Brawl Stars Text Art

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

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

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