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