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