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