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