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

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⠀⠀⠀⠏⣿⢸⠀⠀⠀⠀⠀⠀⡿⢿⠀⠀⠀⠀⠀⠀⡇⣿⠹⠀⠀⠀ ⠀⠀⠃⣿⣼⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣧⣿⠘⠀⠀ ⠀⠀⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⣿⢿⠀⠀ ⠀⠇⣿⢰⠀⠀⠀⠀⠀⠁⠟⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⡆⣿⠸⠀ ⠀⣿⣿⠀⠀⠀⠀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⣿⣿⠀ ⠁⣿⣸⠀⠉⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⠈⠀⣇⣿⠀ ⡇⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⢸ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸ ⡀⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣀⣄⣤⣤⣤⣤⣤⣦⣶⣷⣿⣿⣿⢀ ⠀⡄⣿⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⢠⠀ ⠀⠀⡄⣿⢻⠈⠀⠀⠀⠀⠀⠀⠇⠸⠀⠀⠀⠀⠀⠀⠁⡟⣿⢠⠀⠀ ⠀⠀⠀⡄⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢠⠀⠀⠀ ⠀⠀⠀⠀⣆⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣰⠀⠀⠀⠀

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