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⠀⠰⣄⡦⣄⡆⠀⣤⢰⢠⣤⣀⣄⣀⣀⢠⣠⣤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⢎⠱⢊⠲⣰⠃⡴⢃⠭⣐⣣⡞⡡⢎⣿⠰⢌⢣⣑⠮⡐⢎⡱⡌⢣⢃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢦⡒⠚⠋⢠⠃⠀⢿⠀⡼⠀⢻⠌⠀⠀⡱⠁ ⠀⠀⠀⠀⠁⠈⠀⠀⡀⢁⠀⡈⠀⣈⡚⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⡌⠦⡙⡌⡱⣇⠞⣑⢊⠦⣽⢃⠖⣱⣯⢃⠞⣰⠞⡡⢎⡵⡪⢼⢡⢳⢂⢽⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⡘⠀⠀⠘⠀⠁⠀⠀⠀⣠⠞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⠗⠾⠲⠗⠈⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⢻⢏⠀⠀⠀⡟⡘⣌⠒⢥⡘⢴⣎⠓⣌⢎⢾⡕⠛⣳⣿⢃⠎⡼⣁⣎⣵⠟⠊⢀⠀⡇⢺⡌⢾⠀⢀⡼⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀ ⠀⠀⣄⢰⣆⣄⣀⣤⠀⠀⠀⣀⠀⡄⣆⡂⠀⡆⢀⠀⠀⠀⠀⡀⢰⠀⢀⣀⡀⠀⠀⠀⠀⠀⢳⠻⠜⠀⠀⠀⢰⡙⢔⠢⢍⠢⡜⣸⠆⢭⢞⡎⡟⠀⢠⣿⠇⢎⣞⠕⠊⣥⣄⣑⣤⡉⠀⣏⢼⡌⣽⡴⠯⠤⣧⢡⠆⠀⠀⠀⠀⡆⢀⠀⠀⢀⣈⢦⡀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀ ⠀⠀⠙⠋⠉⠑⠁⠑⠀⡹⠉⠉⠀⠑⠉⠈⠙⠛⠈⠉⣘⡃⠀⠛⠚⠉⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢌⠢⡍⢆⢓⡰⡇⢎⡏⣼⠒⢷⣠⢻⡋⡼⠊⠀⠀⠀⠹⠀⠀⣨⠛⠒⣇⢺⡇⣇⣁⣀⠀⠸⡎⣦⠀⠀⡀⢰⡟⠌⢄⡴⡋⢀⡦⢝⠦⠤⢤⡜⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⡀⠀⣀⡀⠀⡄⠄⠀⠀⣀⣀⠀⢤⢄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⢀⡾⡑⣊⠱⡘⡌⢆⣱⡭⡓⢬⢇⠚⣼⢋⡾⡱⠁⠀⠀⠀⠀⠀⠉⠐⠃⠀⢰⡧⡏⣿⠉⢠⢟⡟⠄⠙⣞⢤⣰⣡⣏⣱⡈⠑⣥⢌⢟⣀⡜⠒⣺⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠛⠂⠃⠈⠛⠙⠛⠛⠚⠂⠙⠘⠋⠲⠙⠛⠀⠸⠀⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⢳⡿⠀⣠⢋⠦⡑⠬⡑⡜⣠⢃⡷⣡⡳⢋⢆⣹⠇⢎⡳⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢿⡑⡇⠈⠁⢉⠱⠀⠀⢃⣟⠟⠻⣻⠍⣿⣇⠸⡈⢪⡀⣱⠞⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⢠⡠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⠤⣚⣤⠷⠒⠛⠒⠳⢮⣤⡋⢦⠵⣱⡭⠞⡝⡸⡼⠁⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⣠⠋⠘⠶⠄⠸⠀⠀⠀⠈⠦⠀⠉⠒⢠⠇⠙⢒⠽⢿⣿⠋⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀ ⠀⠀⠀⠘⠊⠖⢆⢶⠻⠍⠻⠿⠆⠘⡖⠚⠃⠰⠦⠛⠛⠷⠶⠀⠶⠖⠻⠇⠀⣷⡇⠸⣡⢔⣧⠿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣿⡗⠋⠁⠀⡸⠰⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠏⣔⡠⡌⡘⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⡸⠀⠀⢸⣴⠟⠁⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⡰ 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⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠖⠁⠛⠎⠙⠛⠋⠇⠰⠛⠢⠙⠲⠀⠼⠄⠘⠳⠶⠙⠳⠀⢹⠛⠛⢳⠀⠰⠄⠘⠓⠶⠋⠻⠄⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠉⠑⡒⠪⠴⠄⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⡄⣊⡬⠒⢹⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣵⢢⢌⡀⢀⡀⠀⠰⠉⠉⠐⠒⢒⡒⡂⠧⠔⠤⠬⡳⣄⣐⣶⠖⠋⢁⣠⡞⠁⠘⣅⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦⠶⠿⠃⠀⠗⠾⠾⢸⡐⠶⢄⠴⡄⢸⠕⠾⠾⠇⡴⡄⢀⣇⠀⠶⣤⡰⠦⡄⠐⡶⠶⠾⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠈⠳⡲⠤⣀⡀⠀⣔⠄⠀⠉⠀⢀⠀⠀⠁⠳⠟⠻⢟⡀⢐⡞⠁⠈⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡳⡀⠀⠀⠀⠁⠊⠭⠉⠒⠒⠢⠤⠥⢂⣀⣀⠀⠀⢔⡀⠀⣽⠁⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣀⣴⢡⣼⠰⡦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠑⠋⠝⠦⣄⠀⢪⡧⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⡧⢪⠀⣄⠦⠝⠋⠑⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡦⠰⣼⢡⣴⣀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠁⣽⠀⡀⢔⠀⠀⣀⣀⢂⠥⠤⠢⠒⠒⠉⠭⠊⠁⠀⠀⠀⡀⡳⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠈⠁⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠈⠁⡞⢐⡀⢟⠻⠟⠳⠁⠀⠀⢀⠀⠉⠀⠄⣔⠀⡀⣀⠤⡲⠳⠈⡈⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠟⠾⠶⡶⠐⡄⠦⡰⣤⠶⠀⣇⢀⡄⡴⠇⠾⠾⠕⢸⡄⠴⢄⠶⡐⢸⠾⠾⠗⠀⠃⠿⠶⡦⠐⠀⠀⠀⠀⠀⠀⠀⠀⣅⠘⠁⡞⣠⢁⠋⠖⣶⣐⣄⡳⠬⠤⠔⠧⡂⡒⢒⠒⠐⠉⠉⠰⠀⡀⢀⡀⢌⢢⣵⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢹⠒⡬⣊⡄⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠄⠴⠪⡒⠑⠉⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⠀ ⠀⠄⠻⠋⠶⠓⠘⠄⠰⠀⢳⠛⠛⢹⠀⠳⠙⠶⠳⠘⠄⠼⠀⠲⠙⠢⠛⠰⠇⠋⠛⠙⠎⠛⠁⠖⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⡦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⣀⠀⡀⠀⠀⣰⠀⠀⢰⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢣⠀⠀⠀⠎⠀⠀⠀⠀⠄⡮⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⠉⠀⠙⠙⠁⠉⠈⠉⠈⠁⠈⠂⠊⠉⠀⠈⠀⠸⠁⠈⠘⠉⠈⠘⠆⣉⠹⠉⠂⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡆⣶⠀⠀⠀⠀⢆⠈⠀⢸⠘⠁⠀⠁⠋⢤⣏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣘⣀⣀⡀⣤⣀⣀⣃⠀⠄⣤⠰⣀⢀⢣⢠⡀⣀⢰⣤⡀⣀⢆⢀⠀⢀⠀⣀⣀⣰⡠⣠⣗⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠃⠀⠀⢆⠈⢸⢹⢼⡵⢀⡇⠀⣿⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠘⠀⠀⠂⡿⠀⣾⣼⠀⠀⠁⢞⣼⢰⢰⡁⠸⡇⠀⣎⡀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠊⠤⢀⠃⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⢠⡀⢖⠖⣖⡰⣄⠀⡆⣴⢠⠇⠈⡀⢸⡂⣰⡤⣤⠀⣇⡶⡖⢠⣧⠀⠖⣶⣤⠀⢹⠀⠀⠁⠋⣼⠀⠀⠁⣞⣀⠀⠀⠁⠊⠴⣀⠀⠃⠂⡆⢈⡄⡧⠀⢀⠀⡀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠊⠔⡠⢀⠀⠁⠐⡧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⡀⣀⠀⠀⠀⠀⣀⠀⢀⠁⡿⢂⢸⠀⠁⡶⢀⠀⠋⠔⢀⠈⠀⠀⠀⠀⠠⠀⡄⠱⠀⡀⠑⠀⠀⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⠔⡠⣀⠀⠀⠁⠂⠠⢀⠀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠄⠀⢇⡴⠖⠧⠞⠃⠖⠐⠄⠿⠹⠛⠖⠰⠁⠛⠾⠶⢰⡀⣤⠗⠄⠸⠀⠀⡀⠱⡆⣹⢌⢸⠀⡇⢡⠚⡠⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢣⠈⠀⠀⠀⠀⡀⢢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢰⠀⠀⠀⠀⠀⠀⠀⠁⠒⣤⣁⣰⣀⣀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠠⢄⢠⠀⢠⠀⠀⠤⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⠀⠀⡇⣸⢻⠤⢹⠚⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠙⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠁⠉⠂⠀⠀⠀⡀⠀⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀ ⠀⠁⠁⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⢞⢴⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢢⠈⠀⠀⠀⠀⠀⣄⠲⠙⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢀⣀⠀⡀⠼⠘⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀ ⡏⡏⣀⠁⢸⣼⣻⢿⡾⣋⢾⠀⠀⠀⡞⣦⠸⠀⠀⠀⠀⠁⠃⠋⠴⠓⠀⠀⠀⠀⠋⠔⠠⣉⠔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⠈⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠋⡼⢀⠀⠀⠀⠀⡇⡔⢿⠙⠉⠂⠓⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⡆⠀⣀⠀⣀⣀⠀⣄⣤⢀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⡗⡧⣤⣀⣞⠀⠀⠋⡱⠈⢄⠶⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠙⠀⠀⠀⠀⠀⠀⡀⢦⠙⠁⠋⡾⣧⠈⠀⠀⠀⠀⠁⡇⠡⣗⡆⠼⠊⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⣿⠀⠁⠀⠀⡆⡄⠀⡄⠀⠀⡟⢀⡄⡲⠤⠒⡙⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⠀⠀⠀⠀⠀⠀⠀⡀⣦⢙⡐⠢⢻⠀⠀⠈⠕⢂⡜⡙⡧⢃⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠙⠀⡞⠀⠀⠀⠀⠀⠸⢸⠀⣿⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⢍⠯⠤⠤⠤⠤⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡄⢷⠢⢻⠀⠀⠠⠈⠋⢎⠡⡼⠳⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢾⠸⡇⡿⢸⠃⢸⠀⠀⠀⠀⠀⢽⢸⠀⣿⠏⣺⠀⠀⠀⠀⠀⠀⠀⡄⠳⡉⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠚⠒⠒⠶⠴⠤⣤⢣⠈⠀⠀⠀⠀⠀⠀⠀⠀⢫⣗⣀⠤⡓⠟⣻⠤⢋⡤⠘⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⢸⢹⡏⣧⢼⣧⢠⠀⠀⠀⠀⠀⣤⢸⠀⣿⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠿⣿⣿⣿⣿⣿⠿⠙⠀⠀⠀⠀⠀⢏⠑⠈⠀⠀⠀⠀⠀⠁⣿⡈⠁⠟⣷⣼⠒⢎⢁⡴⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢨⣷⡇⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⢰⠀⡄⠀⠀⠀⠟⢸⠤⠒⠁⠈⠉⠜⣲⠐⠀⠂⠐⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠒⠅⡫⢛⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠃⢠⠀⣄⠢⠀⠀⠀⠀⡟⣸⣿⣶⣫⡷⣱⢌⠱⣡⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⢠⡄⡠⠀⣄⢰⠀⠀⠀⠀⠀⠁⠉⠉⠉⠂⠒⠒⡖⣴⢸⠀⠀⠀⠀⣑⠀⠄⠂⠄⠀⠀⡠⠒⠀⠉⠀⠠⠀⠀⠥⠤⠀⡁⣀⠀⠀⠁⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣰⠀⠀⠀⠀⠀⠀⠀⡿⣴⡏⣱⢞⢣⣹⠤⡘⡱⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠒⠐⠤⠤⡠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⢀⠠⠐⠁⠈⠀⠀⠀⠀⠒⢅⠑⠀⠠⠂⡁⠢⠈⠄⡀⢀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⡞⣿⡤⡟⡄⠟⢤⠋⣠⠞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠂⠀⠀⠀⠁⠟⠺⠕⠀⠒⠀⠀⡈⢄⠐⠀⠀⡀⡠⠲⠑⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⡟⣷⢨⢱⢺⣡⠲⣅⠚⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⡇⠀⠀⠁⣿⣿⢸⠀⣀⠠⠈⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⢀⣧⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⡿⡄⡏⣄⡈⠼⣀⠀⠀⡁⠌⢠⡇⣸⣤⠀⡼⣠⢿⠸⠀⠀⠀⠀⠀⠀ ⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⠈⠉⠉⠉⠁⡍⠉⠏⣿⣿⣿⢹⠀⠀⠀⠀⢄⠢⠁⠀⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡖⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⡟⣽⠇⢱⢣⣹⢖⡠⠀⠀⠀⠀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀ 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