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

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