠐⢿⣷⣌⢳⡀⠀⠑⠸⠯⠉⠑⠒⢢⡟⠁⠘⣿⣶⡍⠻⣬⡷⣧⠀⢳⠀⠨⡄⠀⢈⠆⢹⡀ ⡜⠁⣼⠇⠀⠈⡆⠈⡆⠀⢸⠐⣾⠃⠀⣿⡖⣶⡽⣿⠀⣧⠀⠀⠀⠀⠀⠀⠀⣾⠀⣷⣶⣷⣹⣿⠀⢹⡾⢾⢀⣾⡀⠀⡇⠀⢸⠀⠀⢣ ⣠⡾⢼⡁⠀⠀⠹⡄⢱⠀⢸⠐⣻⠀⠀⣿⣏⣿⣧⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⢿⣿⢿⣻⠀⠀⡷⠞⠉⣯⡇⢀⡇⠀⣸⠀⠀⠘ ⣿⡝⣾⠀⠀⠀⠀⢳⠈⢇⠸⡀⠹⡄⠀⠘⢇⣐⡨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣔⣂⡸⠃⠀⢸⠓⠂⢰⢿⡇⢰⠀⢀⡇⠀⠀⠀ ⣷⣛⣼⠀⠀⠀⠀⠀⠣⡈⢆⢇⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠋⠁⢀⡷⢫⣗⡸⠀⡼⠀⠀⠀⠀ ⢷⣝⣾⡄⠀⠀⠀⠀⠀⠑⣌⢾⡀⠀⠀⠀⠀⠀⠀⣠⡖⠒⠒⠒⠒⠒⠒⠒⠒⠦⠤⣄⠀⠀⠁⠁⠀⠀⠀⡜⠛⣫⣷⠃⡼⠁⠀⠀⠀⠀ ⠸⣿⣸⣇⠀⠀⠀⠀⠀⠀⠀⢣⣇⠀⠀⠀⠀⠀⢸⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⡇⠀⠀⠀⠀⠀⢸⣧⢿⢿⡟⡸⠃⠀⠀⠀⠀⢀ ⣧⠘⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⢠⡿⣼⡹⣾⡟⠁⠀⠀⠀⠀⠀⢸ ⠈⠁⠈⠻⡽⡄⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠓⢦⡀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⢀⣴⣟⡳⢧⣻⡽⠀⠀⠀⠀⠀⠀⢀⡯ ⣿⣶⣤⣄⣹⡽⣆⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠚⠉⠀⠀⠀⢀⣠⣴⢯⡳⣞⣿⣷⣹⡇⠀⠀⠀⠀⠀⢀⣾⢳ ⣿⣿⣿⣿⣿⣿⣯⠷⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣒⣦⢤⣤⣠⣀⣄⣠⣤⣤⣴⣶⢻⡽⣻⣮⣗⣻⢼⣻⡟⢾⡇⠀⠀⠀⠀⢀⡾⣭⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣽⣳⢦⣀⠀⠀⠀⠀⠀⠹⡏⠁⠉⠓⠦⣉⡉⠛⣙⣩⠵⢚⠩⠳⣽⣽⣼⣿⣾⣷⣷⣿⣿⠆⠀⠀⠀⣠⣾⣻⣾⣿
●█▀█▄つε�🡈🝑🄤🡈🝑�⣿⣼⢃⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡘⣷⣿⣿⣿ ⣿⣿⢐⡾⣶⣤⣤⣴⢰⣵⣭⣭⣭⣭⣬⣶⣷⠂⣿⣿⣿ ⣿⣿⢣⡿⣿⣿⣾⢰⡀⣦⣷⣿⣿⣿⣿⣿⢿⠙⣄⣧⣿ ⣿⢶⡋⢟⠿⠾⠃⠟⠿⠿⠿⠿⡛⣟⣿⣿⣿⣿⠜⡠⣿ ⣼⡟⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⡏⣿ ⠐⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢀⠄⡏⣿ ⠝⡎⣿⣿⣿⢻⣆⣿⣿⣿⣿⣿⣿⣶⣤⣀⠄⠄⡟⣿⣿ ⣿⠻⡘⣤⣤⣤⢤⡄⣤⣤⣤⣠⠄⠄⠄⠄⠄⠃⣿⣿⣿ ⣿⣿⣿⣿⠻⠛⠐⠄⠄⠄⠄⠄⠄⠁⠉⠛⠹⡷⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢿⡸⣧⣿⡽⣿⣿⣿⣿⣿⣾⠅⣛⣽⣯ ⣿⣿⣿⣿⣿⣿⣿⠐⡤⣶⣤⣶⣶⣶⣶⣼⢏⣿⣿⣸⡞ ⣿⣿⣿⣿⣿⣾⣓⢇⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣧⡹ ⣿⣿⣿⣿⣿⢸⠼⠤⠤⠤⠦⠓⠄⣿⣿⣿⣿⣿⣳⣿⡿ ⣿⣿⣿⣿⣿⠸⢀⠄⠄⠄⠄⡄⠘⣽⣿⣿⣿⣼⣿⣿⣿ ⣿⣿⣿⣿⣿⢸⠈⠄⠄⠄⠄⠄⢸⣧⣿⣿⣿⣭⣿⣿⣿ ⣿⣿⣿⣿⣿⣯⢹⠈⠄⠄⠄⢀⢄⡙⣭⣻⢸⣟⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣾⢀⠄⠧⠄⡇⣿⣻⠟⣻⢀⡇⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢈⠄⠃⢛⠄⡇⣾⣿⣕⣤⠰⠄⣶⣿⣿ ⣿⣿⣿⣿⣿⣿⢀⠄⠄⣶⠠⡀⡐⠃⠠⡀⢀⠄⡇⣿⣿ ⣿⣿⣿⣿⣿⣿⠠⠄⠄⠄⠄⠄⠄⠄⠐⠄⠄⠄⡇⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠁⡟⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢿⠛⠉⠄⠄⠁⠄⠉⠛⠛⣿⣿⣿⣿

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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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⠀⠀⣠⣶⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣶⣄⠀⠀ ⠀⣾⣿⡿⠋⠉⠉⠙⠻⣿⣿⣷⣄⣠⣾⣿⣿⠟⠋⢉⡉⠙⢿⣿⣷⠀ ⢸⣿⣿⠀⢠⣤⣤⣤⠀⠀⠙⣿⣿⣿⣿⠋⠀⠀⣤⣼⣧⡄⠀⣿⣿⡇ ⠘⣿⣿⡄⠈⠉⠉⠉⠀⣀⣴⣿⣿⣿⣿⣦⣀⠀⠉⠹⠏⠁⢠⣿⣿⠃ ⠀⠹⣿⣿⣷⣦⣤⣶⣿⣿⣿⠟⠁⠈⠻⣿⣿⣿⣶⣤⣴⣾⣿⣿⠏⠀ ⠀⠀⠈⠙⠛⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠛⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⣿⣿⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⣄⠀⠀⢸⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⢿⣿⣧⡀⠈⣿⣿⣇ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⣄⡀⠀⠻⣿⣿⣦⠸⠟⠛ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣷⣤⣈⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣶⣶⣦⣤⣀⣙⡻⢿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⢠⣤⡄⠀⣿⣿⣿⣿⣿⣷⣶⣶⣿⠀⣤⣤⡄⠀⠀⠀ ⢸⣿⡇⠀⣉⣉⣉⣉⣉⣛⣛⣛⣟⠀⣿⣿⡇⠀⠀⠀ ⢸⣿⡇⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⣿⣿⡇⠀⠀⠀ ⢸⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⡇⠀⠀⠀ ⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠉⠉⠛⠿⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⣀⣴⣾⣿⠿⠛⠉⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⢿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠁⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠈⠻⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠐⠲⢼⡏⠀⠈⠟⠻⢷⣄⣀⣀⣸⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣸⠟⠛⠛⠛⠛⠛⣿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠻⣧⣴⣶⡛⠉⠙⠲⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⢿⣦⡀⠀⠀⢀⣴⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⡿⠋⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣳⡄⠀⠀⠀⠀ ⠀⠀⢀⣼⣟⡼⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠉⠻⣿⡄⠀⠀⠀ ⠀⠀⣾⡿⠋⢠⠛⣿⣧⠀⠀⠀⠀⠀⣾⠟⠛⠛⠉⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠉⠉⠛⢿⡿⣿⣦⠀⠀⠀⢀⣼⣿⢿⡀⢢⡈⢳⡄⠀⠀ ⠀⣼⠟⢀⣠⢇⡼⠛⢿⣷⣄⣀⡀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠈⣿⠀⣤⣤⣾⣿⣏⠀⣻⣆⠻⡷⣿⡆⠀ ⠘⣿⢻⠋⢁⡾⢷⣤⡾⢻⣿⣿⣥⣀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢠⠖⠛⠛⢶⡀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠸⣿⣤⣿⣿⣿⡁⠉⢻⣿⡙⢷⣄⣼⡇⠀ ⢸⡿⢶⡶⠋⢠⡟⠀⣠⡿⢻⣿⠿⣿⡟⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠘⠲⠦⠶⠛⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⢹⡟⢿⣦⣀⣿⢷⣄⢸⡍⣷⠀ ⢸⡇⢸⣷⣴⡿⣦⣼⠋⣀⣼⣧⣴⡿⠀⠀⠀⠀⠀⠀⢠⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣆⠀⠀⠀⠀⠀⠀⠀⣿⣷⣼⣧⣄⣽⣿⡇⠸⣹⡟⡇⢸⡆ ⣾⠀⣾⢸⡄⢀⣾⢻⠟⢻⡘⠁⣾⡇⠀⠀⠀⠀⠀⢀⣾⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⣿⣆⠀⠀⠀⠀⠀⠀⢸⣿⡇⡿⢸⡏⠉⢻⣀⣻⠇⢱⢸⣇ ⣿⠀⡇⠀⢻⡟⠹⡀⡇⢘⡇⠀⣿⣧⠀⠀⠀⠀⣠⣿⣿⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⣿⣷⡀⠀⠀⠀⠀⢸⣿⣇⠁⣾⡇⠀⣾⢹⣿⡀⢸⠀⣿ ⣿⠀⡇⠀⣼⠁⠀⣇⣀⣸⠟⠟⣟⣿⢿⣶⣶⡿⠟⠉⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠙⠿⣷⣤⣤⣴⣿⣿⣌⢻⡟⣧⣠⡏⡼⣸⡇⠘⠀⣿ ⢸⣇⠀⣰⣿⡇⣠⣏⠉⢿⠀⢸⡿⠁⠀⢸⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⠉⠁⢹⡏⢸⡇⠀⣽⢃⡇⡟⢿⡀⢸⡇ ⠸⡟⠿⡟⠈⡏⠉⢻⠀⠸⡆⣾⠁⠀⠀⠘⢿⣿⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣾⣿⣿⡃⠀⠀⠘⣿⢸⠀⢠⡟⠸⢰⠇⣸⣿⣿⠁ ⠀⣿⠀⡇⠀⣇⠀⠘⣇⠀⢿⡿⠀⠀⠀⢀⣾⡟⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠁⠈⣿⣷⡀⠀⠀⢿⣾⠀⣼⠃⠃⡾⠀⡿⢸⡇⠀ ⠀⢻⡄⢸⠀⢸⡀⠀⢹⡄⢸⡇⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⢸⣿⢠⡏⠀⢰⡇⢰⠇⣸⠇⠀ ⠀⠸⣧⠀⡆⠈⣧⠀⠀⢷⣼⠇⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⢻⣿⠁⠀⣾⠀⡸⢀⣿⠀⠀ ⠀⠀⢿⡄⠘⡀⠘⡆⠀⠘⣿⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⢸⡏⠀⢸⡇⠀⠃⣸⡇⠀⠀ ⠀⠀⠈⣷⡀⠁⠀⠹⡄⠀⣿⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⢸⣧⣀⣿⠀⠀⢠⣿⠀⠀⠀ ⠀⠀⠀⠘⣷⠀⠀⠀⢻⡾⠋⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠙⣿⡇⠀⠀⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⡀⠀⠈⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⡇⢀⣼⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣦⣴⠏⠀⠀⠀⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠀⠀⠀⠹⠿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠛⠿⢿⣿⣷⣶⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠛⠛⠛⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠛⢻⣿⣿⠀⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠁⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣷⣶⣶⣶⣤⣤⣤⡴⠶⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⢈⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠘⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠈⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⠀⠀⣸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡟⠹⣿⣆⠀⠀⠀⠀⠀⠀⣰⣿⠏⢻⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⢻⣿⡄⠀⠀⠀ ⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀ ⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀ ⠀⣾⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣷⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⡟⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⢻⣿⣿⡇ ⢸⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⡟⢻⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⡇ ⢸⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⡟⠀⠀⢻⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⡇ ⠀⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠀
⠀⠀⠀⠀⡀⠀⠀⠢⠨⣔⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠤⢖⣚⠳⢒⠀⠀⠘⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡈⢭⠟⠁⣀⣭⢀⠀⠈⠁⢆⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣆⠀⠀⠀ ⠄⢐⡋⡤⠀⠈⢎⠃⠑⠜⠀⢰⣷⣦⠶⠞⠛⠛⠛⠲⠤⠤⣊⣾⣿⢠⣯⣕⢄⠀ ⠐⡯⣴⣤⠀⡐⣼⠕⡀⠘⠀⣿⣿⠃⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣫⠿⢛⠆ ⠘⢴⣻⢷⠠⡷⡟⡈⢣⠀⢀⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⢛⠛⠦⠃ ⠈⠈⠻⡌⢑⡝⣴⣿⠌⠃⢸⡇⠠⣿⣿⠿⠿⢟⠻⡛⢿⣿⣿⣷⣴⣿⣷⣿⡆⣹ ⠀⠀⠀⠀⢈⠻⡮⣮⠀⢠⠸⣷⢸⣿⣿⣿⣿⣷⣦⠘⢄⣛⣛⡻⠟⠋⠈⠫⠿⠁ ⠀⠀⠀⠀⠀⢕⢽⣮⢦⣋⢆⣿⡀⣿⣿⣿⣿⣿⣿⡇⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢇⣿⣿⣿⣮⣻⡗⣿⣿⣿⣿⣿⣿⣿⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢐⣿⣿⣿⣿⣷⣿⣿⣿⣿⠿⢋⡷⠾⣧⣤⣤⣤⣒⣉⡡⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢉⣉⣉⣉⣋⠑⡆⢙⣢⣤⣤⡬⠤⠍⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠉⠍⠛⠛⠉⠀⠀⠻⢿⠿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠏⡟⢰⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⢿⣇⢸⠀⠀⣇⣴⡆⡈⠁⠀⠀⣠⠘⣁⠁⣼⣯⣴⠀⠘⠋⠉⢸⣡⣀⠈⠙⠿⠿⣿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⠏⢸⣿⣿⣷⣶⣿⣿⣿⣿⣾⣷⣾⣿⣾⣿⣷⣿⣿⣏⡆⣠⣤⣴⣿⣿⣿⣶⣦⣄⠰⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡏⢀⣾⣿⠟⠙⠉⠉⠉⠙⠛⠛⠛⠟⠛⠛⠛⠿⢿⣿⣿⡿⠿⠛⠋⠟⢿⢿⣿⣿⣿⡆⢿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠃⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⣾⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⣰⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣟⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⡙⢻⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠟⢿⣶⠙⢿⣿⣿⠁⠀⠀ ⠀⠀⠀⢸⣿⠓⠀⣠⣴⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣾⣿⣶⣦⡀⠀⠀⠀⠀⠀⢀⡀⢻⡧⣸⣿⣿⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠐⠟⠉⣀⣀⣉⡉⠋⠉⠁⠀⠀⠀⠀⠶⣻⠿⢛⣋⠉⢉⣉⠉⠻⢿⣆⠀⠀⠀⠀⠈⠻⣿⣷⢙⣿⣿⠀⠀⠀ ⠀⠀⠀⢸⣧⠀⡄⢰⣾⣿⡿⠟⠛⢿⣿⠆⠀⠀⠀⠀⠀⢻⣿⣿⣟⣿⠿⠷⠿⢷⣄⠙⠀⠀⠀⠀⠀⠀⣿⣿⣄⢀⣿⠀⠀⠀ ⠀⠀⠀⣸⡇⠀⢻⠈⠁⠀⣀⡰⡦⠿⠋⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⢀⠀⠀⠈⠙⢷⣶⠀⠀⠀⠀⠈⣿⣿⣿⣿⣇⡀⠀⠀ ⠀⠀⢸⢻⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠈⠙⠋⠀⠀⠀⠉⠃⠀⠀⠀⠀⢻⣿⠀⡠⣌⣻⡆⠀ ⠀⠀⡿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⡘⠃⠸⡏⡇⠀ ⠀⠀⣧⠋⡇⠀⠀⠀⠀⠀⠀⠀⡠⢾⣇⣀⠀⠀⠀⠀⠀⠀⠈⣻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣦⠀⡇⡇⠀ ⠀⠀⣇⣇⣧⠀⠀⠀⠀⠀⢠⡞⠁⠀⠉⠙⠳⣄⣀⣀⠴⠛⠉⠉⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣿⣿⠀⣧⡇⠀ ⠀⠀⢸⠀⢸⡄⠀⠀⠀⠀⠛⠀⣠⣤⣶⣾⣿⣷⣶⣷⣦⣴⣶⣦⣤⣈⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠾⠋⢠⠞⡞⠀⠀ ⠀⠀⢸⡀⢸⡇⠀⠀⠀⠀⣠⡞⣋⡽⠛⡽⣻⣿⣯⣷⣽⣝⢻⣿⡙⡻⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢠⡾⠁⠀⠀ ⠀⠀⠀⠻⢾⡇⢀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⡼⠳⡤⠴⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠈⠓⢿⣿⣿⡿⠛⠋⣥⣄⣀⣀⣀⣀⣤⣤⠿⠛⢿⣿⣿⣿⣿⡷⠶⠒⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠟⠉⠻⣿⣦⣄⡀⠀⠀⠀⠀⣶⣄⠀⣰⣦⡀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠁⠀⣼⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠏⠀⠀⠀⠈⢦⡉⠉⠛⠓⠶⠶⠿⠿⠿⣿⣿⣿⣿⣶⣶⠾⠿⠛⠉⠀⠀⠀⢀⣼⡿⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀ ⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⠴⡆⠀ ⠈⠱⡄⠀⠀⠀⠀⠀⡠⠖⠲⣄⠀⠀⠀⠀⠀⠀⠙⠾⣝⠶⢶⣦⣤⣤⡴⠚⣩⠞⠁⠀⠀⠀⠀⣄⣀⡀⠀⠀⠀⠀⠀⣠⠇⠀ ⠀⠀⠙⣄⠀⠀⢀⡾⢣⠶⣄⠈⢣⡀⠀⠀⠀⠀⠀⠀⠈⠛⠢⠤⣤⠤⠴⠚⠁⠀⠀⠀⠀⠀⣸⠃⣈⠙⣦⠀⠀⠀⣴⠋⠀⠀ ⠀⠀⠀⠙⡆⠀⠸⡀⠸⣄⣿⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⡾⠻⣆⠀⠀⠀⠀⠀⠀⠀⣰⣯⠟⢹⡇⣿⠀⢀⡼⠃⠀⠀⠀ ⠀⠀⠀⠀⠘⣆⠀⠻⣄⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣰⡟⠀⠀⠹⣧⡀⠀⠀⠀⢀⡴⠃⠈⠛⠋⣰⠃⢀⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣦⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠳⡄⠀⢰⣿⠀⠀⠀⠀⠘⢿⣄⠀⣠⠟⠀⠀⠀⠀⣰⠃⣠⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠘⢦⣿⠁⠀⠀⠀⠀⠀⠈⢿⣟⠁⠀⠀⠀⠀⣴⠃⢠⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠙⢦⡀⠀⠀⠀⢠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⢀⡼⠁⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠛⢆⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⢀⠞⠁⢀⡟⠀⠀⠀⣠⠤⣤⢠⡤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠈⠳⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡉⠀⢀⡾⠀⠀⠀⣾⡅⢸⢸⢀⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⣸⠃⠀⢀⡀⠛⠁⠘⠃⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣰⡟⠀⠀⣼⣏⡛⡯⡇⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀⠀⠘⠀⠀⠃⠉⠻⠄⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣛⣋⠉⠉⠉⠉⠉⠒⠲⠤⣤⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠒⠒⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⡴⡱⣿⠦⡀⠀⢀⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡉⠒⣺⠭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡑⠀⡿⠀⠈⠞⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡰⠁⠸⡇⠀⠀⡀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣀⣠⠄⠒⠈⠀⠀⠀⠀⠀⠀⢠⠏⠀⠁⠉⠀⠈⠛⢥⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡠⠖⠋⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀⢔⡏⠀⠀⠀⠀⠸⣷⠠⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠔⠋⠉⠀⠀⠀⠈⠉⠙⠒⠦⣄⡀⢠⢣⠊⠀⠀⢀⠆⠀⠀⠀⢀⠊⠀⢠⢁⡎⡸⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣅⠀⠀⠀⡼⠀⠀⢀⡔⠁⠀⣠⡇⡞⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣒⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⡇⠀⢠⡞⠀⢀⠔⢹⡎⠀⡞⠀⠀⠀⠀⠀⠀⢠⡒⠒⠷⠿⠷⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠇⢀⢻⢃⣴⠁⠀⢨⠇⣸⠁⠀⠀⠀⠀⠀⠀⢸⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⡈⠸⠃⡇⢰⠀⡜⢀⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⢄⠀⠀⢳⠀⠀⣸⢁⢆⡼⡡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢣⠀⣼⠰⢠⣇⠮⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⠁⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠲⢤⡀⣃⣷⣡⢷⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⢄⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀ ⠰⡇⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡴⠋⠁⠀⢠⠎⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⠁⠢⡀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀ ⠀⢧⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢸⡠⡶⢀⡜⡰⣡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠈⠲⣄⡀⠀⠈⠳⢄⠀⠀⠀⠀ ⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠳⡄⠀⠀⠘⠁⠗⠃⢿⡟⠙⣿⡈⡄⠀⠀⠀⠀⡄⡀⣰⡟⠀⠀⠀⠀⠀⠀⠈⢯⡑⠢⠄⣀⠑⠢⢀⣀ ⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠦⣀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⡇⠀⠐⢣⢹⡀⠀⡆⣼⣴⠗⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠻⣄⠀⠀⠀⠀⠀⠀⠀⠸⡴⠚⡟⠢⢄⣀⠀⠳⣄⠀⡟⢲⠒⡇⠀⠀⠀⢑⡇⡼⠛⠉⠁⡼⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⢸⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢳⡀⢷⠀⠀⠈⠙⠒⠬⣿⣇⣸⡀⡇⠀⠀⢀⠏⢹⠀⠀⠀⣰⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠳⣸⠀⠀⠀⠀⠀⣠⠃⠀⢨⣧⡇⠀⠀⡼⠀⡟⠀⠀⢠⠇⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀ ⠀⠀⠈⢧⠀⠀⠀⠀⠀⠈⢳⢦⡀⠀⠀⠀⠙⢆⠀⠀⣀⠔⠁⢀⡠⢛⣿⠀⠀⢰⠃⢀⡇⠀⠀⡞⠀⠀⠀⠀⠹⡢⢀⠀⠀⠀⠀⠀⠀⠘⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠈⢧⠉⣳⣤⣀⠀⠈⠳⣮⡥⠴⠚⠉⠀⢸⡏⠀⢀⡟⡀⢸⠁⠀⢸⠁⠀⠀⠀⠀⠀⠱⡀⠑⢤⡀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠈⢿⡁⢀⡏⠑⢢⢤⣈⠳⢄⡀⠀⠀⢸⠇⠀⡼⠀⠑⢿⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠈⠓⠦⣄⡀⠀⠑⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⣀⠙⢼⡀⠀⣿⠀⠈⠉⠓⠻⠶⣄⣸⠀⢠⣧⡀⠀⠈⡇⠀⢸⠈⢲⢄⡀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠉⠐⠒⠓⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡿⢷⡤⣿⢤⠀⠀⠀⠀⢀⡤⣧⣄⣼⣽⣽⠀⠀⢳⠀⠀⢳⡢⠧⠌⠒⠤⢄⣀⡀⠀⠈⠑⠤⢀⣀⣀⠠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡼⠧⠼⠼⠀⠀⠀⠀⢿⣰⡇⢸⡆⣹⠀⠀⠀⠸⡄⠀⢄⢹⠓⡄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇ ⠀⠀⣼⣦⡀⠀⠀⠀⠀⠀⣀⣤⠀⣠⣶⣶⣿⣿⣿⣶⣦⡀⠀⢸⣿⣿⣿⣿⡆ ⠀⠀⢻⣿⣿⣿⣿⣿⣷⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⠀ ⠀⢀⣾⠟⠙⢿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⠃⠀ ⠀⢸⣿⣴⣧⡞⢿⣧⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠏⠀⠀ ⠉⠽⣿⣿⣿⣋⣙⢿⣟⣭⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⠛⠛⠻⣿⣷⣽⣿⣿⡿⠁⠀⢹⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠹⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⢠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚。⋆୨♡୧⋆ ˚。⋆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠶⠶⠶⠤⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠶⠶⠦⠤⣄⡈⠙⠲⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠈⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠉⠑⠦⡀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠹⡄ ⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⣠⡀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢳⣀⡇ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠀⠀⠀⠀⠀⣷⠖⠋⠉⠑⠒⠦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⢧⡀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⠀⠀⣀⡤⠤⢤⣘⢦⡙⠢⠤⢤⡤⠴⠋⡇⠀⠀⠀⠐⠶⠀⠀⠀⢸⠀⠀ ⠀⡼⢁⣴⣶⣶⣌⠑⠉⠑⢠⠞⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀ ⢸⠁⣿⣿⣿⣿⣷⠷⣄⠀⣏⣀⡴⠊⠀⠀⠙⠦⢄⣀⣀⣀⡤⠚⠁⠀⠀ ⠸⡄⣿⣿⣿⣿⣿⣿⡏⢳⣄⣀⠀⠀⠀⠀⠑⢦⣀⣀⣀⡄⠀⠀⠀⠀⠀ ⠀⢳⡸⡿⣿⣿⣿⣿⣿⣿⣤⣿⣩⣿⣩⣷⣶⣤⡀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠱⣝⢿⢻⣿⣿⣿⣿⣿⣿⠻⠿⢿⣿⣿⣿⣿⣦⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⠙⢦⣿⠛⣿⣿⣿⣷⣦⠀⠙⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⠯⣼⡿⠛⡿⣇⠀⢹⣿⣿⡿⣰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢛⣒⢛⣋⡩⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢹⠄⡀⢀⠀⠀⡿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢀⠰⢉⡧⣿⢺⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⡑⢂⡱⡜⢿⡀⠀⠀⠀⠐⠀ ⣿⠘⠤⣲⣰⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⡘⠆⠃⣇⣿⢺⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡑⡌⠡⡼⣏⠸⣠⣄⢈⠀⠀ ⣿⢿⠀⢀⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠃⢀⢩⡧⣿⢻⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡈⢱⡖⡍⢻⢀⠀⠀⠀⠀ ⣽⣿⠸⠐⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠤⢋⡧⣿⢹⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠤⡃⠤⢚⣯⠘⠀⠀⠀⠀ ⣾⣟⢻⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡰⠜⡯⣟⣼⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠘⣩⠖⣍⢻⠀⠀⠀⠀ ⣽⢾⣿⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠄⡨⠖⣏⡃⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠔⡃⠤⢚⣯⠈⠀⠀⠀ ⣻⣽⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⡒⢎⣏⡇⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠒⣎⠇⣎⢹⠀⠀⠀ ⢾⣳⣿⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡁⠴⢛⣯⡁⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡁⠰⢍⢢⡜⣿⠀⠀⠀ ⣟⣯⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠠⡱⢎⣿⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡨⠕⣊⠭⣗⠸⠀⠀ ⢻⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⣁⡓⢧⢸⠔⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠣⢆⡙⡧⢸⠀⠀ ⡽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠥⡂⡱⣾⠀⠀⡦⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠑⢢⡜⡎⢽⠀⠀ ⡽⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠜⠃⣡⡿⢻⠟⠹⠋⡟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡉⠦⢃⢰⣾⠀⠀ ⡷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢂⡁⠆⠡⣿⣤⣀⣷⣿⣿⣤⣷⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡱⢆⡡⢽⠀⠀ ⣷⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢡⠠⡘⠣⣾⢀⠀⠀⡉⣿⢬⠀⠀⡀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢁⡰⢓⢡⡷⠀⠀ ⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠂⡁⠟⣾⢀⠀⠀⠀⡀⣿⡐⠀⠀⠀⠀⢧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠡⡱⠢⣑⡷⠈⠀ ⡿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠏⡴⢆⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣼⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡡⠒⣡⡜⡯⠀⠀ ⡷⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⡾⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⣦⠙⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠒⠌⣃⠠⢳⡌⣟⠀⠀ ⣻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢈⢠⠐⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠂⣄⠹⠀⠀⠀⠀⠀⡘⠁⠄⡃⠄⡑⠢⣌⠚⢡⣾⠀⠀ ⡵⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⠂⡀⢶⠈⠀⠀⠠⠄⠂⡐⠎⡁⠰⢎⡃⡔⢏⢸⠀⠀ ⣳⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⢂⠁⣆⠑⠀⡐⠎⢁⡰⠎⢃⡄⠘⢱⡬⡟⢀⠀⠀ ⡾⣟⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠌⠂⠁⠠⡐⡌⠆⡈⠱⢌⠡⠴⡈⠴⡓⣸⠀⠀⠀ ⣟⢧⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠆⠀⡐⠂⢁⢢⡐⠱⡌⠆⡈⠖⣈⡿⢀⠀⠀⠀ ⡼⢿⣯⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢀⡐⠌⠁⠤⡈⠢⡐⢌⡑⠦⢏⣰⠀⠀⠀⠀ ⣽⡞⣿⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⠌⠂⠄⠈⢂⠔⢂⡡⠟⣼⠀⠀⠀⠀⠀ ⡳⣽⣸⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠁⢂⠄⢈⡐⢋⡷⣼⠀⠀⠀⠀⠀⠀ ⣼⡟⢰⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠂⢡⡀⠞⣫⣼⠀⠀⠀⠀⠀⠀⠀ ⣜⡿⢀⠀⠀⠀⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠐⠁⡼⢏⣰⠀⠀⠀⠀⠀⠀⠀⠀ ⣞⢰⠀⠀⠀⠀⠀⡄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠃⢥⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⢠⠀⠀⠀⠀⠀⠀⡀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡱⡿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⠈⠀⠀⠀⠀⠀⠋⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⢱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠀⠀⠀⠀⠀⠀⠋⡷⣎⡞⢿⠈⠀⠀⠀⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⢑⡦⡟⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠟⣾⣡⣸⢍⠂⣄⢻⠀⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢨⠱⢂⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⡇⣩⠴⢋⠤⠒⣈⠑⣇⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⠆⡉⠤⡘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⢃⢆⠡⢶⠻⢉⠠⡐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠉⢢⡜⣟⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⢈⡱⢂⠤⡘⣆⢿⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠴⢋⢠⢽⡎⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠈⡰⠁⢂⠄⠩⣄⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣹⠇⣡⠖⢩⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⢸⠌⡀⠀⠀⠀⠐⠠⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢾⡉⡰⢜⡻⣇⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡃⢸⠀⠀⠀⠀⠀⡁⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢿⠠⡱⢆⠳⣇⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠂⠀⣿⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⢊⠀⣿⣉⠤⣣⡕⡪⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠁⣼⠁⠉⠛⠛⠛⠿⠿⠛⠛⠉⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠋⠟⡿⣾⣛⣳⠾⣟⢿⢯⣿⠓⣘⡕⢻⢰⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢀⠀⠀⠀⠁⠔⢔⣠⠀⣠⣀⠀⢀⠀⢀⡀⣀⣄⢦⣷⢽⠻⠙⠈⠀⢸⠀⠀⠁⠛⡿⣶⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡥⣬⡷⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠏⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣆⡶⣟⢯⠙⠋⡿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡧⣿⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠁⣸⠀⠀⡿⣯⣿⣷⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⢿⣋⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠵⣿⣟⠻⠙⡀⣷⡋⢤⠀⠀⠀⠀ ⠀⠀⠀⡇⡯⢀⠀⠀⣿⣿⡧⣿⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣟⣯⣏⠿⣯⠀⡂⣿⢀⠀⠀⠀⠀ ⠞⡿⢤⡿⡎⠀⠀⠀⣄⡤⣶⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡶⣻⣺⣴⢀⠀⠀⣗⢹⠦⠷⠹⠀ ⡟⢠⠁⣿⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡎⣜⠀⡃⣿⠀ ⣧⠈⡇⣿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡬⢩⠟⣿⢰⠀ ⠁⢄⠟⣹⣇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣉⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢣⣕⢻⡴⢠⠀⠀ ⠀⠢⡀⢸⠀⡄⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣠⠀⠅⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡗⣠⠐⢊⡱⣷⠀⠀⠀⠀ ⠀⠀⣇⢸⠀⠀⠀⠀⣄⠷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⡀⠀⠀⠀⡀⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠝⣑⣠⠀⠀⠀⠐⣈⡷⠘⠀⠀⠀ ⠀⠀⡇⢨⠀⠀⠀⠀⠀⠀⡀⣷⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣽⣄⢀⠀⠀⠀⠀⠀⡐⡇⢸⠀⠀⠀ ⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠀⠀⠀⠀⠀⠀⠀⡐⢂⢿⠙⠀⠀ ⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠁⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢨⠀⠀⠀⠀⠀⠀⠀⢁⢸⣀⢳⠀ ⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⢧ ⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡾⠀⠀⠀⡀ ⠀⠀⠀⠀⣟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢙⠀⠀⠀⠀ ⠀⠈⠀⠇⣱⢾⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠘⠀⠑⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢆⠘⠀⠀⠀⠀⠀⠉⠟⣾⣻⣧⠹⠀⠀⠀ ⡰⠀⠀⡇⡀⢸⡇⢌⠻⠛⠉⠉⠁⠄⠈⠀⠀⠀⠃⠒⠒⠞⠤⡿⣠⣀⣀⢁⠋⢠⠀⠀⣃⢀⠀⣇⣸⣄⣦⣒⣝⢬⠶⠒⠀⠀⠉⠉⠋⠟⡿⣇⣽⣿⣷⢲⣿⠘⠀⠀ ⠀⠀⠀⡇⠘⢹⡏⠰⣇⢾⢹⡀⣆⣿⣿⣇⣿⢿⠻⠙⠈⠀⠃⣼⠀⠀⠀⡏⣰⠀⠀⠀⡄⠸⠂⡀⢿⠘⠂⠍⠒⠤⣠⣀⣄⠘⢀⠀⣿⣿⣿⠀⡡⣿⡇⣼⡿⣿⠀⡏ ⠀⠀⠀⠀⢳⣇⣿⠰⡇⢸⣻⠀⠀⣇⣿⠈⣿⣷⣿⣿⣾⢧⡿⢘⠀⠀⠀⣰⠀⠀⠀⠀⠀⢧⠁⠄⣿⢴⣠⢀⠀⠀⠀⠀⡇⢿⠀⡇⢽⣰⣿⠀⠀⣿⡇⣼⡟⣿⠿⣸ ⠀⠀⠀⠃⡷⠘⣷⢹⡀⢠⣿⠀⠀⡀⣾⣧⣇⡀⣿⣿⢿⣏⢠⣇⠀⠀⠀⠀⠀⠁⠜⠀⠁⡏⠰⡯⢀⠀⠀⠀⠀⠀⠀⠃⣾⣀⠁⣼⠀⠇⣸⠀⠀⣿⡇⣸⣿⣯⣼⠀ ⢳⠈⠀⣸⡇⢿⡌⣧⠘⠀⣆⡌⠘⠀⢸⡇⡼⠀⣿⣿⣿⣸⠀⡇⠀⠀⠀⠀⠏⣾⣫⠷⠹⣈⠐⣿⠀⠀⠀⠀⠀⠀⠋⣿⢀⠃⣾⠄⠁⡞⠀⠀⡇⣸⣄⡏⣼⣿⠙⠀ ⠂⢟⠟⢿⡆⡽⢻⡄⣷⠸⠀⢀⢸⠀⢸⡇⣸⠁⣿⢳⣾⠀⠀⡇⠘⠈⠋⡿⣼⣞⢯⣳⣽⢿⣋⣿⠀⠀⠀⠀⠀⠏⣯⢠⠃⡼⢨⠁⡿⢠⠀⠀⡿⢀⠃⣾⠏⣰⣿⠸ ⠀⡎⣻⣬⠳⣌⣳⢿⡈⢳⠘⠀⢿⠀⢠⡿⠡⡟⣣⣿⢠⠀⠀⡇⠿⣿⣿⣿⣶⣴⣤⣷⡿⣿⣿⣿⠀⠤⠀⠈⠇⣸⣸⠁⣼⣇⠀⡟⣰⠀⠀⠏⣰⠁⡾⢥⡼⠁⢹⢸ ⠏⣭⢞⣭⠶⣟⠻⣍⢶⠙⡀⢤⡉⢨⠇⣻⡟⢿⣯⣼⠀⠁⠋⡶⣤⣠⢀⠀⠀⠀⠀⠀⡀⣦⣷⣿⠀⠀⠀⠀⡧⣀⢹⡏⣂⡙⠀⣼⠀⠀⠏⣰⠃⡵⠟⣾⢀⡞⡟⢀ ⢾⣍⠽⣣⣜⠳⣌⣇⣤⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⠟⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢳⠈⠀⠀⡀⢹⡆⢹⠀⠄⠂⢁⠠⠟⣰⠀⢋⡿⣴⠋⡵⡞⢀⢸ ⢞⢣⡹⢧⡌⠳⣀⠰⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣽⠛⠘⠁⠘⠈⠀⠀⠛⠞⠤⠠⠒⠑⠈⠀⠀⠀⠀⣤⠛⠉⠀⡀⢻⣿⠙⠀⠀⠻⡷⣠⠋⡽⣾⣩⠿⢞⣠⠁⡟⢠ ⡜⢮⡙⢢⡜⠣⣀⠀⠋⡿⣿⣿⣷⣿⣿⣿⣿⣿⣻⣞⢵⣸⠵⠀⠀⠀⠀⣀⣀⠄⠤⠤⣤⠠⠏⣟⢆⣉⡀⣷⢿⠿⣿⣿⣿⣿⢿⠻⠿⣿⣿⣿⣾⣴⣠⠉⠟⣴⢀⠀ ⡖⢌⡱⢎⡌⠀⠃⡿⣿⣿⣿⢧⡟⣿⣵⣟⢿⣿⣰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣖⣆⣇⣏⢛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢶⠶⡴⣤⣀⠀⠀⠀⠀ ⢣⣌⡓⠌⢀⠀⣿⣧⣾⢠⣾⡟⣿⣰⡰⡟⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠃⡠⢀⢧⠀⠀⠀⠀⠀⠀⡀⣄⠳⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⢨⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠱⡌⠒⢀⠀⡇⣼⡟⢠⡁⢿⣽⣾⡀⠇⣿⢁⠈⠀⣋⣛⣛⠤⠀⠀⠀⠀⢤⠒⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣻⢿⣿⣿⣿⣿⡿⣿⣿⠘⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡜⠀⠀⠀⡇⢸⣟⠀⣿⣾⣇⢨⠀⣧⣿⣿⠸⡍⣯⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠏⠭⠤⠑⠀⠀⣷⡸⣖⣿⣿⣿⢧⣿⣿⣿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⡜⠈⠑⠢⡇⣽⣿⠀⣿⢠⡄⠀⠠⡿⣿⣤⣿⣿⣿⣿⡿⣾⣷⠻⠙⠙⠀⠀⠀⠀⠁⠋⡶⣾⣿⢿⠈⢧⠈⡇⣿⠄⣇⣿⣿⡔⣿⣿⡧⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⡀⡄⠀⢠⡄⣿⣷⠀⣽⠀⡀⠀⠃⣿⢠⠀⣿⣀⣄⣿⣿⠈⡇⣄⣷⣿⢽⠢⠎⠈⡄⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⢘⡡⣿⣿⡚⣷⢸⡿⢸⠈⠠⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⡟⠈⢹⠀⠀⠀⡇⣼⠀⠀⡇⢸⠀⢹⡄⣷⡟⢻⠉⣧⣿⢻⣯⣿⠈⡀⣿⣬⣾⣷⣹⣇⣹⡆⣿⢾⠈⣿⣿⡐⣾⠇⣿⢀⠀⠁⠂⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢸⣷⠀⠀⠰⡇⢺⠙⠈⣤⣻⣈⣾⣶⣽⣦⣿⣦⡻⣤⣿⣿⡆⢹⠀⣇⢿⢸⡀⣯⣿⢢⠀⣷⢿⠀⣏⣼⡏⢣⣿⢠⠄⠀⠈⠀⠐⠀⠀⠈⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⣿⡇⠸⠀⠀⡇⢈⠀⣀⠦⣷⢿⢸⠀⡀⢷⡈⢤⣇⠸⣷⣿⠀⣯⠀⡿⣿⠀⠀⣟⣿⠀⢁⡤⣹⢀⡿⢃⣿⣾⢨⡀⠁⠀⠀⠐⠀⠂⠄⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⣳⣿⠀⠀⡆⠘⠀⠀⠀⡆⣿⣟⠸⠀⡇⢦⠘⠀⣷⠃⣸⠀⣟⠋⣿⢻⠛⠓⣿⢾⡤⠀⠇⢸⠏⣱⣿⣾⢁⠀⠂⠀⠀⠠⠀⠈⢀⠁⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣀⢱⠀⠀⢸⠀⠀⠀⡇⣷⢸⣇⠈⡃⠀⢧⠀⣇⠃⢰⣀⣿⣿⣾⠀⠀⡞⣏⢀⠃⢀⡞⠃⣻⡿⣴⠀⠀⠂⠀⠀⢀⠀⠠⠀⠂⠀⠀⠐⠄ ⠀⠀⠀⠀⠀⠀⠉⠛⡴⣀⢳⡀⠱⠀⡇⠀⠀⠀⡄⡼⢸⠀⢳⠀⠀⡇⢸⡇⡄⠀⠇⣿⣾⢀⠀⡞⣏⣸⠃⢰⠖⢫⣽⡿⢠⠀⠠⢀⠀⠂⠄⡀⠀⠈⢀⠂⠀⡀⠀⠄ ⠒⠒⠄⠤⣤⣠⣀⠁⠀⠀⡀⠳⡈⢤⠑⢠⠃⠀⠀⢣⢸⠀⡇⠈⠀⡼⠀⣼⠀⡅⡾⣿⠀⠀⡀⠟⣼⠃⣠⡁⠏⣿⡼⢀⡀⠀⠈⠠⢀⠀⠂⠄⠀⠀⠄⠀⠈⢀⠂⡀ ⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢆⠑⡀⠠⠈⢣⠀⡄⢸⠀⠀⢸⠃⢠⡇⢀⠁⡴⢁⠠⠀⠃⡿⣰⠀⠀⠟⡿⣾⣠⠁⡀⠀⠐⠀⠁⠄⡀⠀⠁⠄⡀⠀⠐⠀⠄⠀⡁ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⡀⢤⠓⠈⠀⢄⠑⡄⠑⠀⢠⠀⠃⢡⠞⣠⠜⢀⠁⠞⣴⢀⠀⠋⡿⣴⣠⠄⡀⠀⠀⠠⠀⠀⠠⠀⠂⡀⠀⠀⠐⠠⠀⠠⡀⠀⠐ ⠀⠀⠄⠀⠀⠂⠀⠀⠂⠀⠀⠂⠀⠀⠂⠀⣀⢤⠒⠙⢈⡀⠠⠐⠁⢋⣤⠀⡠⠀⠀⣠⠁⠉⠛⠶⣤⢀⠈⢀⠀⠐⡀⠀⠀⠠⢀⠁⠄⠀⠈⢀⠁⠂⠀⠠⠀⢀⠈⠄ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣀⢤⠿⠬⠶⡶⢶⠶⠴⣤⣤⣠⣄⠀⠀⠂⠀⠀⠀⠠⠀⠈⢀⠀⠄⠀⠈⠁⠀⠈⠁⠀⠈⠄⠀⢀⠈⠁⠀ ⠀⠀⡀⠀⠀⢀⠀⡀⠀⠀⢀⠀⡀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡿⢸⠀⠀⠄⠀⠀⠄⠀⠀⠠⠀⠄⠀⠀⠐⠠⠀⠐⠀⠂⡀⠀⠐⠀⠐⠀⠈⠐⠀⠈⠐⡀⠁⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠁

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⠀⠀⠀⠀⠀⢀⡴⡒⠒⠲⠶⠒⠒⠛⠓⠲⠶⠒⠒⠚⠓⠶⠶⠤⠤⠤⠶⠶⠦⠤⠤⠴⠶⠦⠤⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⠀⢱⠀⠀⠀⢀⠴⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠶⠋⣀⡀⠸⡆⠀⠀⢏⠀⠀⡠⠃⢰⣄⠀⣸⣇⣀⣴⠇⠀⠀⠀⣶⡀⢀⣿⠀⠀⣤⠀⠸⠤⠊⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠏⠀⡜⠁⢸⠀⠙⡄⠀⠀⢉⢉⠀⠀⡠⠛⠉⠉⠉⠉⠉⠳⣄⢀⠴⠊⠉⠉⠉⠉⠙⢧⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⠀⠀⢇⠀⡼⠀⠀⢱⠀⠀⠉⠁⠀⡞⠀⠀⠀⠀⠀⡠⠤⣀⠈⡏⠀⢀⣀⣀⡀⠀⠀⠀⢱⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢛⡗ ⣷⡀⠀⠀⠈⠙⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡎⣴⣿⡎⡆⠸⠀⡏⣶⣷⣽⡄⠀⠀⠀⡇⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡼⠋⠀ ⠈⢳⡄⠀⠀⠀⣀⡀⠀⠘⡆⠀⠀⠀⠀⣧⣀⣀⣀⠀⠘⠪⠭⠛⢠⡇⠀⠑⠭⠭⠞⠀⠀⣀⣸⣀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣴⠚⠺⣟⣩⠷⡄⠀ ⠀⠘⣧⠀⠀⡎⠀⡇⠀⠀⡇⠀⠀⠀⠀⡅⠈⠀⠘⠙⢦⣀⡠⠖⠁⠈⢢⣄⣠⠤⠔⠂⠉⠀⢀⡸⠀⠀⢸⡆⠀⠀⠀⠀⠐⡇⠑⡶⣏⣀⢆⡇⠀ ⠀⠀⠙⣦⠀⠧⠴⢁⣀⣀⢡⠀⠀⠀⠀⠀⠈⢻⡀⠀⠉⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⡤⠴⠖⠋⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠙⡆⢀⣈⣡⠟⠀⠀ ⠀⠀⠀⠈⡇⠀⠀⢸⠀⠈⡏⡄⠀⠀⠀⠀⠀⢸⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⡤⠤⣭⠶⠄⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣰⠃⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢧⡀⠀⠸⡄⡰⠁⢱⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇⠀⠀⡇⠀⠀⢠⠖⠓⢢⠀⢇⠀⠀⠀⠀⠀⣰⠃⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢱⡀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠀⠀⠀⠸⣤⠤⠊⠀⣾⣀⣀⡀⠀⣰⠋⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣧⣄⡀⠎⡐⠈⡆⠀⣰⠆⠀⠘⢏⠉⠙⠛⠟⠛⠿⣿⣿⡇⠀⠀⠀⠀⠀⣀⠤⡄⠀⢸⠋⢠⡶⠗⢚⣡⠾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⠀⠹⡋⠀⠀⠃⠀⠠⠒⢢⠀⢄⠙⠒⠶⠶⠶⠶⠞⠛⠀⠀⠀⠀⠀⠀⠧⠴⠃⠀⢸⠀⢀⣻⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⣇⣀⠀⠀⠀⠣⠤⠊⠀⠀⠉⠛⠚⠛⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⠤⡴⠋⠉⠉⠙⡟⠛⠉⠙⠛⠻⢟⡉⠉⢉⠟⢖⠒⡻⠻⣍⢉⡽⠛⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡄⡟⣶⣶⣦⠴⡧⠤⠤⠤⠤⠤⠤⠬⠭⢥⣤⡼⠉⢷⣤⣤⣁⡀⣀⣀⣀⣠⡶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠉⠉⠀⡇⠀⠛⠛⠛⠛⠀⠘⠛⠛⠛⢧⠀⡸⠛⠛⠛⠁⠙⠛⠛⠛⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠇⠘⢶⣤⣄⣀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠸⣆⠸⣏⠉⠉⠉⠉⠉⣹⠏⠉⠉⠉⠉⠙⠯⣍⣉⣉⣀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⣦⠸⡗⠋⠀⠈⠙⡗⣶⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⠶⠃⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣶⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⢀⣾⣿⣿⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣤⣶⡄⠀⠀⠀⠀ ⢠⣿⣿⣿⣼⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀ ⠘⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⠀⠀⠀⣴⢛⣠⣤⣀⠀⠀⠀⢀⣠⣤⣀⠀⠐⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⢀⡿⠋⠁⠀⠉⠻⣦⡾⠋⠀⠀⠈⠹⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀ ⠀⠀⢸⡁⣶⡆⠀⠀⠀⣸⠁⠀⠀⣤⡄⠀⢸⡄⢰⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀ ⠀⠀⠘⣧⡀⠀⠀⣰⠞⠹⣆⠀⠀⠉⠀⢀⡾⠀⢸⣿⢟⡻⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⢀⡾⠛⡿⠋⠁⠀⠀⠈⠳⠦⠤⠴⠟⠁⠀⠈⠁⢛⡷⣽⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⠁⠀⠳⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠷⣤⣄⣀⣀⣀⣀⣠⣤⣤⡤⠶⠿⠆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠙⠧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣦⣀⠀⣀⠤⣄⣤⠶⠛⠁⠀⢻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⣼⣿⣿⣧⣤⠚⠉⠀⠀⠀⠀⣠⣿⡟⢳⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡸⣿⣿⣿⣿⡏⠀⠀⠀⢀⣤⠾⢻⡏⠀⠀⢻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⣿⣿⠛⢿⣤⡴⠾⠋⠁⢴⣿⠀⠀⠀⠈⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢹⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢀⣼⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣻⣇⣀⣷⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇⠀⠀⠸⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣶⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠃⣨⣿⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡿⠻⢿⠿⠻⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣦⣿⣧⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣰⡆⢠⠀⣄⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣼⣿⠉⠛⠛⠻⠶⠶⠶⣦⣴⣶⣼⣿⢿⡇⣸⠀⣿⡼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠰⢶⣦⣤⡄⠀⠀⠀⠈⠛⢻⡞⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣸⠃⢸⠃⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣈⠛⡷⠶⠂⠀⣹⣦⡿⣤⣄⣀⣀⡀⠀⢻⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠛⠛⠛⠛⠛⣏⠈⠳⣦⣍⣉⣉⣡⣤⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢀⡇⠀⠀⢿⠀⠉⠉⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣶⣄⣀⣠⣼⣿⡀⠀⣸⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣾⣿⣿⣷⣦⣤⣴⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠛⠉⠀⠈⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠒⠂⠴⠊⠉⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠉⠓⣤⡀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀⠜⠕⠒⠀⠀⠀⠀⢀⡬⢦⡀⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⠎⢀⡔⠉⠉⠲⡀⢸⢁⣀⣀⣱⠾⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠾⡤⠒⠒⢚⡇⠘⡧⣀⡠⠾⡄⢱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠀⠀⠀⠀⠠⣌⡆⠀⠈⠒⠒⠊⠀⢀⡸⠀⠀⠀⠘⡜⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⢀⣠⣶⣶⡄⠀⠀⡇⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡄⠀⠀⠸⣿⣿⣛⣛⣻⠋⠀⠀⡜⠀⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠘⠻⠿⠿⠟⠁⡠⠎⠀⠀⠀⣇⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⡤⡀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⡠⠤⠤⣀⠁⣸⠀⠀⠀⠀⢨⢀⣀⣀⠀⠀⠀⠀⠀⠗⠒⣇⡀ ⠀⠀⠀⡸⠀⠀⡜⠀⠀⠀⠈⠋⠀⠑⢄⣠⠤⡜⠋⠀⠀⠙⡄⠀⠀⠀⠀⠈⠁⡜ ⢔⠒⠊⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡜⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⡴⠁ ⢈⣲⣤⡀⠀⣀⢗⣖⣵⣯⣽⣑⠦⡀⠀⠀⠀⣀⠀⠀⠀⠘⢎⡀⠀⢀⡠⠊⠀⠀ ⠘⢄⠀⠀⠀⢳⣿⣿⠿⠿⠿⣿⣿⣯⣢⢄⣀⣹⣄⣀⣀⡤⣞⣽⠚⠁⠀⠀⠀⠀ ⠀⠀⠑⢤⣀⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣷⣿⣮⣥⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀ ⢀⣀⣤⣾⣿⣿⣿⣷⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠟⠛⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡎⣿⢩⠖⠈⠐⠒⠒⠒⠴⠫⢍⢢⠀⠀⠀⠀ ⠀⠀⡼⠁⠀⠀⠀⢀⣂⠀⠀⠀⠈⠐⠼⡜⠀⠀⠀⠀ ⠀⠀⣇⠀⡀⡘⠣⠀⠀⠀⣀⣠⠀⠀⢠⠱⡀⠀⠀⠀ ⠀⠀⢈⠦⢦⠮⣀⠀⠀⠀⣀⣁⠢⡕⣸⠀⢱⠀⠀⠀ ⠀⠀⡜⠀⣠⠀⠾⠅⣀⡀⠩⠬⠀⢃⠇⡆⠀⡆⠀⠀ ⠀⢠⠁⢠⠇⠣⢄⠀⢋⠅⠀⣀⠜⠉⠀⢱⠀⢰⠀⠀ ⠀⡜⠀⢸⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠸⡀⠈⡆⠀ ⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢡⠀ ⢠⢀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀ ⢸⢁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⡆ ⢗⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⡺ ⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⠀⣿⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⣿⣄⠀⣠⣾⣇⠀⠀⠀⣀⣤⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⢰⠟⣿⠿⠋⠘⠿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⣼⡿⠿⢿⣷⣶⣴⣿⠏⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⣿⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⣿⣇⠀⠀⠈⢛⣿⡟⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⢻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀ ⢹⣿⠀⠀⠀⣼⣿⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠿⠟⠛⠛⠻⣿⣆⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀ ⠘⣿⡇⠀⠀⣿⣿⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡿⠟⠛⢩⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀ ⠀⢹⣿⡄⢰⣿⡇⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣾⡿⠟⢻⣿⠁⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣼⣿⡇⠀⠀⠀⢸⡇⠈⠉⢹⣇⠀⣸⣧⠀⣼⣿⡆⠀⠀⢠⣿⣧⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⢸⣿⠀⠀⢸⣿⣄⣿⣿⣷⣿⠿⣿⡄⠀⣼⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠸⣿⡆⠀⣿⣿⣿⡟⠋⠙⠁⠀⠙⢿⣶⣿⠃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣶⣶⣤⣀ ⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠈⣹⣿ ⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏ ⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠹⣿⣦⣀⠀⠀⢀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠈⠛⠿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣧⣀⣀⣿⣧⣀⣼⡟⠀⠀⠀⠀⠹⣧⣀⣀⣿⣇⠀⣰⡷⠀⠀⠀ ⠀⠀⣰⠟⠉⠀⠀⠀⠀⠈⠙⢷⡄⢀⡴⠚⠉⠀⠀⠀⠀⠉⠻⣇⠀⠀⠀ ⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⡴⢋⣭⣽⣷⠀⢷⠀⣰⢚⣭⣽⢣⡀⠀⠀⠀⠘⡇⠀ ⢸⡀⠀⠀⠀⠀⠈⣇⢿⣿⣿⣿⠀⡾⠀⢧⢿⣿⣿⢇⡇⠀⠀⠀⢀⡇⠀ ⢸⣧⣤⣤⣤⣀⠀⠈⠓⠾⠒⠁⣰⣇⠀⠈⠓⠾⠶⠛⠀⠀⣀⡤⠼⢄⠀ ⢸⠁⠈⠠⠄⠛⠳⣄⠀⣀⡤⠞⠁⠈⠳⣄⡀⣀⣠⠴⠖⠋⠁⠀⠀⣰⡇ ⠀⠀⠐⢲⡶⠄⠠⠟⠉⠉⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⣀⣠⡴⠾⠋⠀ ⠀⠀⠀⢸⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣋⡉⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⡶⠶⠶⢶⣶⣶⠶⠒⠒⣶⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣀⣀⣀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢷⣄⣀⡀⠉⠀⠀⠉⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⣤⣈⣉⣙⡛⠛⠛⠛⠛⠉⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣷⣶⣤⣀⣤⣴⣶⣶⣶⣶⣦⣤⣀⣤⣶⣾⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠠⣤⣀⡀⠹⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⠃⢀⣀⣤⠄⠀⠀ ⢀⠤⢤⣤⣬⣙⠳⣿⣿⡿⠀⢀⠀⠈⣿⣿⠁⠀⡀⠈⣿⣿⣿⠞⣋⣥⣤⠤⠤⡀ ⠀⢀⡤⠤⢤⣼⣿⣿⣿⣿⡀⠸⠀⣠⣿⣿⣄⠐⠇⢀⣿⣿⣿⣿⣧⡤⠤⢤⡀⠀ ⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠉⠉⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⠛⠿⢿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⡿⠻⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⣿⡿⠟⠛⠋⣽⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⣼⣿⣿⠏⢸⣿⣿⡏⠻⣿⣷⡀⠀⠀ ⠀⢠⣿⡟⠁⠀⠀⠀⠀⣼⣿⣿⡟⠀⢸⣿⣿⡇⠀⠈⢻⣿⡄⠀ ⢠⣿⡟⠀⠀⠀⠀⠀⣼⣿⣿⡿⠀⠀⢸⣿⣿⡇⠀⠀⠀⢻⣿⡄ ⣸⣿⠇⠀⠀⠀⠀⣼⣿⣿⣿⠁⠀⠀⠘⢿⣿⡇⠀⠀⠀⠘⣿⣇ ⢿⣿⠀⠀⠀⠀⣰⣿⣿⣿⣇⣀⣀⣀⣼⣦⡙⠇⠀⠀⠀⠀⣿⡿ ⢸⣿⡇⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⢸⣿⡇ ⠀⢿⣿⡀⣸⣿⣿⣿⠟⠉⠉⠉⠉⠉⣿⠟⣡⡆⠀⠀⢀⣿⡿⠀ ⠀⠈⠛⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠠⠾⠿⠇⠀⣠⣿⡿⠁⠀ ⠀⠀⣰⣿⣿⣿⡟⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠋⠀⠀⠀ ⠀⣰⣿⣿⣿⡿⠰⠿⣿⣶⣶⣶⣶⣶⣶⣿⠿⠟⠉⠀⠀⠀⠀⠀ ⠀⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⠞⠋⢀⣠⣤⣴⣶⣶⣾⡿⠶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡾⠋⠀⢀⣴⠟⢉⣾⣿⣿⣿⡿⠿⠗⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⠟⠀⠀⠀⠸⠏⠀⠛⠉⠉⠁⠀⠀⣀⣤⡀⣴⠶⢶⣶⣲⡶⠀⠀⠀ ⢀⣾⡟⠀⠀⠀⠀⠀⢀⡀⢰⡄⣶⢻⡷⣾⡏⢶⡆⣿⣋⣹⡿⠻⡦⠀⠀⠀ ⣸⣿⠀⠀⠀⣶⣟⡿⢸⡇⣸⡇⣿⠻⠷⠙⠛⠛⠁⠉⠁⠀⣀⣤⣤⣤⠀⠀ ⣿⣿⠀⠀⠀⣿⣯⡿⠘⠛⠛⠀⠀⣀⢀⣤⣄⠀⢰⣿⣦⣾⡿⢋⣉⣉⠀⠀ ⣿⣿⠀⠀⠀⠉⠁⢀⠀⢀⣶⡆⣾⣿⢸⣿⣿⣷⣼⣿⣿⣿⣧⣈⣹⣿⠀⠀ ⢸⣿⡆⠀⠀⠀⢸⣿⣰⣿⠏⠀⣿⣿⢸⣿⡇⠙⢿⣿⠇⠉⠛⠛⠛⠉⠀⠀ ⠈⢿⣿⠀⠀⠀⢸⣿⠻⣿⣷⡄⣿⠟⠘⠛⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠈⢿⠀⠀⠀⢸⠿⠀⠈⠉⠁⢀⣀⣀⣠⣤⣴⣶⣾⠆⣴⡿⠁⠀⣠⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠋⠀⢀⣴⣿⣿⠋ ⠀⠀⠀⠀⠀⠀⣤⣴⣤⡀⠀⠀⠈⠉⠙⠛⠉⠉⠉⠀⠀⣠⣴⣿⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⡿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⣠⣴⣶⣶⠀⣿⣿⣿⠉⠉⠉ ⠀⣴⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⠀⠀ ⢸⣿⣿⡿⠉⠀⠈⠀⣿⣿⣿⠀⠀⠀ ⢹⣿⣿⣷⡀⠀⠀⣰⣿⣿⣿⠀⠀⠀ ⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀ ⠀⠀⠙⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣼⣿⣀⣹⣿⡆⠀⢤⡄⢤⣄⢤⡤⠀⢤⣤⣤⣤⣤⢤⣄⠀⢤⣤⡤⣤⣤⣤⢠⡄⠀⣤⢤⡤⢤⡠⣤⠤⣴⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢹⣿⡇⠉⠉⢿⣿⡄⢸⡇⠀⢹⡏⢿⣠⡟⢹⣿⠤⠄⢸⡿⣷⣼⡇⠀⣿⡇⠀⢸⡇⠀⡇⢸⡇⣎⠀⣿⠶⠌⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠾⠿⠀⠀⠀⠘⠿⠿⠾⠿⠴⠛⠁⠘⠏⠀⠼⠿⠦⠖⠸⠃⠀⠙⠇⠀⠿⠇⠀⠘⠷⠚⠇⠾⠇⠘⠿⠿⠶⠶⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⡤⠀⢲⣶⣶⡄⠀⠀⠀⣰⣶⣶⠖⠀⢲⣶⣶⠶⠶⢶⣶⠀⠀⠀⠀ ⢀⣀⠀⠀⠀⠀⠀⢀⣸⣿⣉⣀⠀⢟⡉⠉⡉⣿⣿⢉⣉⣙⣛⣘⣿⣇⣀⡀⣿⢿⣿⡄⠀⣼⡿⣿⣿⢠⣤⣬⣭⣭⣤⣤⣤⣬⣤⣤⣀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢇⣿⠰⠻⣿⣾⡿⠵⣿⣿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣍⠁⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢰⣶⡆⠀⣼⣿⡆⠀⠹⡿⠁⠀⣿⣿⡀⠀⣸⣿⣿⣤⣤⣤⣤⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠴⠟⠛⠂⠀⠀⠀⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠻⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣼⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢣⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡼⠏⣼⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⢹⣿⢻⣿⣿⣿⣦⣄⠀ ⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⣸⠟⠛⠿⠶⢾⣿⣿⣿⣿⡿⠗ ⠘⢿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣿⠐⡀⠀⠰⠘⣿⣿⣿⣿⡄⠀ ⠀⠀⠈⠉⠛⠻⠿⣶⣶⠄⢸⣿⣧⣄⣀⠀⢀⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢞⣿⣿⣿⣧⣾⣶⣿⣿⣿⠿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣼⢄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠧⠈⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠀⠀⠀⠀
ੈ✩‧₊˚૮꒰˵•̀ﻌ•´˵꒱ა₊˚‧✩ੈ
(`ඞ`) ⚫️👾
🐬⚫🎨
⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤ ⣿⢾⡽⢾⡽⢾⡱⢾⡵⢯⡷⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉ ⣿⣻⣼⣻⣝⣻⣝⣫⣟⣻⣝⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⣿⣻⢾⣻⢾⣻⣞⣳⣞⣳⣟⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟ ⠿⠽⠮⠽⠮⠽⠮⠵⠯⠽⠯⠽⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶ ⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤ ⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉ ⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
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