⠀⠀⠀⠃⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠆⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢷⣤⣬⣷⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢙⢿⣧⢄⣀⡀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⣀⣤⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⠝⠳⠾⡿⢿⣋⠵⣿⣿⣛⣟⡿⣿⣿⡗⠖⠲⣤⡄⠂⡨⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⣄⣜⠛⠋⢈⡀⢻⣿⣿⡿⠁⣭⠓⠒⢢⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠀⠀⠀⠀⢀⡔⠃⠈⠀⣀⣠⣀⡈⠃⢠⣄⣇⣁⠀⠋⢀⣀⡀⠐⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⣾⢥⣶⡆⠈⣟⣿⣿⣿⣆⠀⠹⡽⠃⢠⣾⣯⣿⢿⠂⠤⣬⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢷⠀⢹⠛⠋⣿⡰⣌⡙⠋⠑⣫⠀⠀⠀⠀⣿⠚⠛⢋⡪⣤⠞⠋⣻⠀⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⢻⣦⠀⣻⡚⣹⠕⢃⡀⠉⣷⣤⣼⣶⠎⠂⠈⣵⠀⠀⠀⠀⢸⠃⢁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣁⡀⠐⢿⣇⠂⠀⠀⠀⠻⣿⣿⠟⠀⠈⠥⠈⣁⠀⠄⠠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣧⡱⠄⢚⡿⡢⢀⢐⣶⣤⡾⠷⣀⣀⡀⠀⠠⠒⠀⠀⠒⢮⠀⠀⠀⠠⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡿⢿⣿⣮⣀⠵⠼⠡⠢⠁⠀⠀⠀⠀⠀⠀⠈⢠⣄⢀⣠⡤⠏⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡾⡾⠀⠚⠻⣿⣿⡿⣵⡦⣤⣶⣶⣤⣶⣶⣶⣶⡶⠾⣾⠟⠉⠁⠀⠀⠘⠮⡀⠀⠀⠀⠀⠀⠀ ⠀⢀⠾⣹⠷⢄⠀⠜⠺⡯⣇⡛⠷⣿⣿⣿⣿⣿⣾⣿⣦⡤⣄⡀⠠⢀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀ ⠀⢸⠁⠉⠑⠢⢍⡉⠁⠐⠿⠿⣿⣿⣿⣿⣿⣿⠿⠻⠓⠒⠘⢷⣦⠼⣥⡍⠐⠂⠀⠈⣷⠀⠀⠀⠀⠠ ⠀⢼⣜⣞⠀⠀⡀⣫⣶⡄⠀⠀⠘⠿⣿⠟⠉⠉⢳⡤⠀⠈⠀⢺⠁⠀⠈⡆⠀⣤⣒⡀⠘⡄⠀⠀⠀⠀ ⠀⢸⠋⠐⠀⡀⠃⠀⠿⣿⣶⣾⠤⣠⣴⠀⠀⠀⠈⠀⠀⠀⠀⢈⠀⠀⠀⢠⡀⠜⠁⠀⠀⣾⠀⠀⠀⠀ ⠀⢸⡁⠐⠈⠀⠀⠀⠀⠈⠹⠁⠀⠈⣾⡆⠀⠀⠀⠀⢄⠀⠀⢘⠀⠀⠀⢸⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⢧⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠈⠂⠀⢸⢀⠀⠀⠁⢠⢄⠀⠀⠀⡏⠀⠀⠀⠀ ⠀⠀⢈⣗⠀⠀⠐⠡⠈⠀⠀⡠⠐⠀⠀⠈⠁⠀⠀⠀⢠⠀⠀⡺⠂⠀⠀⠀⠁⠰⡡⠄⡾⡀⠀⠀⠀⠀ ⠀⠀⠚⠹⣷⣄⠀⣷⠄⠀⡜⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⡀⠠⣀⠀⠀⠀⠀⢠⢀⠄⠉⢆⡀⠀⠀ ⠀⠀⠀⠀⣿⣻⣿⡪⣅⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡡⠐⠉⢆⠀⡀⢀⢨⡟⡀⠐⠀⠙⢄⠀ ⠀⠀⠀⠀⢿⠈⠝⣇⠀⠙⣶⣄⣀⠀⣀⠀⢀⠀⠀⠀⠠⠤⠁⠀⠀⠐⠀⢣⣰⠃⠈⡇⠇⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⢽⠓⠀⢾⡆⠀⠉⠻⢿⣷⣷⡀⠁⢀⠀⠀⠀⠀⣄⡠⠊⣤⣦⠈⠃⠁⠀⣇⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠟⠀⣚⡇⠀⠀⠀⠀⠈⠉⠻⠶⣬⣖⣀⢰⣤⠿⠗⠛⠋⠁⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡏⡀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠆⠀⢰⠢⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⢸⢣⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡾⣵⡆⠀⠀⢸⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡏⠉⠀⠀⠈⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠄⠀⠀⠀⠀⠀⠀⣹⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⡀⡠⠀⠀⢀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠁⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡄⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣤⡶⠄⠀⠛⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠉⠉⢹⡇⠈⠙⡁⠀⠀⣾⡿⠃⠀⠀⠀⠈⠀⠈⢀⣩⣥⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⣄⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣦⣤⣄⣀⠀⠀⠀⠀⢠⣿⣛⣈⣧⣄⣤⡄⠀⠀⠋⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠈⠉⠙⣿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⢀⣀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄⠀⡄⢀⣤⣄⠀⠰⣿⣿⣿⣿⣿⡟⣛⣿⣿⣆⠀⠀⠀⢋⣿⣿⢯⣿⡧⠍⠀⠀⢀⣴⣶⣿⢿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠹⣧⢛⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠁⣀⠀⠀⠀⠀⢀⣿⣿⣇⡰⢿⣸⣿⡀⠀⠀⢸⣟⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⠸⣿⣾⡇⠛⠀⠀⣠⣿⣿⣿⣷⣾⣿⣿⠿⣿⡇⠐⠶⠶⣀⣶⠾⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠀⠀⠸⣿⣿⣼⣿⣿⣿⣿⣧⠀⣄⠀⠻⣮⣻⣿⣿⣿⣿⢋⣿⣿⠀⠀⠀⠀⢈⢱⠀⠀⠀⢰⣿⡿⢻⣿⣿⣿⣿⡇⢠⡾⠁⠀⠀⢀⣼⣿⣤⣽⡇⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀⠀⢼⣿⠿⠛⠋⠉⢹⣿⡄⠹⣿⣀⠈⠙⠛⠙⠉⠉⠉⠛⣛⣤⠀⠀⠀⠛⠀⠀⠠⠀⢸⣿⡟⠲⠿⣿⠿⣿⡴⠋⣁⣤⣤⣴⡿⠛⠉⠤⢻⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⣸⣿⠀⠀⠀⢐⡎⣯⠿⣦⡚⢋⠿⣦⠀⡀⠀⠀⠀⢰⣿⢏⡄⠀⠀⠀⢸⡆⠀⠁⢿⣿⡅⠀⠀⢀⣠⡤⠾⠛⠉⠻⠏⠁⠀⠀⠀⠘⠛⣿⡄⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⣿⣿⣆⠀⠀⠀⠹⣿⠰⢮⡍⢻⣇⣰⡆⠇⠀⠰⡶⠉⠁⣿⣿⣮⡉⠀⣠⣝⣶⣶⣾⠈⢿⡆⠀⠒⣍⡰⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⢸⣿⣳⡟⠳⠶⠶⠮⢥⡀⠒⠾⣿⠉⠀⠀⠠⡤⠀⠀⠀⣽⣿⣿⣿⣿⣯⣿⣿⣿⡉⠀⠀⠀⠀⠀⠘⢿⠟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡆⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠉⠁⠀⠀⠀⢀⣾⢻⣿⡟⠀⠤⠔⠶⠀⠰⠖⠀⠀⠻⣿⣿⣿⣿⣏⣻⣿⣿⠇⠀⠀⠘⠛⠃⠀⠈⠓⠈⢀⣐⡀⠀⠀⡄⠀⠀⠀⣿⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣽⢿⣤⣤⣦⠀⠀⠀⠛⢉⣩⣥⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠟⠋⠀⠀⠀⠉⠈⠉⠛⠁⠠⣶⡎⠉⠉⠙⠓⠈⠻⠶⢶⡿⠁⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣛⣯⡄⢶⡦⠀⠀⣠⣿⠿⣛⣭⡄⢀⡀⠀⠀⢀⣤⣤⠀⠀⣠⣌⣿⣯⡁⠀⠄⣀⠀⠀⠀⠀⠐⠛⠀⢰⡦⢤⡍⠁⠐⠂⢤⣄⣀⡈⠓⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⣇⣀⡴⢶⠛⠁⠐⢚⣿⠋⢡⡞⠁⣠⠃⣨⣾⣷⣤⣬⣶⡾⠿⠿⠧⣄⣠⣌⣀⢆⠀⠀⠀⣤⡐⠤⠀⠈⠁⠀⠀⠀⠀⠀⠙⠳⣯⠀⠀⠀⠀⠀⠀⠀⠉⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣥⣾⡿⣋⡰⠃⠀⠠⢞⣻⢃⣼⠏⠀⣰⠏⡼⠋⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠙⠛⠟⠋⠻⣦⠳⡈⠙⢢⠀⠀⠀⠀⠀⠀⢤⣴⣖⠐⠛⢦⣀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣴⢟⣷⣿⣿⣥⡄⠀⣴⣿⢣⣿⠏⠀⣸⠃⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡱⡄⠀⣀⠀⠀⢦⣄⡶⠾⢧⠀⠀⠐⢀⠈⢣⡀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣶⡿⢻⡿⠀⠀⣠⡾⣿⣯⣿⣿⣶⣿⣋⣴⢊⡄⠄⠀⠉⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⣀⠈⡄⠀⠀⠀⣷⢻⣶⡘⣷⣿⣶⡽⠇⠀⠀⠀⠀⠀⢰⣄⠀⢹⡆⠀⠀⠀⠀⠀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⣾⢿⣴⣿⠇⠀⠘⠉⠙⢶⣿⣿⣿⠟⣱⣿⣿⡟⣴⢠⣦⢠⣴⣶⣾⣶⣶⣶⣶⣦⣴⣶⣶⣾⣷⣾⣿⣿⡿⢿⣿⣿⣿⣿⣯⢿⣿⡜⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⡀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⣿⡇⣠⣿⡏⠀⠴⠆⣀⣀⠈⠀⠹⣿⣾⡻⣿⡿⢰⣿⣼⣿⡆⣿⣿⣿⣟⣻⣿⣿⣝⣯⣿⣟⢯⣽⣿⣿⡟⠛⠓⠉⠉⠈⠙⠿⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⢿⡝⢻⣾⣧⣄⡀⢠⡄⠀⠘⠛⢿⣿⣯⣍⣿⠀⠛⠛⢻⣿⣵⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣽⣿⣿⣦⣤⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⡇⠘⢂⡾⠋⡉⠛⠛⣦⠀⠈⠁⠈⠀⣈⠿⠟⠻⢿⣷⣧⣄⡛⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣢⠤⠭⢤⣶⠦⠀⠀⠘⠓⢤⣤⣀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣽⠛⢁⡉⠛⠳⠷⣦⣀⣈⠛⠛⠛⠛⠛⠉⠀⢠⢼⣿⣿⣿⣿⡛⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣯⣀⣀⠸⣿⣿⣷⣄⣀⢀⣻⡛⢉⠉⠙⠳⠦⣄⡀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀ ⠀⠀⢸⡇⠀⠈⠁⠀⠰⢀⠀⠈⠛⠷⣤⡀⠀⠀⠀⠀⠀⠹⠿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠿⠁⠋⠀⠈⠀⠀⠈⠀⠉⢻⣿⣷⣿⡿⠿⢿⣾⣷⡶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀ ⠀⠀⠀⣧⠀⢸⢀⣤⠀⠀⠀⣤⠀⠀⠲⣽⡲⣤⣀⠀⠀⠀⠀⠀⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣦⣀⠀⠀⠀⠀⠀⠈⠓⠀⢀⣸⣿⡿⠉⠀⠀⠀⠙⣿⠁⠀⠀⠀⠀⠀⣀⣤⠤⠄⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆ ⠀⠒⢤⣿⡇⢘⣾⣃⡤⠀⣤⡀⠀⡀⠀⣘⢿⣦⣽⡷⠄⠀⠀⠀⠀⠀⠘⠛⠻⢿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠘⣿⣧⠰⠀⠀⠀⠀⠀⠀⠈⠉⣿⠀⠀⠀⠀⠀⠀⢸⣶⠀⠀⠀⣴⣟⠉⠀⢀⡀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢻⣿⡿⢟⠁⠀⠀⠀⠀⠀⠶⠄⠐⠛⢿⣿⣿⡷⢀⣀⣀⠀⣴⠀⠀⠀⠈⠙⡛⠁⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠙⢿⣯⡟⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⡏⠀⠈⠙⠶⠀⠀⡀⠀⠛⠀⠰⠆⢬⣿⣿⣿⣿⣩⣭⣿⣿⣦⣤⣀⢤⣤⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠈⢗⣲⠋⠁⠀⠀⠀⠀⠀⠘⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡅⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠟⠋⠁⠉⠙⢷⡙⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠁⠀⠀⠀⢸⡄⠀⠀⠀⠀⠠⠀⣾⡟⣶⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡁⠀⠀⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠈⣇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣇⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠙⣄⠀⠀⠀⠀⣸⠀⠀⠆⠀⠀⠀⠉⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⣿⠀⣰⠇⠀⠀⠀⠀⠀⠛⡸⠿⠻⣦⡀⠀⠀⠀⠀⣀⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠿⣷⢰⣇⠀⠀⠀⠀⠀⡴⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠰⢦⠀⠀⠀⠀⠈⠉⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠱⣾⡷⢾⡁⠀⠀⠀⠀⠀⠀⠀⠹⠆⠐⣎⠻⡆⣄⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣆⢨⠀⢄⠀⠀⠀⠠⠴⠟⠀⠀⠀⠀⠀⠀⢀⡰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢀⡹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠘⠸⣦⢤⡿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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