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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠤⠤⠤⠔⠒⠢⣄⡀⠀⠀⠀⠀ ⠀⣠⣤⠤⠐⠒⠒⠂⠒⠊⠉⠉⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⡀⠀⠀ ⠀⡇⠈⠁⠉⠙⠢⠄⠠⣄⡀⠀⢀⡀⠤⠒⠒⠤⠔⠋⠉⠑⠚⠉⠈⡉⠉⢀⠝⠀⠀ ⠀⡼⠀⠀⠀⠀⠀⣀⡀⠘⡀⢦⠀⠀⡀⠀⢠⠀⠀⢠⠀⠀⠀⠀⠼⠇⢀⠇⠀⠀⠀ ⠀⡇⠀⠀⠀⠠⣾⠿⠃⡜⠀⠀⡳⠔⠋⠉⠓⢤⡴⠚⠙⠓⢶⠀⠀⡠⠞⠀⠀⠀⠀ ⢀⠇⢀⣤⠀⠀⠀⠀⠀⢱⠀⢸⠁⠀⣰⣿⣿⡆⢱⢀⣶⣿⡆⣧⢸⠀⠀⠀⠀⠀⠀ ⢸⠀⠘⠁⠀⠀⠀⠀⢰⠉⠇⢸⡀⠀⠻⣿⡿⠃⣸⠘⣿⡿⢃⣇⠜⠀⠀⠀⠀⠀⠀ ⢨⠀⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⠑⠤⣀⣀⡠⢞⣩⣗⠒⠚⠁⣇⠀⠀⠀⠀⠀⠀⠀ ⢎⠀⠀⠀⣠⣾⡿⢠⡋⠀⠀⠈⠀⠀⡀⠀⠀⠀⠙⢦⣀⣀⣸⠟⠀⠀⠀⠀⠀⠀⠀ ⣸⠀⠀⠀⠛⠋⠁⠀⡗⠀⠀⠐⠊⢩⡏⠉⠙⣷⣒⣋⣏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⢣⠀⠀⠀⠀⠀⠀⢸⠀⠤⠀⠀⠀⠨⣍⣉⠽⠁⠀⠤⢿⡀⣜⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠐⠛⢀⣀⣀⣀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠿⢶⣾⡍⢲⠀⠀⠀⠀⠀⠀ ⠱⢤⣀⢸⠀⠀⠈⠙⢲⣄⡤⢴⢠⣤⣴⣾⡟⣻⣏⣀⣤⣼⣿⣽⢏⠀⠀⠀⠀⠀⠀ ⠀⢸⠤⣝⣆⠀⠀⡴⣍⣉⣑⣺⢛⡚⠻⠿⠿⠿⢿⣿⣿⣿⣁⣨⠟⠙⣦⣄⣀⡀⠀ ⠀⠸⣦⣿⣿⣷⣶⣦⣿⣿⢿⡍⠛⣛⣿⣿⣷⣶⣿⡿⠂⠠⠤⢅⠀⣐⢮⡳⢾⠃⠀ ⠀⠀⠈⠙⠛⢷⣼⣇⣠⠤⢾⠛⠋⠉⠈⠛⡟⡟⠋⠀⠀⠀⠀⠀⠑⢌⡢⣝⠢⣵⡆ ⠀⠀⠀⠀⠀⠘⠻⠿⡿⡷⠛⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣤⣇⣇⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡇⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣟⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣷⣷⣤⡾⣿⣷⣄⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠿⠯⣭⣉⡉⠁⠀⠐⠒⠛⠛⠒⠒⠒⠒⠒⣲⠂ ⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀ ⠀⢀⣴⡯⠴⠒⠚⠛⠛⠉⠉⠙⠛⠓⠲⠤⣄⠈⢳⡄⠀⠀⠀⢴⡋⠀⠀⠀ ⢀⡾⠉⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢈⠑⢆⣳⠀⠀⠀⠀⠙⢄⠀⠀ ⣼⠁⠀⡈⠀⠀⠀⢀⡼⠁⠀⠀⠀⢀⡤⠖⢻⠀⠀⠹⠀⠀⠀⠀⠀⠈⢳⡀ ⣿⠀⢰⠁⠀⠀⢠⢻⠁⠀⠀⣠⠖⣉⣀⡄⠘⡇⠀⠀⣠⡀⠀⠀⢹⠛⠒⠻ ⣿⠀⡏⠀⠀⣰⠃⡇⠀⡠⠚⠋⠁⠀⠀⠁⠀⢷⠀⢸⠀⢻⠀⠀⠀⢳⡀⠀ ⢸⡄⡧⣤⣴⡧⢼⢠⠞⠀⢠⠤⢖⢒⠛⡻⠛⢹⡀⠀⡇⠀⡇⢀⡀⠀⢧⠀ ⠀⢿⡇⢰⡓⠨⢹⠃⠀⠀⠀⠀⠀⠁⠉⠀⠀⠈⡇⠀⡧⠞⠁⠀⡏⠳⢼⠀ ⠀⠈⣇⡟⣇⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⣰⡇⠀⠁⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠿⡇⠈⠲⣄⠀⢀⣀⡀⠀⠀⠀⣀⡤⡾⠁⡇⠀⠀⠀⠀⢠⡇⠀⠀⠀ ⠀⠀⠀⣧⢰⠀⠀⢳⣌⠀⣈⡤⠖⠋⠁⠀⡇⠀⣇⠀⡄⠀⠀⣼⠁⠀⠀⠀ ⠀⠀⠀⢸⣸⠀⠀⢸⣘⡯⢽⠇⠀⠀⠀⠘⡗⢤⡏⢸⡇⠀⣰⠇⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⡆⠀⡟⠉⠲⡞⠀⠀⠀⠀⣠⠽⠒⣧⢿⠇⣰⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢿⢳⢠⠗⢄⠀⠹⡄⠀⠀⣰⠃⠀⢰⠟⡾⣰⠛⢦⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠊⢿⠀⠀⠑⢄⠙⣄⣰⠃⢀⠔⠁⠠⠟⠁⠀⠈⣇⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠉⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠁⣰⣿⣿⣿⡿⠿⠻⠿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠀⣴⣿⣿⣿⠉⠀⠀⠀⠀⠀⠈⢻⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣼⣿⣿⡏⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀ ⠀⠀⢰⣿⣿⡿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⠁⠀⠀ ⠀⠀⣿⣿⣿⠁⣿⣿⣿⡇⠀⠀⠻⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⢰⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⢸⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⢉⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣇⠀⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⢸⣿⣿⣿⣷⣦⠀⠀⠀ ⠀⠀⢻⣿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀⠀⠉⠉⠻⣿⣿⡇⠀⠀ ⠀⠀⠀⠛⠿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠈⠹⣿⣿⣇⣀⠀⣠⣾⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠛⠋⠉⠉⠁⠀⠀ඞඞ ඞ ඞ
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⢋⣉⠠⠀⠀⠀⠉⣉⡴⠖⢢⠈⠳⣄⠙⠲⠦⣀⡀⠈⠉⠛⠶⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠛⢁⡤⠞⠉⠀⠀⠀⣠⠴⠛⠀⢀⡴⠃⠀⠀⠘⢆⠀⠀⠀⠉⠳⢤⣀⠀⠀⠉⠳⣦⡀⠀⠀⠀ ⠀⠀⠀⢠⡾⠋⢠⡜⠋⠀⠀⠀⠀⡠⠞⠁⠀⠀⢀⡞⠁⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠈⠓⢦⣄⠀⠈⠻⣆⠀⠀ ⠀⠀⣰⡏⠀⡴⠋⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠹⣧⠀ ⠀⣰⠏⢀⡼⠁⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⢹⡆ ⠀⡟⠀⡾⠁⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣿ ⣼⠇⢰⠇⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿ ⣿⠀⣿⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣀⣀⣀⣀⣀⣀⣄⣤⣤⣾⣤⡿ ⣿⠀⣿⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⠋⠈⠀ ⣿⠀⢿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀ ⠛⠓⠚⠛⠒⠒⠒⠶⢶⣖⠲⠶⠶⠶⠶⠶⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⢤⡈⠛⠶⠤⣤⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⣄⠉⢹⡀⠀⢿⣿⣿⣿⣿⣿⣿⡿⣿⡏⠙⠻⣿⡿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠋⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠤⣤⡟⠀⠀⠀⠀⠀⠸⡿⢦⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⣀⢀⣠⡤⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣷⠈⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠋⠁⠀⠀⢀⣠⣤⠴⢶⡶⠒⠒⠒⡿⠀⠀⠀⠀⠀⠀⠀⢻⡀⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⣈⣤⣧⠶⠟⢻⠁⠀⠀⣼⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠁⠀⠀⠀⣸⡇⠀⢀⡏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡿⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⡇⠀⢸⠃⡄⠀⠀⡈⢿⡀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⠀⣿⢰⡇⠀⠀⠀⠈⠛⠲⠤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⣀⣿⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢹⡿⣿⣟⡟⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢿⠟⣾⠟⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢰⠀⠁⠀⢸⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⣼⠀⠀⠀⢸⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⢰⡇⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⡇⠀⠀⠀⠘⡇⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣸⠀⠀⠀⠀⠀⣿⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡿⠀⠀⠀⠀⠀⣿⡄⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡆⠁⠀⠀⠀⠀⣀⣴⣾⣿⣿⣷⣶⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⠀⠀⠀⠀⣼⣿⣿⣿⠿⠟⠛⢛⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣄⢀⢻⠀⠀⠀⠀⣿⡟⠉⠀⠀⠀⠀⢈⣄⣱⣀⠀⠀⢀⡀⣀⢀⠀⠀⠀⠀ ⠉⠉⢸⢸⢸⠀⠀⠀⠀⠹⡇⢀⢤⣤⡴⠺⡟⠿⠻⢹⡄⠀⢨⡏⣞⢱⠃⠀⠀⠀ ⠀⠀⡌⢸⡌⠀⠀⠀⠂⢰⣻⠐⠛⠛⡡⢄⣙⠶⡤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⣸⡇⠀⠀⠀⠀⠈⢧⣷⡐⢬⣤⠾⠽⢓⡇⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⣿⡟⡽⣻⠗⠀⠀⠀⠐⢧⠈⠉⠀⠭⠜⣀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠀⣿⡏⠃⠘⠀⠀⠀⠀⠀⠸⡄⢄⢤⣤⣤⣿⣽⡿⠉⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠛⠛⠉⠭⠴⠶⠶⠶⢖⡶⢺⠀⠀⠉⢁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣲⣯⣝⣫⣿⣾⣿⣿⣶⣶⣷⣶⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⢟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠛⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠏⠙⠻⣿⣿⢟⢿⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠷⣄⡀⢠⣿⣿⣿⣿⠈⠉⠁⠈⢿⣿⣿⡟⣥⡀⣠⡿⠿⣿⣎⢿⣿⣷⣿⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡏⡹⠋⠉⠀⠀⠀⠀⠙⠾⢿⣿⣿⣿⣴⣾⣷⡿⠻⣿⣿⣧⣹⣿⠻⣿⡀⣹⣾⣾⡟⠋⠛⢿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢿⣳⡀⢻⣏⢻⣧⣿⡄⣿⡿⠋⠃⠉⠉⠄⠀⠈⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠹⣿⣷⣾⠿⠷⣾⣿⣿⣿⣬⣟⠛⢀⠂⢀⠀⣀⣥⡄⠀⠈⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢷⢿⣷⡹⣿⣿⣶⣶⣆⣼⣿⣽⣿⣯⣶⣲⣶⣿⣧⣿⣿⣿⡀⣰⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⡼⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣠⡶⠿⠿⠽⠀⠀⠀⠀⠈⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣤⢴⡒⠀⠀⠀⠀⠀⠀⠀⣠⠟⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⢀⣢⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡷⣿⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠙⠆ ⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⣤⣈⡻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣆⠈⠻⢮⣙⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠻⡔⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⡟⣼⡟⠀⠀ ⠀⠀⢸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠻⡄⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣼⣽⠃⠀⢠⢰⣿⣿⣿⣿⣿⣿⣿⣟⣼⣫⡿⠃⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣦⣀⣀⠀⠀⠀⠀⢀⣀⣤⡤⠖⠒⠋⢙⡟⠁⢊⠟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⢿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣯⠳⣤⡀⠀⠈⠻⣏⡀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿⣿⠟⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣧⣀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣄⡉⠁⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⡟⢳⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⢰⣿⣿⣿⣿⢿⣿⡏⠻⣟⡛⠀⠹⠦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢻⣿⢿⣿⣿⢿⣿⣿⣿⢙⣿⣦⣀⠀⠀⠀⠀⢀⣤⠞⠉⠀⢀⣼⣿⣿⣿⣿⢾⣿⣿⡄⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢨⡏⢸⣿⣿⣾⢻⣿⣿⣟⡿⢿⡍⠳⣤⡤⠞⠋⠀⠀⣀⣴⣾⣿⡯⠻⡿⢿⣣⠝⣯⡙⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣠⢾⣿⡿⠗⠃⣿⡟⠉⠀⡏⣿⣾⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⡏⠀⠓⠈⠻⣍⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣦⣀⠈⠉⠉⠀⠀⠈⠑⠁⠀⠀⢠⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣴⣾⣿⠋⠈⠻⠿⢿⣿⠿⣿⠿⠿⠛⠉⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣴⣿⣾⠁⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⠖⠚⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠱⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠛⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⣿⣿⠷⣄⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⢿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠋⠀⠈⢷⠀⠀⠀