⣿⣿⣾⣿⣿⡿⠟⠀⢘⢍⣿⣿⣿⣿⣿⣿⣿⢿⣧⠾⠿⠿⢿⣿⣿⣿⣿⣿⣿⣾ ⣿⣿⣿⡿⠟⠃⠀⠀⢀⢼⣿⣿⣿⡿⠟⠛⢏⠻⣭⡅⠀⠂⠀⠙⠋⣷⣜⣿⣟⣿ ⡻⣿⡿⠇⠀⠀⠀⣠⠩⣿⣿⣿⢏⣤⢆⣼⡜⣦⣈⢿⣦⠀⠀⠀⠀⠈⢛⣿⣿⣿ ⣿⠟⠁⠀⠀⢀⠒⣮⣮⣿⡿⠀⣾⣳⠟⠙⣿⣌⣿⡄⢿⣿⣂⠀⠀⠀⠀⠟⣿⣿ ⣾⠀⠀⠀⠠⢶⣮⣿⣿⣿⠃⢘⡩⠉⠐⠒⠛⠻⣿⣷⠘⣿⣿⣣⡀⠀⠀⠀⢹⣿ ⠃⡔⠀⠀⠀⠠⠈⢿⣿⡇⢀⣼⣽⠀⠐⡿⠷⠄⢻⣿⡀⣿⣿⣧⡇⠀⠀⠀⢰⣷ ⣸⡝⡀⠀⠀⠀⠀⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢥⣿⡇⡿⣿⠺⡇⠀⠀⢐⣿⣇ ⣝⣻⣷⡀⡀⠀⠀⠀⠘⢿⣷⠀⠀⣀⣀⢀⡄⢴⣿⣿⡘⣝⣿⣺⠃⠀⠀⠐⢿⣿ ⣺⣿⣟⡿⣕⠀⠀⠀⠀⠀⠉⢷⡔⢷⣤⠎⠁⠨⣿⢧⢴⠳⣿⣿⠀⠀⠀⠨⣿⣿ ⣿⣟⣳⣷⡷⣮⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⣀⠐⣃⣂⣲⣟⡟⠁⠀⠀⠀⢨⣿⣿ ⢍⣏⣊⡟⣿⣾⣟⠆⠀⠀⠀⠀⠀⠊⠟⠛⠟⡨⣿⠦⡓⠟⠃⠀⠀⠀⠀⣸⣿⣿ ⣓⣶⣷⣏⠻⡽⣗⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣟⣿⣿ ⡘⣿⡉⣟⡿⣕⡅⣂⡉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣷⣿⣿ ⣺⣿⡬⣧⡫⠒⠈⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿ ⣾⣿⠷⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣿ ⣟⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿ ⡯⣷⠂⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⣼⣿ ⣿⣽⡂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡼⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣿ ⡇⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠘⠗⡄⠀⠀⠀⠀⠀⠀⠀⠀⣬⣾⡿⣿ ⣿⣿⡟⣿⡖⣦⣔⣔⣀⡤⣶⠍⠀⠀⠀⠀⠀⠉⠉⠃⠒⠤⣤⣴⣶⣿⣿⣿⣿⣿ ⠙⣿⡗⠿⡿⣿⣿⣿⣯⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣟⣿ ⣿⡟⢷⡶⣯⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⡳⣟⣿

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⣿⣟⡳⠿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⡶⢷⡟⣿ ⣿⣟⣿⣿⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣯⣿⣿⣿⡿⠿⡗⣿⠙ ⣿⣿⣿⣿⣿⣶⣴⣤⠤⠒⠃⠉⠉⠀⠀⠀⠀⠀⠍⣶⡤⣀⣔⣔⣦⡖⣿⡟⣿⣿ ⣿⡿⣾⣬⠀⠀⠀⠀⠀⠀⠀⠀⡄⠗⠘⠀⠀⠎⢀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⡇ ⣿⣿⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠿⡼⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⡂⣽⣿ ⣿⣼⠀⠀⣦⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢀⠀⠀⠀⠀⠀⠀⠀⡄⣠⠀⠂⣷⡯ ⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣛⣟ ⣿⣶⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠷⣿⣾ ⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠈⠒⡫⣧⡬⣿⣺ ⣿⣿⣷⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡉⣂⡅⣕⡿⣟⡉⣿⡘ ⣿⣿⣟⠳⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡷⣗⡽⠻⣏⣷⣶⣓ ⣿⣿⣸⠀⠀⠀⠀⠃⠟⡓⠦⣿⡨⠟⠛⠟⠊⠀⠀⠀⠀⠀⠆⣟⣾⣿⡟⣊⣏⢍ ⣿⣿⢨⠀⠀⠀⠁⡟⣟⣲⣂⣃⠐⣀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⣮⡷⣷⣳⣟⣿ ⣿⣿⠨⠀⠀⠀⣿⣿⠳⢴⢧⣿⠨⠁⠎⣤⢷⡔⢷⠉⠀⠀⠀⠀⠀⣕⡿⣟⣿⣺ ⣿⢿⠐⠀⠀⠃⣺⣿⣝⡘⣿⣿⢴⡄⢀⣀⣀⠀⠀⣷⢿⠘⠀⠀⠀⡀⡀⣷⣻⣝ ⣇⣿⢐⠀⠀⡇⠺⣿⡿⡇⣿⢥⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠻⠀⠀⠀⠀⡀⡝⣸ ⣷⢰⠀⠀⠀⡇⣧⣿⣿⡀⣿⢻⠄⠷⡿⠐⠀⣽⣼⢀⡇⣿⢿⠈⠠⠀⠀⠀⡔⠃ ⣿⢹⠀⠀⠀⡀⣣⣿⣿⠘⣷⣿⠻⠛⠒⠐⠉⡩⢘⠃⣿⣿⣿⣮⢶⠠⠀⠀⠀⣾ ⣿⣿⠟⠀⠀⠀⠀⣂⣿⢿⡄⣿⣌⣿⠙⠟⣳⣾⠀⡿⣿⣮⣮⠒⢀⠀⠀⠁⠟⣿ ⣿⣿⣿⢛⠈⠀⠀⠀⠀⣦⢿⣈⣦⡜⣼⢆⣤⢏⣿⣿⣿⠩⣠⠀⠀⠀⠇⡿⣿⡻ ⣿⣟⣿⣜⣷⠋⠙⠀⠂⠀⡅⣭⠻⢏⠛⠟⡿⣿⣿⣿⢼⢀⠀⠀⠃⠟⡿⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⢿⠿⠿⠾⣧⢿⣿⣿⣿⣿⣿⣿⣿⢍⢘⠀⠟⡿⣿⣿⣾⣿⣿

⣀⣄⠷⣛⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠔⣀ ⠀⠀⠀⡀⣄⢦⠳⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠖⡤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣇⣦⢶⠿⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠶⡶⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⡾⢀⠀⠀⠀⠀⣀⣀⣤⢤⠶⠶⠓⠛⠛⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠋⠛⠛⠛⠛⠛⠚⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠙⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠛⠛⠒⠶⠴⡤⣤⣀⢀⠀⠀⠀⠀⡀⠳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣈⣀⣀⣌⣤⣤⣶⣽⣤⣴⣤⣤⣴⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣥⣤⣤⣤⣴⣤⣶⣤⣮⣤⣠⣤⣠⣀⣀⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠔⡠⢀⠀⠀⠇⢀⠀⠀⠀⡀⢳⠈⠀⠀⠚⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠳⠀⠀⠁⡔⢀⠀⠀⠀⡄⠘⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠔⡠⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠔⢀⠀⠀⠀⠀⠀⠀⣆⠈⠀⠀⠀⠀⠀⢄⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⡀⢄⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ 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