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⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠁⠀⠀⢲⣀⣀⣀⣀⣀⣀⣉⣀⣀⠀⣸⠉⠙⠲⣴⡀⠀⠀⠻⣆⠀⡀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⡏⠳⡏⠈⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⣙⣷⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⢳⡀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⡖⠋⢉⡷⠄⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠘⠇⣸⠇⠀⠀⠹⣄⠀⠀⠀⠀⡆⠀⠀⠀⢱⡀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀ ⠀⠀⢠⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢀⡀⣀⡿⡟⠀⠀⣾⣶⠀⠀⠀⠀⠀⠀⠀⠳⡀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡍⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢾⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⢀⣦⣀⠧⠀⠀⠀⠀⠀ ⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣷⣄⠀⠀⠀⠛⠒⠚⠉⠉⠉⠉⠉⠉⢉⢷⡤⠀⢾⢻⣗⣦⡀⠀⠀⠀⠀⠀⠹⣄⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣐⣏⣦⣄⣤⡴⣆⣶⣶⣶⣶⡟⠂⠀⠀⠷⠞⠆⠀⠀⠈⠈⠃⠀⠉⠉⠉⠉⠉⠉⠀⠀⣀⡤⠀⠀⠀ ⠀⠀⢼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⣸⠀⠺⣯⣷⣽⣆⠀⠀⠀⠀⠀⠘⢦⢻⡀⠀⢀⡄⡀⢠⠀⢀⣀⣠⣀⣀⣄⣈⣷⣄⣤⢴⣲⣦⣼⣒⣖⣿⣶⠦⡶⢷⠶⠟⠟⠻⠿⠁⠑⠈⠀⠀⠀⠉⠉⠉⠀⠀⠀⠁⣠⣘⢀⣡⣱⡀⠀⠀⠀⢀⣐⣀⣀⣠⣥⣥⢬⠤⠿⠽⠯⠿⠖⠒⠚⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⢷⡀⠀⠀⠀⠀⣀⠀⣀⣀⣤⠤⠤⠖⠒⢻⡭⠃⠀⢠⣿⡜⠚⢾⠦⣤⣤⣶⣶⣦⠬⣷⣷⡶⠾⠿⠿⠝⠛⠛⠛⠛⠛⠋⠛⠏⡉⡀⠉⣩⣁⣁⣉⣁⣉⣱⣤⠤⠤⠤⠤⣤⣤⣤⠤⠤⠴⠒⠒⠒⠚⠉⠉⠉⠉⠉⠉⠉⠁⠈⠁⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠣⢧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⢤⣤⡤⣴⢿⣱⣙⡦⠀⠀⠀⢉⠉⠁⠀⠀⠀⠀⠀⠀⠈⡅⣠⡼⠋⠀⠙⢦⣌⣁⣀⣈⣀⣉⣠⣤⣤⣤⣬⡴⠤⠤⠤⠒⠒⠒⠒⠚⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠈⠙⠉⠙⠋⠭⠝⠒⠛⠚⠛⠛⠋⠛⠛⠉⠉⠉⠉⢉⠑⠀⢀⣄⠀⣄⣀⣈⣧⠤⠶⠶⠗⠒⠒⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠚⠒⠲⠶⠤⠤⠴⠲⠤⠔⠒⠒⠒⠒⠚⠛⠚⠛⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠠⣄⠀⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⢡⡔⠈⠉⠁⠐⠒⠀⠱⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣵⣡⣔⣂⣈⠁⣠⣤⣤⡤⣬⡿⣧⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢂⣴⣽⣋⡟⣜⣯⣾⣮⠎⣩⠛⣩⣷⡟⠀⠀⠀⣀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢙⡅⣾⣏⡏⡟⣽⣷⣿⣽⣿⣿⣾⡿⢻⣿⣿⣶⣶⣿⣿⣿⣿⡷⠶⣤⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣪⡾⠟⠋⢙⠇⢠⣽⣿⣿⢿⡿⣟⡄⢸⣿⣿⡷⠟⠿⠿⣭⣉⠅⠲⠯⢭⣻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠁⠀⠀⡜⢻⠀⢸⡟⡾⠃⡟⠀⠙⢻⣾⣿⢿⢂⣀⠀⠀⠀⠻⣿⣶⢴⣢⣜⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡐⠪⠄⣀⠀⠀⠈⡅⠈⢄⠘⠁⠃⢀⠀⠀⡄⢸⠮⠗⠡⠸⢶⡍⠑⠂⢲⣧⣝⠿⣌⡛⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣔⡀⢀⢀⡀⠉⠒⠤⡀⠀⢪⣀⠀⠀⢈⢷⣴⣻⠋⣳⠄⠀⠀⠀⠀⣀⠀⣸⡿⣿⣿⣾⣿⣿⣿⣿⣿⢮⡉⠁⠀⠀⠀⠀ ⠀⠀⠀⢠⣃⣀⠈⠉⠑⠲⢯⡴⠢⡈⠱⣼⣦⣄⠀⢸⠙⠁⢁⠤⢷⣄⡀⠖⠉⣀⡽⠷⡟⢩⡵⣩⡧⣽⣿⣿⣿⠷⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠎⠀⠀⠹⣿⠲⣤⡀⠈⠑⢄⡩⠀⢟⣷⠦⡀⠀⡰⠁⣼⠛⠉⠀⠈⠁⢀⡀⢔⠋⣁⠜⣽⣿⣿⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡞⠀⠀⠀⠀⠻⣄⣈⣛⣑⣄⠀⠙⣦⣻⣤⠱⣔⣰⠁⠈⢿⣤⠃⠀⠀⠀⠀⡐⣡⠊⣠⠞⣯⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡘⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠙⠢⣤⡸⣿⠉⠀⢆⢙⢄⠀⣰⢬⠀⠀⠀⠀⠀⠐⣛⣊⡤⠜⠁⣙⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠃⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢹⢳⠀⠈⡄⠳⣯⡤⢼⠃⠀⠀⠀⢰⠚⠇⣍⠠⠔⢋⠜⠁⣹⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⠀⠀⡜⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢿⢀⢀⠔⣇⣠⡼⣿⡟⠁⠀⠀⠀⠙⢺⠋⠁⢀⡔⢁⠀⣰⠋⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀ ⣧⠀⠀⡇⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⢘⡮⡉⠴⣾⣣⣹⣾⡧⠔⠚⠋⠉⠑⢺⢄⣠⠊⠀⠀⢠⠃⠀⠀⠀⠳⡌⢦⠀⠀⠀⠀⠀ ⠸⡣⡄⡇⠘⢦⡀⠙⠒⠤⠀⠀⠀⠀⠀⠀⠀⢸⡧⡞⡿⢾⣲⣿⠀⠀⠀⠀⠀⠐⢿⠇⠳⡀⢀⣀⡜⠀⠀⠀⠀⠀⠘⢄⠑⠦⡀⠀⠀ ⠀⢣⠀⢡⢠⡀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⣒⡋⠱⣜⢟⢄⢿⣿⠀⠀⠀⠀⠀⢠⣾⡆⢠⣽⡟⢄⠀⠀⠀⠀⠀⠀⣠⠔⠒⠈⠉⠑⢆ ⠀⠈⣆⠈⢿⠎⡲⢤⣁⠀⠀⠀⠠⠤⠤⠒⢊⡵⠀⠈⢎⢯⢾⣿⠀⠀⠀⠀⠀⠠⣾⡄⡆⢉⡕⠁⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠘