Darlin In the Franx Emojis & Text

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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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⠀⠀⠀⠀⠀⠠⡔⠳⣴⠼⢎⣳⠘⣎⠳⣄⡘⢿⣽⣿⣿⣿⣿⣿⣧⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣿⣿⠏⠉⠉⠉⠳⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠔⠓⢦⡘⢦⢀⡍⠀⠸⡄⠒⢽⣦⣝⣿⣿⣿⣿⣿⢿⣧⣤⠬⠭⠍⠉⠉⠋⠯⠭⢿⣿⣿⣟⣿⠏⠀⠀⠀⠀⠀⢳⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠘⢷⡶⠽⠏⢹⡀⠀⠀⢻⣀⣄⡀⢉⣹⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣯⣍⣉⣒⡲⢤⣄⠀⠀⢧⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠛⠚⠷⠶⠿⢤⣖⣂⣀⣀⠀⠻⢅⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⣿⣹⣿⣿⠇⠀⠀⠀⠉⠉⠑⠻⢶⣞⡀⣀⣀⣨⣿⣄⡀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠟⠁⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⢀⡴⠋⠀⣀⣀⣙⣉⠿⢃⡴⠶⠶⠶⠶⠤⢄⣀⡀⠀⠉⠳⣄⡀⢹⡙⢯⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣰⠿⠖⠛⠉⠁⠀⠀⠘⢷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢤⣀⠙⢦⡇⠀⠳⢄⣠⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⡼⠁⠀⢀⡾⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣹⣶⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢠⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⡾⠁⠀⢠⠞⠀⠀⣠⢿⠇⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠥⠤⠤⣄⣀⣀⣀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢀⡎⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⣼⠁⠀⣰⡏⠀⢀⡜⠁⡜⠀⢰⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠈⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⡾⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢠⠃⠀⣸⡟⢀⣶⠏⠀⣰⠇⠀⣏⡇⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⢸⠁⠀⠀⢠⡏⠀⠀⠀⠀⠀⢀⡟⠀⢠⣿⣳⡟⠁⢀⡼⣿⠀⣸⢻⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⠀⢻⣣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠘⠀⠀⡾⣿⠋⠀⣠⠟⢠⡇⢰⣿⣾⡇⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣧⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡜⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢀⡴⠃⠀⢸⠀⢸⡿⣿⡗⠦⣀⢸⣻⠀⡆⠀⠀⠀⠀⠠⡄⠀⠀⢰⢠⠀⠀⠀⠇⠀⣸⣷⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡴⠋⠀⠀⠀⣸⠀⡏⣿⠀⣇⠀⠀⣻⣿⣄⡇⠀⠀⠀⠀⡇⡇⠀⠀⢸⢸⠀⠀⠀⢸⠀⢧⣯⢯⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠋⠙⣿⣿⡟⣛⠻⣿⣿⣿⣶⣿⣳⠄⣽⣿⡿⡟⠦⠀⠀⢠⣇⠇⠀⠀⢸⣼⠀⠀⠀⢸⠀⢸⢹⠸⣝⡇⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⣸⠃⠀⠀⣰⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠘⣿⡇⢿⣿⠈⠉⠿⠉⠻⣿⣥⣿⣿⣧⣇⠀⠀⠀⢸⣿⠀⠀⠀⡟⡟⠀⠀⠀⢸⠀⢸⡎⡇⢻⣳⠀⠀ ⠀⠀⠀⢀⠁⠀⠀⢀⡏⠀⢀⣞⡿⣝⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠈⠻⢬⣍⣠⣞⡃⠀⠀⠈⠛⢿⣏⢻⣹⣾⠀⠀⣸⣿⠒⠦⢼⣿⠇⠀⠀⠀⣾⠀⢸⡇⡇⠈⣿⡇⠀ ⠀⠀⠀⢀⠀⠀⠀⣸⠁⠀⣼⡼⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠈⣿⣿⠀⢠⣿⡟⠀⠀⣾⣼⠀⢸⠃⢸⡏⠀⡼⡇⡇⠀⣇⡇⠀ ⠀⠀⠄⠚⠀⠀⢠⡏⠀⢀⡏⢣⠀⣴⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⣼⣿⣷⣿⣦⣯⣿⠀⡏⠀⣼⡇⢰⡇⣧⡇⠀⢸⡇⠀ ⠀⠀⢀⠀⠀⠀⡾⠀⢀⡎⢻⡀⢢⠀⡧⡆⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠀⡿⣿⡏⡜⠀⢰⡿⠁⣾⢠⡿⣿⡀⢸⠀⠀ ⠀⠀⡸⠀⠀⣰⠃⠀⡼⠁⢸⣧⠈⢷⣧⢇⠀⠀⠀⢸⡀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠿⠶⠋⢰⢿⡟⣀⡶⣻⢇⡼⢻⡞⠁⡇⢻⡇⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⢰⠃⠀⢸⣿⠗⣤⡹⢹⡀⠀⠀⠘⡇⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⡏⠺⠻⣿⣿⠃⠈⠁⢸⡇⠀⢻⠀⢿⡄⠀ ⠀⠀⠀⠀⠞⠀⢠⡟⠀⠀⣼⡿⠀⠀⣹⢸⣇⠀⠀⠀⢳⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⣸⠇⠀⠀⠙⣿⡇⠀⠀⠸⡇⠀⢸⠀⠈⠛⡀ ⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⣿⠇⠀⠀⣿⡄⣿⡀⠀⠀⠘⣇⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠙⢶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢻⣷⠀⠀⠀⣇⠀⢸⠀⠀⠐⡁ ⠀⠀⠀⠀⠀⢰⠃⠀⠀⢠⡟⠀⠀⢀⣿⡇⢻⣧⠀⠀⠀⠹⡆⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠹⡝⢻⣽⣷⠖⠂⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢸⠀⢸⠀⠀⠀⠁ ⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⠃⠀⠀⢸⠃⢹⡈⣿⣧⠀⠀⠀⠹⣄⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡆⠑⢤⡄⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⠀⠀⠀⠀⢸⠀⠀⠀⡏⠀⠈⣇⢸⡏⢧⠀⠀⠀⠙⢧⡀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠻⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢠⠀⠀⠀⠀ ⠀⠀⠀⢁⠇⠀⠀⠀⠀⣸⠀⠀⣸⠃⠀⠀⣽⡆⠹⣬⣷⡀⠀⠀⠈⠻⣦⡀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢦⣀⠀⠀⠉⠉⠉⠉⠒⠲⠶⠒⠲⠾⠷⠶⠶⠦⠼⢤⣀⣀⡀ ⠀⠀⠀⡜⠀⠀⠀⠀⠀⡇⠀⢀⡟⠀⠀⢠⠏⠘⢆⠙⣌⠙⢦⣀⣠⠴⣾⣷⠶⠶⠶⠾⣿⣳⣦⣀⣀⣠⠞⢩⡿⠀⠀⠈⠙⣲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⢠⡇⠀⢸⠀⠀⠀⡞⠀⠀⠈⠳⣤⠝⠋⣩⠿⠏⠀⠀⠀⠀⠀⠀⠀⠙⠧⣀⡼⠁⢠⣿⣁⡤⠼⠶⠋⠁⠀⠈⣙⣢⣤⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚ ⠀⠀⡄⠀⠀⠀⠀⠀⢸⡇⠀⣸⠀⠀⣼⠧⠴⠶⠾⠟⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡾⠥⢄⣀⣀⣠⠤⠔⠚⢉⣠⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠇⠀⢠⠛⠀⣀⡀⢀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⣀⠟⢀⣠⠤⠖⠊⢉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⡀⡀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠉⣹⡏⣇⠀⠀⠀⠀⠈⠉⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠟⠒⠂⠀⠀⠐⢿⡇⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠀⢀⠔⠉⠀⠀⠀⠀⢀⡀⢀⣀⡘⣿⣾⠋⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠄⠀⠀⡇⠀⠀⠀⠀⠀⣿⣬⡞⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠙⢦⠟⠉⢉⠒⠛⠄⠀⠀⣀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡄⠀⢀⠂⠀⠀⠀⠀⠀⠸⣯⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⢣⡀⠀⠀⠀⣟⣆⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⢸⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⣿⠐⠐⣄⢿⠀⠀⠀⣹⡸⡀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀ ⢸⣧⡀⡞⠀⠀⠀⠀⣠⡟⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⡀⠀⢸⡇⠀⠀⣿⣰⡄⠹⣾⠀⠀⠀⢸⢳⣧⠀⠀⠀⡀⠀⠘⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⡇⠀⠀⢀⡜⡹⢠⠀⠀⠀⢸⡄⠀⢸⠀⡇⠀⡇⠀⢼⣿⠂⠀⡋⢻⣷⡀⢹⡇⠀⠀⢸⣆⠻⠀⡀⠀⢱⠀⢀⢣⠀⠀⠀⠀⠀⠀ ⠹⣿⣿⠃⠀⠀⡜⠠⢻⡏⠀⠀⠀⢶⣽⠀⢸⠀⢸⣧⣷⠀⢀⣯⣧⣤⣧⣾⡆⠱⣄⡧⠀⠀⠈⣟⣦⡆⢇⠀⠀⠃⠈⢞⡆⠀⠀⠀⠀⠀ ⠀⢻⣿⠀⠀⣼⠀⢨⠛⠇⠀⠀⠀⣸⣿⡄⢸⠀⢸⢿⣿⣶⣿⢿⣿⣿⣿⢿⡿⡶⢹⠁⠀⠀⠀⣿⣝⣿⣾⠀⠀⠸⡀⠈⢿⡄⠀⠠⣶⣾ ⠀⠈⡯⠀⠀⠇⠀⢸⢠⡆⠀⠀⠀⣿⠹⣧⢸⣶⣸⠈⢿⠉⠀⠀⢁⠛⠛⢸⠕⠀⠸⡄⠀⠀⠀⣿⣿⣭⣻⠀⠀⠀⡇⠀⠈⢷⠀⢀⡹⣿ ⠀⠀⠁⠀⠀⠀⠀⢸⠸⡇⣦⠀⠀⣿⡿⣿⣿⡟⠯⠃⠀⠁⠀⠀⠨⠶⠖⠋⠀⠀⠀⡇⠀⠀⠀⣿⠣⡀⢿⠆⠀⠀⢀⠀⡀⠈⢿⠗⠊⠉ ⠀⠀⠀⠀⠀⠃⠀⠘⡄⣧⣿⣆⠀⣿⡀⢛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⣇⠀⠀⣸⠀⠀⠀⢸⣄⡇⠀⠈⢇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⣾⣿⣧⣸⣇⢸⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡼⠋⣰⡟⠀⠀⠀⠘⣿⠁⠀⢀⢸⣤⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠁⢻⣿⣿⡆⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣿⣾⣿⠃⠀⡸⠀⢰⣿⠀⠀⣜⣸⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡆⢸⣿⠇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⠃⠀⢠⠃⠀⣜⠇⠀⣰⣿⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠁⢸⡟⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢠⠀⣿⠃⠀⢀⠎⠀⢠⡏⡇⣰⡟⢩⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⡆⢸⠃⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢺⡇⠀⢈⠀⠃⢠⠄⡜⠀⢠⢮⠃⣷⠏⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⡇⠈⠁⠀⠀⢸⣿⡿⣷⣤⡀⠀⠀⠀⠀⣠⣴⠟⠁⠀⣿⠃⠀⡆⠀⣼⠏⡸⠀⢠⠋⡼⢀⡏⠀⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠃⢸⠀⠀⠀⢸⣿⣇⣿⣿⣿⣶⣤⣶⣿⣿⡁⢀⡠⢾⣿⠀⢠⠁⢠⡏⢠⠁⠀⢁⣼⡇⢸⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡹⠀⠀⠀⠀⠀⡈⠀⠀⠀⣼⣿⣿⢿⣧⣿⣿⣿⣿⡿⠟⠋⠁⡠⢺⡇⠀⠘⠀⣸⢀⠃⠀⠀⣾⠏⠁⠸⠀⠀⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣿⠟⣼⢟⡻⠛⠉⠀⠀⠀⡠⠊⠀⣸⠀⠀⡆⠀⣇⠏⠀⣠⣾⡟⠀⠀⡆⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣹⠏⡜⢡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠸⠀⢰⡏⠀⢠⣿⠿⢷⠄⢰⠧⢄⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣿⠊⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠃⠀⣜⠀⣰⡟⠁⠀⠀⠀⠃⠀⠀⢘⠟⠁⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢍⠙⠛⠿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠋⣡⢀⣀⣀⣀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠙⠻⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢻⣅⡴⠋⠀⠀⠀⠀⠀⠀⠉⢹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠘⡯⠒⠊⠉⠉⠉⠉⠉⠉⠒⢤⣻⣧⠟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠛⠢⣈⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀ ⠀⠀⢀⣾⡿⠃⠀⠀⠀⠰⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡆⠈⢣⡀⠀⠀⠀⠀⠘⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀ ⠀⠀⣾⡿⠁⠀⠀⠀⠀⣠⡀⣻⠀⡀⠀⢠⡇⢀⠀⠀⢸⡀⡀⠀⣸⣀⠀⡇⠀⠀⢀⠀⠀⡄⠀⠀⢻⢆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀ ⠀⣸⣿⠁⠀⠀⠀⠀⢰⠋⠁⠀⡀⢳⠀⠀⡇⠘⡄⠀⢨⠁⡇⠀⣿⢯⣆⠃⠀⠀⢀⠠⡀⡄⡀⠀⠈⣎⢆⠀⠀⠀⠀⠀⠀⢀⡄⢿⣷⠀ ⢠⣿⡏⠀⠀⠀⠀⠀⢸⢠⠀⠀⡇⣼⣇⠀⣿⠀⣇⠤⣼⢲⡗⠀⣟⠀⢻⡇⠀⠀⡄⢀⣷⡇⠘⡄⠀⠘⣆⢧⠀⠀⠀⠀⣴⣿⡟⠘⣿⣧ ⣸⣿⠀⠀⠀⣀⣀⣀⣐⣾⣇⡆⢱⣼⣿⡁⢹⡈⡇⠀⣿⣾⡿⣶⢾⣶⠼⠀⠀⠀⡇⢘⢻⡇⢀⢰⡀⠀⠈⢿⡇⠀⣀⣠⣿⣿⡇⠀⣿⣿ ⣿⣿⢀⡴⡏⠁⣶⣾⠟⣿⣿⣷⣀⣇⠙⣿⡇⠁⠉⠀⠁⠀⠵⠼⠞⠁⢰⠀⠀⢸⠀⣸⣿⡇⠈⡄⣷⠀⠀⡀⢹⠉⣉⠠⣀⡿⠃⡀⢸⣿ ⣿⣿⠋⠀⠹⣶⣿⣇⡄⣼⣿⠿⣿⣿⡀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢠⢻⣿⡇⠀⣷⠿⠀⢀⡧⠞⣉⡴⠊⠁⠀⠀⠀⢸⣿ ⣿⣿⠀⠀⡼⠉⢻⣽⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⠀⡞⣿⣷⡇⠀⢸⠖⢊⡡⠔⠋⢁⡠⠤⠒⠒⠠⢴⣿⣿ ⢹⣿⠀⡼⠀⠀⢹⡎⠉⠉⠀⠙⠘⢻⣟⠧⣀⠐⠢⠄⠠⠤⠀⠀⠀⢰⠃⢀⠇⣼⣧⡿⣿⡇⠀⢸⡖⠉⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⣿⣿ ⠘⣿⣿⡧⠤⠄⣀⣳⡀⠀⠀⣰⠀⡸⣿⠀⢈⡗⢄⠀⠀⠀⢀⣤⣶⡏⠀⡜⣰⢻⡟⠀⣸⣷⠀⠈⣿⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏ ⠀⢹⣿⡄⠀⠀⠀⠀⠙⢻⣶⣿⠏⠀⡏⠀⡸⠀⢀⣿⡶⣻⣿⡿⡽⠁⡘⣰⢃⡟⠀⠀⠙⣿⠀⠀⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀ ⠀⠀⢿⣷⡀⠀⠀⠀⢀⡜⢻⣿⠀⢸⠁⠀⠁⠀⢸⡿⣿⡟⢋⡠⠇⠚⠳⠧⣉⠀⠀⠀⠀⣇⡧⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀ ⠀⠀⠈⢿⣿⣄⡀⠀⠞⠀⢘⡇⠀⠂⢀⠆⠀⡴⠛⣩⠟⠁⡜⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⢻⢣⠈⠅⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⠀⠀ ⠀⠀⠀⠀⠻⣿⣯⠙⠒⠲⠾⡇⠀⠀⡌⠀⢸⠀⠴⠁⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠘⡏⣶⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⢀⣾⠀⠀⢸⡀⠀⠀⢀⡞⢣⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣦⣱⣹⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀⠞⡏⠀⢀⠇⠘⣄⣠⠎⢰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣿⡇⠀⠀⠀⣠⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣅⣀⣜⡠⠔⠛⠃⢠⠟⠀⢱⡀⠀⠀⠀⠀⣀⣀⣀⣸⣿⣿⢃⣠⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⣤⣄⣀⡆⠀⠀⠈⣷⡀⠠⣖⠉⠀⢀⣀⣤⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⣀⡤⠖⠒⠋⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠓⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠶⠋⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡿⢿⣧⣀⡠⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠤⣀⠀⠀⠀⣴⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣧⣾⡟⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣾⣿⣿⡇⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⣠⣾⡿⠁⢀⣠⠤⠒⠊⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠤⣄⡀⠀⠀⢹⣿⣸⠁⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠁⠀⠀⡴⠿⢈⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠘⣿⢹⢆⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⠀⢀⠎⣠⠖⢹⡾⠁⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⣜⠈⢦⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⣼⢀⠀⢀⡾⠋⠀⠀⢀⠀⠀⡀⣸⠀⠀⠀⠀⡇⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠈⠳⣈⣇⠀⢠⡀⢣⠀⠀⠀⠀ ⠀⠀⢰⠃⡼⠀⠀⠀⡀⠀⠀⡎⠀⢠⠃⡟⠀⠀⠀⢰⢡⠀⡆⠀⠀⠀⠀⠀⡆⠀⡆⠀⠀⠀⠀⠀⠀⢿⠀⠀⠘⢾⠀⠘⡇⢸⠀⠀⠀⠀ ⠀⠀⡏⢠⠃⠀⠀⢠⠃⠀⢸⠁⠀⣸⢀⠇⠀⠀⠀⣸⣸⢰⡇⠀⠀⠀⢸⢸⠃⠀⠃⠀⠀⠀⠠⠀⠀⢸⠀⠀⠀⢸⠁⠀⡇⠀⡇⠀⠀⠀ ⠀⠀⠀⠸⠀⠀⠀⡜⠀⢀⡇⠀⢀⡇⢸⠀⠀⠀⠀⡇⡇⢸⡇⠀⠀⠀⣸⡸⠀⢸⠀⠀⠀⠀⢸⢰⠀⢸⠀⠀⠀⡇⠀⠀⢧⠀⡂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡗⠀⣼⠀⢀⣾⡇⢸⠀⠀⠀⢰⣷⡇⣾⡇⠀⠀⠀⡇⡇⠀⣼⢰⠀⠀⠀⣸⢸⠀⢸⠀⠀⠀⠇⠀⠀⢸⠀⡇⠀⠀⠀ ⠀⠇⠀⠀⠀⠀⢸⠇⢰⡏⠀⡸⡟⣅⣬⣀⣀⣀⣻⣻⣇⡟⡇⠀⠀⢀⣿⠃⢀⣿⢸⠀⠀⠀⣿⡌⠀⢸⡀⡄⢰⠀⠀⠀⢸⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⢀⢿⠃⠀⣷⢃⠀⡏⠀⠀⠀⣹⡇⣿⠁⡇⠀⠀⢸⣹⠛⢻⢻⡻⠛⠓⠒⣿⣿⡀⢸⡇⡇⣿⠀⠀⠀⢸⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡾⢸⠀⢸⢹⠈⠁⡇⠀⣀⠀⣿⣿⢸⠀⡇⠀⠀⣼⡇⢀⡏⢸⡇⠀⠀⢰⣻⣿⠀⣸⣇⢿⡇⠀⠀⠀⡌⠀⡇⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⣯⠃⡎⠀⡎⡎⠀⡆⢇⠀⠀⠁⣿⣿⡆⠀⡇⠀⢠⣷⠁⡸⠁⢸⡇⠀⠀⢸⣿⢻⠀⣿⢻⢺⠀⠀⠀⠀⡇⠀⢰⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⣿⠀⡇⢀⣇⡇⠀⠧⠼⣤⣴⣄⠟⠹⠃⠀⠉⠀⠈⠟⠠⢷⣶⣚⠧⠄⠀⣿⣹⢸⠀⡇⢸⣾⠀⠀⠀⢀⡇⠀⢸⡆⠀⠀ ⢸⠀⢠⠀⠀⠀⣿⠀⠟⠛⠛⠻⠿⠿⠛⠛⠋⠁⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠈⠛⠿⠷⠶⣿⠾⣿⡿⠀⠀⡏⠀⠀⠀⢸⡇⠀⠈⢇⠀⠀ ⢸⠀⠸⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⢠⠇⠀⠀⠀⣾⡇⠀⠀⠸⡀⠀ ⠘⡄⠀⡇⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣸⠀⠀⠀⢀⣯⡇⡆⠀⠀⢧⠀ ⠀⡇⠀⢧⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡼⠀⣇⠐⡄⠈⣆ ⠀⡇⠀⢸⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢀⠞⠀⡟⡇⠀⣿⠀⠘⡄⠘ ⠀⡇⠀⠸⡄⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠛⠋⠉⠉⠉⠙⠓⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡜⠀⢰⠃⡇⠀⢿⡀⠀⢯⢆ ⠀⠁⠀⠀⡇⠀⠀⢸⡞⣆⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢰⠃⢀⡞⠀⣇⠀⢸⡇⠀⢸⡀ ⠀⠈⠀⠀⢹⠀⠀⠘⡇⠸⣧⡀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⢀⣠⣿⡇⢀⠇⢀⡾⡇⠀⢿⠀⠈⣿⡄⠀⣇ ⠀⢀⠀⠀⠸⡆⠀⠀⢳⠀⣿⢸⡷⣄⡀⠀⠀⠀⠀⠉⠀⠀⠀⠤⠖⠁⠀⠀⠀⠀⠀⣀⣴⡏⢸⡿⢀⡞⠀⡼⠀⣿⡀⠀⠀⠀⢹⣇⠀⠸ ⠀⢸⠀⠀⠀⣧⠀⠀⠘⡄⢹⡄⣿⠀⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⣿⣿⠀⢰⠃⡞⠀⢠⡇⠀⢸⢧⠀⠀⠀⠈⣿⡀⠀ ⠀⢸⠀⠀⠀⡿⡇⠀⠀⢷⢸⡇⣿⠀⠘⣇⣿⣷⣦⣄⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⣰⠿⣿⠀⡏⡜⠀⢀⡿⡇⠀⠈⣏⢦⠀⠀⠀⠸⡇⠀ ⠀⢸⠀⠀⢀⠇⢻⠀⠀⠘⣆⡇⣿⠀⠀⣿⣿⣿⣿⣿⣿⡶⢒⠖⠉⣀⣠⡤⠖⠋⠀⠀⢻⡾⡼⠁⠀⡞⠀⣷⠀⠀⠸⣌⢣⣀⣠⠤⡣⢤
⠀⠀⠀⠀⠀⠀⠈⡠⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠀⠀⢈⠻⣿⣿⣻⣿⣿ ⠀⠀⠀⠀⠀⠰⠔⠀⠀⢠⠀⠸⠀⠀⠀⠀⠀⠀⠀⢠⠀⢧⠀⢠⠡⢹⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⠄⢸⡆⠀⠄⢀⠀⠀⠀⡄⠀⠘⡄⠘⠀⠀⣦⢣⣻⣿⣿⣿ ⢀⢰⡄⠀⠀⠀⣇⡜⠀⢾⡇⠀⡇⠸⡆⡄⠀⣇⠀⠀⡇⢼⡇⡄⠁⡼⣿⣶⣿⣿ ⢸⣸⣧⠀⠀⠰⢸⠁⡌⢸⣇⠀⢿⠘⣷⡗⠀⣿⢸⢧⣧⣼⡇⡇⣄⣧⣼⣷⡻⣿ ⣜⣯⢟⡀⠀⠀⢃⣾⢤⡴⠟⢺⢿⠿⠛⠷⠘⠃⢸⠊⣿⠟⣽⠗⠻⣿⣿⣿⣧⠹ ⣿⣷⣿⣥⠀⠀⠈⢜⡀⠙⠢⠬⠬⠟⠀⠀⠀⠀⠈⠈⠉⢸⣿⡀⠀⣿⣿⣿⣿⣧ ⣿⣿⣿⣿⣧⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⡝⣧⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⣿⡗⡣⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣿⣷⠈⢧⠀⠹⢿⣿⣿ ⣿⣿⣿⣿⣷⠘⣷⡀⠀⢊⢆⠀⠀⠀⠀⠂⢉⡠⢉⠝⢿⣿⣿⣧⡀⠣⠀⠡⡻⣿ ⣿⣿⣿⣿⣿⡀⣿⣿⡄⠀⠣⠳⣤⣀⠀⠀⠀⡰⠓⢢⡄⢻⣿⣿⣷⣄⠑⠄⠑⡈ ⣿⣿⣿⣿⣿⡇⢹⣯⢮⣆⢡⠑⡙⣻⣭⢩⠉⢀⣶⣿⣷⡀⢻⣿⣿⡿⣿⣦⡀⠈ ⣟⣿⣿⣿⣿⡇⢸⣿⡜⣿⣆⠆⠐⡌⢺⣥⢶⢻⣿⣿⣿⣷⡄⢻⣿⢁⡿⡷⡀⠑ ⣿⣽⣿⣿⣿⡇⢏⠻⡇⢻⣿⣾⠀⠈⠄⠡⠙⠊⠘⣿⣿⣿⣿⡮⡇⣾⠓⡈⠪⡢ ⢻⣧⢿⣿⣿⢰⣷⡑⢼⢸⢋⢿⡆⠀⠈⢆⢩⠂⢄⡈⣟⡛⠿⠃⢻⣿⡑⢔⢄⠈
⢸⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⢸⡯⠁⠀⠀⠐⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⠀⡠⠔⠈⠉⠀⣀⡘⣧⡇⢄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣯⢎⠀⠀⠀⠈⠀⠀⠈⢞⠉⢄⠓⠀⢠⠀⠀⠀⠡⠀⠀⠀⠀⠀ ⢸⠀⡇⠀⠀⠀⡜⠁⠀⠀⠂⠀⠀⢰⠀⢸⣠⢈⡆⠀⢸⣃⠀⠀⠀⠃⠀⠀⠀⠀ ⣼⣤⠁⠀⠠⡞⠀⠀⡆⠀⠈⠀⡄⢸⡄⢸⢿⡈⢧⠀⢸⡹⢀⠀⠀⠘⠀⠀⠀⠀ ⢻⣿⠀⠠⢱⡞⠀⠀⣵⠀⠀⣦⣇⣨⣥⣼⣼⡐⣼⠆⠀⡷⡆⡄⠐⠈⣧⠀⠀⢀ ⠈⡟⠀⠇⢸⡀⠀⠠⡿⡆⣄⡟⡟⠋⠛⠿⢹⠍⢁⠀⠀⣯⣛⡇⠀⠇⠘⡆⢈⣿ ⠀⠀⠀⠀⢸⢃⣆⠀⡟⣿⡏⠃⠀⠀⠀⠒⠁⠀⢸⡄⠀⡏⠆⡇⠀⢠⠀⠘⡏⠁ ⠀⠀⠀⠀⠀⡞⣿⣦⡧⠰⠇⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⡕⣱⠃⠀⠘⡇⠀⢰⡔ ⠀⠀⠀⠀⢠⠁⡈⣿⢳⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿⡏⠀⠂⠘⠃⣰⡞⠀ ⠀⠀⠀⠀⡎⠀⠀⡏⠀⣦⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⡄⠟⠀⡌⢀⡇⣠⢫⠃⠀ ⠀⠀⠀⢸⠁⠀⡅⠃⠀⢹⡷⣄⡀⠀⢀⣠⠔⠁⡞⠀⠀⡴⠱⢀⢢⢠⠃⡈⠀⠀ ⠀⠀⢀⠟⠀⠀⠀⠀⠀⣸⣷⣿⣿⣶⣿⡯⠄⣪⡇⠸⢰⢡⠁⢠⡿⠸⠀⠇⠀⠀ ⠀⠀⠀⠁⠀⠀⢸⠀⠀⣿⢏⢟⠟⠉⠁⠠⠊⢸⠀⡆⢨⠂⣠⣾⠀⡄⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠢⠂⠀⠀⠀⠀⠀⡎⠰⢀⠇⣰⠋⠉⠠⠉⢒⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠀⠀⠀⣀⡀⠤⠖⠒⠒⠈⠁⠉⠉⠉⠉⠉⠒⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠤⠒⠛⠒⠒⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢋⣁⡤⠤⣀⡀⠀⠀⠀⠀⠉⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠁⠀⠀⠀⠀⠀⠉⠓⠢⢄⡀⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀ ⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠙⢆⣀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀ ⠀⠀⠀⠀⠉⢦⠀⠀⠀⠀⠀⣰⡿⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⡀⠀⢀⣼⡿⠁⠀⣰⠃⠀⢀⠇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⣦⣼⣿⢟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⢀⣾⣿⠁⠀⢠⠇⠀⢀⡞⠀⠀⡄⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡾⣹⡇⠀⢀⡏⠀⠀⣼⠃⠀⠰⠁⢠⠃⠀⠀⢰⢱⠃⠀⠀⢀⠀⠀⠀⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣃⣿⠁⠀⣾⠀⡜⢰⡿⠀⢀⠃⠀⡞⠀⠀⢠⢣⡟⠀⠀⠀⡎⢀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⡟⢿⡄⢰⡇⢠⣇⣾⡇⠀⠸⠀⢰⠁⠠⢀⢣⡿⠁⠀⠀⡼⣡⡞⠀⢰⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⡇⡇⣾⠀⢸⣧⣼⠉⣿⡇⠀⡇⠀⡎⢠⠃⣼⣿⠃⠀⠀⡼⢡⢿⠁⣰⣿⠀⠀⠀⢀⠇⠀⠀⢠⠆⠀⠀⠀⢀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠳⡇⢸⡇⢸⣿⣿⢷⣿⡆⢸⡇⢠⣧⡋⢰⣿⡏⠀⠀⣰⣣⣿⡏⢀⣿⡎⠀⠀⠀⡎⠀⠀⣠⠏⠀⠀⢀⠀⣸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢿⣟⡏⢸⣬⣽⣷⡏⠀⣸⠃⠉⣿⡿⠣⠤⣤⣧⣿⡟⡇⢸⣿⠀⠀⠀⡜⠀⢠⢠⡏⠀⠀⠀⡎⠀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⡈⠘⢹⠇⠀⠉⠓⠃⠃⢻⢿⠀⣸⣿⣧⣄⣠⣿⢻⡿⢳⣧⣾⠇⠀⠀⡸⠀⢠⣿⣼⡀⠀⠀⡸⠀⠀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⠀⢸⠀⠀⠀⢀⠀⠀⠀⠈⠀⠈⠁⠉⢹⠿⣿⣾⣀⣘⣿⡟⠀⠀⡰⠁⢠⣿⣿⣿⠃⠀⢰⣇⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⣼⡄⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠿⠾⠛⢻⣿⠁⠀⡴⠁⢀⠾⣄⣿⠏⠀⢀⡿⠃⢰⣿⡿⡿⣿⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠁⢰⢏⣿⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⢀⡜⠀⢀⣯⣄⣼⡟⠀⠀⣾⠃⠀⣼⣟⣽⣿⠸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⢿⠀⡌⢞⡞⢳⠀⠐⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢀⠞⠀⢠⣿⡾⢹⡿⠁⢀⡼⠷⠒⠚⠻⢿⣿⣿⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⢸⢸⢠⢁⢾⠇⠀⣧⠀⠈⠪⠵⣦⠀⠀⠀⠀⠀⠀⠀⣼⠏⢀⠎⠀⣰⣿⣿⠁⣻⡃⣠⠎⠀⠀⠀⠀⠀⠈⣿⢁⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⣙⣿⡾⡎⢸⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣼⠏⣠⠋⠀⣴⣿⣿⠃⠀⡟⢻⠁⠀⠀⠀⠀⠀⠀⠀⢹⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⣿⡿⠀⠸⠀⠀⢸⡟⢉⣿⣿⠛⣿⣿⣿⣿⣿⣾⠏⡰⠁⢀⣼⠏⣿⠃⠀⡸⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⢠⣧⠃⠀⢠⠀⠀⢸⠀⠸⢿⡏⠀⣿⣿⣿⣿⡿⠃⠀⠀⣠⣾⠏⢠⡏⠀⢠⠃⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠀⡸⡟⠀⠀⢸⠀⠀⠘⡆⠀⠸⣧⣼⣿⡿⢿⡿⠁⠀⠀⣴⣿⡏⠀⢸⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠶ ⠀⠀⣀⠀⠀⠀⢀⢇⡇⠀⠀⢸⠀⠀⠀⠇⠄⠀⣽⣧⣿⣷⠞⠀⠀⣠⣞⣤⣿⠀⣄⠇⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆。˚˙✧˖°📷 ༘ ⋆。˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧。⋆🌻⋆。‧˚⛷🧚‍♀️🛖
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠊⠀⢀⣀⣀⣀⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠞⠀⢠⣾⣿⣿⣿⣿⣿⣶⡀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢷⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠉⠉⠙⠒⠦⣀⠀⠀ ⠀⠀⠀⠈⢧⠀⠈⠻⢿⣿⣿⣿⡿⠟⠁⠀⠀⢸⣿⣿⣿⣿⡆⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⣠⣴⣶⣿⣷⣶⣄⠈⠣⡀ ⠀⠀⠀⠀⠀⠳⡄⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⣠⣤⣄⡀⢠⠏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣧⠀⢣ ⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣶⣦⠉⠉⠁⠀⠀⠀⢸⠋⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⡸⢹⡇⠟⠁⡤⣀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠈⢿⡷⣸⣿⣿⣿⠏⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠃⢠⠇ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠲⡤⠤⠤⠔⢊⡴⢋⡟⠀⢸⣀⣯⣷⡄⢸⣁⣀⡸⡀⣠⣔⡞⢣⠀⢡⣿⣿⠿⡟⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⣀⠴⠃⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡀⠙⠢⣤⠔⠋⠀⢸⠁⢀⠀⠀⠀⠠⣄⠀⠀⠀⠈⠈⣛⠛⠓⠊⠀⢸⣿⣡⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡚⠁⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⡿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⢀⣿⠋⠹⣇⣀⣀⣀⣈⢉⠉⠉⠒⠋⠉⠀⠀⢠⣀⣸⡇⠙⢆⠘⢆⡀⠀⠀⠀⣀⣴⣾⣿⣿⣷⡄⠀⠀⠀ ⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠤⠤⠞⠀⢹⣧⠀⠀⠑⠦⡈⠉⢉⠏⣹⣿⣿⣿⣿⡿⠃⠀⠀⠀ ⠀⡴⠋⠀⢀⣠⠔⠒⠛⠛⠛⠓⠢⣴⠁⠈⠑⢝⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⡀⠀⠀⠈⠛⠥⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⢰⠃⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠑⠬⡻⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⣟⠕⠋⠉⢣⠀⠀⠀⠀⠀⠙⠻⣿⣷⠀⠀⠀⠀⠀⠀ ⢸⠀⡜⠁⠀⠀⣀⣠⠤⠤⠤⢤⣀⠀⡇⠀⠀⠀⠀⠀⠈⠑⠭⢛⡻⠿⠷⠶⠶⠶⠶⠿⣛⡫⠕⠊⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⠀⠀⠀⠀⠀ ⠘⣶⠃⢀⠔⠋⠁⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠖⠊⠉⠉⠑⠒⢤⡀⠈⢧⠀⠀⠀⠀ ⠀⠘⡿⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣀⣀⡀⠀⠀⠀⠀⠀⠙⢦⢸⠀⠀⠀⠀ ⠀⢠⠇⠀⠀⣠⠴⠚⠉⠉⠉⠙⠛⠶⣟⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠋⠉⠀⠉⠙⠢⣄⠀⠀⠀⠘⣿⠀⠀⠀⠀ ⠀⠈⡆⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠢⢕⡲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢔⡿⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⡟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠙⠒⠭⠭⣒⣒⣂⠀⠀⣀⣀⣐⣒⣲⠮⠝⠒⠉⣡⠿⠛⠛⠒⠦⣀⠀⠀⠀⠀⣷⠀⢠⠇⠀⠀⠀⠀ ⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⢸⡦⠋⠀⠀⠀⠀⠀ ⠀⠀⡇⠘⣄⡀⠀⠀⠀⠀⠀⠀⣠⡴⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢿⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⠀⠘⡍⠙⢲⢶⠒⠛⠋⡏⠈⠲⢤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⢼⣄⠀⠀⠀⠀⠀⠀⠀⢸⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣇⢀⣼⠤⠟⠒⠳⣄⣰⠓⠒⠶⣄⡉⠚⠥⣂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⣶⣄⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠉⠑⠚⠭⠵⢒⣒⣶⣤⣤⣤⣶⣒⡒⠲⠿⠛⠋⢹⠈⠿⣶⠶⠛⠉⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡏⠉⠒⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⣉⡵⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡏⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢀⣧⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡴⠖⢿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠈⠓⠶⢤⣤⣤⣀⣀⣀⣠⣤⡶⠛⠁⠀⢸⠇⠈⠉⠉⠉⠉⠉⠉⠉⡩⢻⡀⠀⠀⠀⠈⠙⠳⠶⠶⣤⣤⠶⠶⠚⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⢷⣀⡠⠤⠤⢤⡀⠀⢀⡠⠤⠤⠤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣷⠒⠚⠛⠛⠓⠒⠲⠤⣄⠀⢀⠔⠋⠉⠉⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⢸⠶⣇⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⢯⡀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠚⠁⠀⠈⠑⠢⢤⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣆⣀⣀⣀⣀⡠⠤⠒⠋⠁⠀⠀⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⣾⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⣶⣤⣄⠀⠀ ⢠⣾⡿⠛⠉⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠉⠛⢿⣷⡀ ⣿⣿⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠈⣿⣷ ⣿⣿⣷⣄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⣠⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣄⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿ ⢻⣿⣿⣿⣿⣿⣿⣏⠀⠉⠛⠛⠛⠛⠉⠀⣹⣿⣿⣿⣿⣿⣿⡟ ⠀⠻⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⠟⠀ ⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢸⣿⣿⣿⣿⡿⠛⢿⣿⣿⣶⣤⣤⣄⠀ ⢸⣿⣦⠀⢸⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⡆ ⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⢸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋⠀⠀⢀⣤⣤⣤⡄⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⡟⠉⢻⣿⡆ ⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠉⠁⠀⣸⣿⠃ ⠀⠀⠀⠀⠀⠻⣿⣿⣧⡀⠀⠀⠀⠀⣠⣾⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡟⠻⡟⢻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⢠⣦⣴⡆⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⣿⠿⠷⠾⠿⠿⠿⠾⠿⣿⣿⣿⣿⣿⣆⠀⠀ ⠀⣰⣿⣿⡿⠋⢁⣠⣴⣶⣶⣶⣶⣶⣶⣦⣄⡈⠙⠿⣿⣿⣆⠀ ⢀⣿⡿⠃⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠘⢿⣿⡀ ⠸⣿⡇⠸⣿⣿⣿⠿⠿⣦⡀⠀⠀⢀⣴⠿⠿⣿⣿⣿⠇⢸⣿⡇ ⢀⣿⣿⣶⡇⠀⠁⠀⢀⠈⠃⠀⠀⠘⠁⡀⠀⠈⠀⢸⣶⣿⣿⡀ ⣿⠉⠉⢻⡇⠀⠀⠀⣿⣇⣤⣴⣦⣤⣸⣿⠀⠀⠀⢸⡟⠉⠉⣿ ⣿⠀⠀⣸⡇⠀⠀⠀⣽⠟⠁⠀⠀⠈⠻⣯⠀⠀⠀⢸⣇⠀⠀⣿ ⠹⣷⡀⣿⡇⣾⣷⣶⣿⡀⠀⠀⠀⠀⢀⣿⣶⣾⡷⢸⣿⢀⣾⠏ ⠀⠈⠻⢿⡇⠈⠻⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⠟⠁⢸⡿⠟⠁⠀ ⠀⠀⠀⠈⠻⣦⣀⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⣀⣴⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⣀⣀⣀⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⠟⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣂⣿⣿⡿⠟⣡⡞⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢋⣴⣼⣿⣥⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡠⠔⠂⠈⠁⠀⠀⠈⠉⠉⠛⠻⢿⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⣿⣿⣎⢃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣌⠉⠻⣿⡟⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣦⡁⠙⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣄⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⡏⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⡄⠀⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠉⢹⣿⣿⣶⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⣿⣿⠇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣤⣀⣀⣴⠏⠉⡉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣆⣤⣶⣾⣿⠿⠿⠿⣿⣿⡖⠛⣿⣦⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⢿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠉⣻⣦⠸⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠟⠀⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡇⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠿⠁⠀⠀⢀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⠀⠀⠀⣴⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠉⣿⠋⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠹⠄⠀⢠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡿⢿⡿⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚。⋆୨♡୧⋆ ˚。⋆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠘⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢇⠰⠀⡠⠐⠂⢉⠤⣀⠀⠀⠈⠁⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢃⢩⠀⠀⠰⠈⠀⠀⢈⠳⠀⠀⠀⡀⠉⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⠊⠎⠀⠑⢤⠁⡰⠆⠀⠀⢂⢱⠀⠀⠈⢴⡀⠱⡀⠀⠀⠀⠀ ⠀⠀⠞⡇⠘⡄⠀⢠⡀⠁⢸⣀⠀⢈⡌⣇⠐⡄⡃⠄⠀⠐⡀⠀⠀⠀ ⠀⢰⠂⡈⠠⣟⢄⠉⢱⢷⣿⠳⡗⠛⢁⢪⠁⠠⣀⠈⡠⠀⢰⠀⠀⠀ ⠀⣞⠀⠁⠀⠈⢉⡸⠀⢠⡿⠀⠹⡀⠸⢸⡴⢶⢙⡆⢀⠃⠈⣇⠀⠀ ⠀⡇⡐⠀⠀⠀⠸⡇⢀⣾⠯⡤⣈⡇⢠⡘⢇⣆⡀⡇⠘⠀⠀⠋⡄⠀ ⢠⡇⠁⠀⢳⠀⠀⢷⠿⢣⢠⢴⢀⠅⢸⠂⠀⠉⠀⡇⠀⡇⠀⠀⢣⠀ ⠸⡇⢻⠀⠈⠆⠀⠈⣆⠈⠁⠋⠁⡄⡜⣀⠀⢀⠔⢀⠁⢀⠀⠀⠈⡀ ⠀⣧⡘⠇⠀⠘⡄⠀⠈⢔⠂⢄⡰⣐⣀⣀⠔⠀⢀⣄⡀⠘⢀⡴⢠⠇ ⠀⣧⠓⠛⡄⠠⡈⢆⠈⢌⢺⣶⣬⣀⠀⠘⢄⡠⢺⣝⣛⣡⣤⠤⠋⠀ ⠀⠱⡈⠶⣬⡂⣞⣻⣷⣈⠒⠀⣸⣿⣿⣶⣄⡉⢹⣿⣿⣿⣿⣦⠀⠀ ⠀⠀⠀⠉⢩⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⠛⣻⢿⣿⡿⣿⣿⣿⠏⠀⠀ ⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⠟⠁⢠⡞⠁⣼⠃⣧⡈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠛⠁⠀⠀⠈⠙⢻⠏⠀⢯⠙⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⣀⠔⠁⢀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⢀⠔⠀⠀⠈⡄⠀⠰⢛⣈⣉⠁⠐⠂⢄⠀⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀ ⠐⢟⡄⠀⠀⢀⢆⠔⠉⠀⠀⠀⠈⠐⠠⡀⠁⠠⡀⣠⠀⠀⠀⠀⠄⠀⠀⣸⣿⠏ ⠀⠀⠑⡄⠀⢴⠎⢀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢠⡿⡇⠀⠀⠀⠀⠘⠀⠀⣿⣿⠀ ⠀⠀⠀⠈⡱⡙⢀⠆⢠⠁⠀⠠⠀⠀⠀⠀⠀⠨⣍⡇⠀⠀⠀⠀⠀⠁⢸⢿⠉⠀ ⠀⠀⠀⢀⣇⠁⡌⡀⡄⢠⠀⠃⢀⡾⠀⢠⠡⠀⠸⠁⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀ ⠀⠀⠀⠸⠹⡀⣧⣅⠇⡌⠘⠀⣼⠁⢠⡳⢃⡄⠀⢠⠀⢀⠀⠀⢰⣿⣦⠀⠠⠀ ⠀⠀⠀⠀⠀⢡⡏⢿⡷⠁⡎⢰⠋⢤⣾⢿⢰⠇⢀⠂⣀⠇⠀⡄⢸⡟⠻⠶⢤⡆ ⠀⠀⠀⠀⡖⠀⡇⠀⠀⠈⠁⠉⢑⢲⢄⣸⡞⢀⠎⡴⣿⠀⣐⢠⣿⡇⠀⠀⠀⠈ ⠀⠀⠀⠀⡟⢠⣃⠀⠀⠀⠀⠀⠀⠉⠉⡼⢁⠂⣰⣠⠇⢠⠃⡸⡟⢡⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢆⡆⢂⠁⠆⠄⠀⠀⠀⣰⢃⠂⣼⠏⣟⡀⠈⠉⠉⡖⡸⠀⠀⠀⠀ ⠀⠀⠀⡰⣿⠃⠀⢸⠃⡤⢤⣤⣴⡶⠃⢁⡼⡏⢠⠹⠀⠀⠀⠀⢨⠀⠀⠀⡀⠀ ⠀⠀⢀⠃⡎⠀⠀⠘⠈⢇⡜⡿⡟⠀⣠⡞⢸⠀⠀⡀⠀⠀⠀⠀⢸⠥⣤⣶⣆⠀ ⠀⠀⠁⠘⠁⠀⡆⠀⡄⡘⣰⠇⢀⠴⢸⢡⠆⠀⡠⡇⠀⠀⠀⠀⠘⠀⠈⠻⢿⡀ ⠀⠀⠀⠁⢆⠀⢉⡄⠸⡶⠁⡠⠎⠊⠘⡸⠀⡔⠋⠃⠀⠀⠀⠀⠇⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠉⠀⡄⠀⠀⣀⠠⠌⠁⠒⠤⢀⠀⣠⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡿⠔⠈⠀⠀⡀⠤⠀⠀⠠⠌⣻⡰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⢹⣿⣶⡠⠂⠁⠀⠀⠀⢀⠀⠐⠄⠉⠲⠦⣄⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⣼⠞⡻⠁⠀⠀⠀⠀⠀⡄⢆⠄⠀⢂⠀⢔⠌⠳⡄ ⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⡷⡅⠃⠀⠆⠀⡄⠀⠀⠁⠘⣎⠄⠀⢂⠀⠮⢆⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠝⢰⢰⢸⢸⠀⢡⢂⠀⠃⠀⢿⢚⣄⠊⡀⠼⠩⡄ ⠀⠀⠀⠀⠇⠀⡃⣧⢀⠁⠈⢠⠀⣾⢨⡞⢳⠘⣾⡶⣠⠀⢸⠙⢡⢸⡇⢰⠆⠇ ⠀⠀⠀⠀⢠⠀⢡⢹⠸⠘⡀⠸⡼⠡⣦⣿⡶⣧⠋⢟⡯⣄⣿⡿⠙⣺⠃⣾⠆⠀ ⠀⠀⠀⠀⡘⠀⢘⡻⡄⡀⢳⡀⡗⣋⠿⠉⡀⠀⠀⠐⠀⠁⠩⠦⠘⡷⢫⠀⠘⠀ ⠀⠀⠀⠀⡇⠀⠨⠠⢣⠃⠀⠎⢤⠈⠉⠉⠀⠀⠀⠀⠀⠀⢑⠀⠀⡇⠀⠧⠀⠀ ⠀⠀⠀⢀⠅⠀⠸⣄⠺⡘⠀⠀⡌⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢵⢠⠰⠡⠀ ⠀⠀⡠⠊⠀⢸⡆⡟⣷⢣⠆⠀⠐⡠⠱⡄⠀⠀⢤⠴⠎⡹⠁⣰⢹⠸⢰⢄⡇⢃ ⠂⢀⠃⠀⠀⡜⣠⢹⠉⠂⡼⠀⠀⠱⣣⣘⣦⠀⠀⠈⠉⢂⠜⠁⡆⡆⡈⠢⣻⠀ ⡀⠁⠀⠀⢀⠡⣹⡄⢂⠀⠰⣡⡀⠀⠘⣏⢻⣵⡶⡀⠤⣞⡀⠀⠀⠈⠇⠀⡟⠀ ⠀⠀⠀⠀⢰⡓⣾⠭⠄⢢⣀⢣⢗⢄⠀⠈⢿⣿⣎⢶⣄⠈⢶⡄⠀⡄⠘⢦⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⣠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⠀⢄⠙⢷⣽⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⡄⠀⠀⠀⠱⡀⠻⣿⣿⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠔⠁⠀⠀⠀⠀⣤⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⡄⠀⠀⢆⠘⡄⠹⡾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⡄⠀⠈⣧⠀⠀⠘⡄⠘⣄⢻⣿⣷⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⣇⡇⠀⢸⢿⠀⠀⡀⠀⠀⠀⠀⢻⠂⠀⠀⠀⣿⠀⠀⢹⠀⠀⠀⢧⢇⢹⣎⣿⣿⡿⣿⣿⣿ ⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣾⣿⡇⠀⠈⣾⠀⠀⣧⠀⡀⠀⠀⢸⡇⠀⢰⠀⣿⠀⢀⣿⡇⢀⠀⢸⢸⠀⣿⣿⣥⣴⣿⣿⣿ ⠀⡆⢸⣿⡄⠀⠀⠀⠀⠀⢰⣼⠇⠀⣸⢉⣿⡇⠀⠀⣿⡀⠀⣿⡄⡇⠀⠀⣼⡇⠀⣸⡀⣿⡏⠁⡿⡇⢸⠀⢸⢸⡀⠻⣿⣎⢿⣿⣿⣿ ⢀⡇⣿⣿⡇⠀⠀⠀⠀⢰⠸⡟⠀⢠⠃⠀⣿⣏⠉⠉⢻⡏⠉⣿⣿⢻⠉⠁⣿⡇⠀⣿⢁⣿⣴⣦⣿⡇⣸⠀⣸⣸⣇⣴⣿⣿⣆⢻⣿⣿ ⢸⣷⡿⢿⣽⠀⠀⠀⠀⠀⠇⢣⢠⠏⠀⠀⢹⣿⣄⣤⣾⣿⣶⣿⣿⣿⡀⢀⣿⡇⠀⣿⡼⢿⣿⣻⣿⢃⣿⣠⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿ ⣾⣸⣠⠛⡏⡇⠀⠀⠀⠀⠘⡘⣿⠲⣶⣿⠛⠉⠉⡿⢻⣿⠛⠋⠉⠛⠃⠀⠉⠀⠀⡏⠀⣼⣻⡟⢹⣾⠙⠋⠁⢿⣿⣿⣿⣿⣿⣿⡄⠻ ⣿⣿⣧⣼⣳⢸⡀⠀⠀⠀⠀⢱⡹⡀⠈⠻⢷⣄⠀⢹⣌⣛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠛⠋⠀⣿⣿⡄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡀ ⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢳⣳⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣷⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⢦⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢠⣿⠘⣿⣇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣎⢧⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⣿⣧⠈⢻⣆⠀⠀⠸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡏⢦⢳⡀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⣼⣿⣿⣷⡣⠀⠹⣆⠀⠀⢹⡻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣷⡄⠀⠀⠀⢌⢻⣆⠀⠀⠀⠀⠀⠀⠀⠄⠒⠚⠉⠉⠉⠛⣿⣿⣿⣿⣿⣿⣷⡄⠀⠘⢧⠀⠀⠱⡙⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⣿⣿⣄⠀⠀⠈⢣⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠁⢠⠞⠁⠈⢻⣿⣿⣿⣿⣿⣆⠀⠈⢣⡀⠀⠙⡄⠹⣏ ⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣟⢇⠀⠀⠀⠣⡘⢶⣤⣀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠿⢆⣄⠀⠹⣿⣿⣿⣿⣿⣷⣄⠀⠑⠄⠀⠘⢆⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣿⡞⣮⢳⡀⠘⡄⠱⡈⢻⣿⣿⡗⠒⠤⠤⠴⠋⠀⢀⣤⣿⣿⣆⠀⠹⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠈⢣ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⡘⣷⣷⡄⠸⡀⠑⡄⠙⣿⣿⢦⠉⡷⠀⠀⣰⣿⣿⣿⣿⣿⣆⠀⠹⣿⣿⣿⣿⣿⢿⣿⣿⡶⢄⠀⠀ ⣯⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣇⢹⣿⣿⣄⢡⠀⠈⢆⠈⢧⣞⣉⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⢹⣿⣿⣿⠃⣸⣿⣿⣄⠀⠙⢦ ⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠈⣿⣿⣿⡄⡄⠀⠈⢣⠀⠻⡟⢏⢹⠇⣸⢻⣿⣿⣿⣿⣿⣿⣦⠀⢿⣿⠃⢀⣿⡋⠳⡻⣦⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣦⡈⠻⣿⡇⢹⣿⣿⣿⣧⠀⠀⠀⢣⡀⠘⡄⡟⠐⠁⠀⢻⣿⣿⣿⣿⣿⣿⣷⣬⣇⠀⣾⡿⢣⡀⠈⠪⡙⢄ ⣿⣿⣟⣿⣿⣿⣿⣿⡏⢠⣧⡙⢦⠈⠇⠘⣿⣿⢿⣿⡆⠀⠀⠀⠳⡀⠘⣷⣄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠋⣿⣼⣿⡧⡀⠱⡄⠀⠈⠢ ⠙⢿⣿⡜⣿⣿⣿⣿⡇⣼⣿⣷⣄⠑⣾⠀⣟⢁⠼⣿⡇⠀⠀⠀⠀⠱⡄⠱⡄⠙⠢⣤⣀⢹⡍⣉⣙⡛⠋⠀⠃⣿⣿⢧⣈⠢⣌⢦⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣩⠞⠋⢹⠿⠋⠉⠁⠀⠀⢀⣴⣿⣿⠿⠿⢿⣷⣦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠿⠋⠀⠀⠀⢀⡴⢧⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣻⣿⣷⣦⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⢀⡴⡏⠀⠀⠀⠀⠀⠀⠈⠟⣿⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⣠⠏⠀⠀⠀⡼⠀⠀⠀⠀⠀⣰⡿⠋⢸⠀⠀⠀⠀⡀⠈⠙⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡀⢠⠖⠀⢀⠞⠁⠀⠀⠀⢠⠃⠀⠀⢀⠞⢠⣿⡁⠀⢸⠀⠀⠀⠀⣇⠀⠀⢹⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⣾⣵⠏⣠⠖⠁⡄⣀⡀⠀⠀⡸⠀⠀⣠⠋⣰⣿⣿⡇⠀⡌⡄⠀⠀⠀⣽⠀⠀⣸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣵⣿⣿⣣⠞⣡⢤⠞⠀⣯⠃⠀⠀⣇⣠⠞⢁⣾⣿⣻⡼⠀⢠⢣⠃⠀⠀⢀⡟⠀⠀⣿⡟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠋⡠⠊⣠⠟⠒⢺⣿⠀⠀⠀⣿⣡⣴⣿⠋⠈⣿⣇⣠⣏⠎⠀⠀⠀⣸⠁⠀⣰⣿⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⢋⡴⠋⠀⣴⠃⢸⡉⠛⣿⡄⠀⠰⣿⣿⣿⣦⣌⣿⣯⣰⣿⣏⠀⠀⠀⣰⠃⠀⣠⣿⠃⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⣡⠔⠉⠀⢀⣾⣿⡀⢏⠙⡏⣿⡇⠀⠀⡟⠈⢿⡿⣿⣿⣿⣿⡧⠘⠀⣠⣾⡅⠀⣰⣿⣿⠀⢰⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⡡⠞⠁⠀⠀⣠⣾⣿⣿⣷⡈⠑⠛⢸⣧⠀⠀⢧⠀⠀⠛⠻⣅⡈⠛⠿⡷⣿⣿⠏⢀⣴⡿⠟⣿⣉⡟⢹ ⠀⠀⠀⠀⠀⠀⢀⡠⣶⣿⠷⠋⠀⣠⠖⢀⣾⣿⣿⣿⣿⣿⣷⣤⣄⠈⣿⡄⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠘⠓⢶⣿⣿⣷⣮⣿⣏⣴⡟ ⠀⠀⠀⠀⠀⡴⣫⣾⠟⠁⢀⣴⡿⢃⣴⡟⠑⢋⣿⣿⣿⣿⣿⣿⣿⡄⢹⣷⠀⠈⡿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⡿⣿⣿⡿⣽ ⠀⠀⠀⠀⣨⡾⠛⠁⣠⡶⢋⣟⣵⣿⡿⠋⣰⢫⣿⣿⣿⣿⣿⣿⣿⠸⡘⡏⢇⠀⢱⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠈⠓⢺⣵⣿⣿⣿⣿ ⠀⢀⣴⡿⠋⠀⢀⡼⠋⢠⣾⣿⡿⠋⢀⡾⣱⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢷⠈⢆⠈⡆⠀⢨⣕⣦⡀⠀⠀⠀⠘⠁⠀⢀⣾⣿⣿⣿⣿⣿ ⣾⡿⠋⠀⢀⠴⠋⠀⣠⣿⡿⠋⠀⣰⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⣷⢌⣆⢸⡀⠀⠑⠠⠉⠶⠤⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿ ⡟⠀⢀⠔⠁⠀⣠⣾⣿⠟⠀⣠⡾⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠘⣌⠻⣆⣇⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⠿⣿⣿⣿⣿ ⣠⠞⠁⢀⡠⢊⣽⠟⠁⢀⣴⣿⣾⣿⣿⠋⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡈⣆⠙⢿⣦⣀⣠⣤⣾⣿⣿⣿⡿⠉⠁⣀⠤⠊⣼⣿⣿ ⠁⢀⠴⢉⣼⠟⠃⢀⣴⣿⣿⣯⣿⡟⠁⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡾⣿⣿⣿⣿⣿⣿⣿⠟⣀⠤⢊⣡⣴⣿⣿⣿⠏ ⠔⠁⣠⣾⠏⠀⣠⣿⣿⣿⣿⣿⠏⢠⣾⣿⣿⣿⣿⣿⡿⢉⠇⠀⠀⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣵⣾⣿⣿⣿⣿⡿⠋⠀ ⠀⣰⡿⠃⣠⣾⣿⡿⣻⣿⢿⠏⢠⣿⣿⡟⢹⣿⣿⠟⠀⡞⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠉⠁⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠒⠶⠶ ⣾⣿⣡⣾⣿⣿⣯⣾⠟⢁⡞⢠⣾⣿⠏⢠⣿⡿⠁⠀⡜⠀⠀⣀⠠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠋⠀⠾⠃⣀⣀⣠⣾ ⢻⣿⣿⡿⠋⢠⡿⠃⢠⡟⣠⣿⡿⠁⢀⣿⣿⠁⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿ ⣿⡿⠛⢀⣴⠟⠀⢠⡟⢰⣿⡿⠁⠀⢸⣿⣿⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠟⢁⣰⠟⢁⣾⣷⡟⠀⣿⣿⠁⠀⠀⣿⣿⣿⡆⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢰⡒⢶⠺⢼⠈⣏⠢⣈⠻⣿⣿⣿⣿⣿⡀⠀⣼⣿⣿⣿⣿⣿⣿⣏⣹⣿⡟⠉⠉⠉⢆⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢯⣙⣢⡧⡜⠀⠘⡀⠙⠓⠾⣿⣿⡿⠿⠓⠂⠉⠉⠉⠉⠉⠉⣻⣿⡿⠿⠅⣀⠀⠀⠈⡆⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠒⠴⠷⠤⣽⣈⣠⡁⠀⠀⣟⣉⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⣿⣿⡏⠁⠐⠒⠺⠷⣦⣽⠀⢀⢘⣦⡀⠀⠀⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣱⠟⠁⠀⠀⠀⢠⠆⠀⠀⠀⢀⡤⠊⣁⣀⠸⣙⠟⡠⠤⠤⠤⠤⢄⣀⡈⠙⠧⡀⢻⠻⡗⠚⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⡰⠃⠀⠀⠀⢠⠞⠋⢉⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣌⠺⡆⢈⣦⡶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢠⠋⠀⣰⠃⠀⣠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣿⣿⣃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⡆⠀⠀⡰⠁⠀⠀⠀⢠⠇⠀⣴⠃⢀⠜⢱⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠀⠉⠉⠉⠀⠒ ⠀⠀⠀⠀⠀⠰⠁⠀⠀⡼⠀⠀⢰⠃⠀⠀⠀⠀⡞⠀⣼⢃⣴⠋⢀⡎⢀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⡏⠀⠀⠀⠀⠸⠁⢰⣿⠞⠁⡠⢻⠁⣼⣿⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣿⠋⢀⡜⠁⣸⢀⣿⣿⢄⡀⢸⡇⢀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⠈⣿⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢸⣿⣴⠋⠀⠀⣇⣸⣿⢸⡀⠈⣻⣧⣼⠀⠀⠀⡆⠃⠀⢸⡇⠀⠀⢰⠸⣿⢻⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⢼⡏⠙⣿⡟⣩⡻⢿⣿⣿⣿⡆⣿⣿⣿⠃⠀⠀⣿⠁⠀⢸⡇⠀⠀⢸⠀⡟⡌⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⡼⠀⢠⣼⣿⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠘⢧⡹⠇⢠⡌⠀⠛⢿⣿⣿⣿⣀⠀⢸⣿⣀⣀⣾⡇⠀⠀⣸⠀⣧⡇⢹⡇⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⣿⠋⢹⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⠛⠂⠀⠀⠀⠈⠋⢿⣷⠀⣼⡟⠀⢈⣿⠀⡄⠀⡇⢠⣿⡆⠈⣧⠀ ⠀⠀⠒⠀⠀⡜⠀⣰⡿⠀⢼⣠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣠⣿⣿⣷⣾⣿⢰⠃⣸⡇⡸⢿⣇⠀⡇⠀ ⠀⠀⠀⠀⢰⠁⢠⠉⣧⠰⣸⢺⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⡐⣻⣿⠃⣠⣿⢠⣇⡞⡿⣄⠇⠀ ⠀⠀⠀⢀⠏⠀⡎⠀⣼⣦⡙⢿⡄⠀⠀⠇⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠍⠁⢠⠯⢷⣾⡷⠃⠋⣿⠀⢳⠹⡄⠀ ⠀⠀⠀⠞⠀⡸⠀⠀⣿⠃⠈⡇⣇⠀⠀⢸⡀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⡸⠀⠀⢻⣧⠀⠀⢹⠀⠸⠀⠙⠀ ⠀⠀⠀⠀⢠⠃⠀⢰⡏⠀⢠⣧⢹⡄⠀⠀⢧⠀⠀⠀⠱⡀⠀⠀⠀⠀⠙⢲⣦⣤⣀⡀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢿⡄⠀⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⢸⠃⠀⢸⠻⡘⣷⡀⠀⠈⢆⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠳⣽⠿⠏⠁⠀⢀⡴⠁⠀⠀⠀⠀⠈⣇⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⡼⠀⠀⠀⡜⠀⠀⡎⠀⢧⢹⢷⡀⠀⠈⢧⡀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠈⠣⡀⠑⢶⣋⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⡇⠀⢰⠁⠀⢸⣆⢣⣵⡄⠀⠀⠹⣄⠀⠀⠱⣄⡀⠀⠀⠀⠀⣠⡾⠢⣄⡀⠉⠉⠀⠐⠒⠒⠒⠒⠓⠒⠦⠴⠤⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⡏⠀⢀⠏⠈⢦⠳⢌⡶⢴⣲⠿⠟⠓⠒⠛⢿⡷⠤⡤⠊⣽⠃⢀⢂⡩⠓⠤⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⢸⠃⢰⠃⠀⣼⣀⣀⣤⠝⢉⡴⠋⠁⠀⠀⠀⠀⠀⠀⠉⠺⣁⣰⣛⠒⠉⢉⣀⠀⠄⢚⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⢸⠀⠸⠀⢰⠃⢀⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⡸⠉⣁⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠖⠒⣶⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⢰⣿⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠀⠀⣰⠞⣁⠐⢒⣋⣉⡭⠍⣍⡹⣿⣧⡀⠐⢦⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣷⣞⡵⢋⡴⠚⠉⠁⠀⠀⢠⠀⠙⢮⣿⣥⣄⠈⢧⡀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⣿⣿⡽⠋⠀⠀⠀⠀⠀⠀⢸⣄⢰⡀⡀⠈⢧⠀⠀⢷⡀⡄⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡾⣻⡹⠃⡀⠀⠀⠀⢰⠀⠀⠀⣿⡄⢇⢷⡀⠈⢧⠀⠈⢧⢹⣠⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠇⢹⠃⠀⣇⠠⡄⠀⠸⡞⡄⠀⢸⢷⠸⣼⡷⡄⢬⡃⠀⠘⡆⢿⢧⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⢸⢸⡄⢹⡀⢧⠀⠀⢧⢳⠀⠘⣿⣇⠳⡇⠙⢦⡳⣄⠀⢹⡸⡈⢧⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣹⢀⠸⡞⡇⠀⣧⠘⣧⠀⠸⣿⡄⠀⢻⡟⠂⣹⣠⣤⣭⣿⡀⠈⡇⣷⡈⢧⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣾⠀⣇⢻⡀⠸⣧⠙⣇⡀⢻⣷⠰⣤⣷⡟⣭⣽⡀⠛⠘⡇⠀⢧⡏⢱⡈⢧⡘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⠀⢸⡄⣿⣆⠙⣇⣘⣿⢜⠿⠂⠘⠃⢻⣿⣿⠇⠀⠀⢻⠀⠸⣿⣿⠁⠀⢳⡘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡇⠀⢷⣈⣹⣾⣏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⢿⣆⠀⠀⠹⣌⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣧⠀⠈⣿⣦⠁⠹⡶⠅⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠈⢻⣦⠀⠀⠈⢣⣻⡷⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡆⠀⢹⡎⣷⠀⠀⠀⠀⠈⠉⠀⠀⢀⡀⠀⠀⠀⠀⣸⠇⢠⠿⣇⠀⠹⣷⡀⠀⠀⠁⠙⢮⡙⢦⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⢷⡀⠘⡇⡸⣷⣄⠀⠀⠀⠤⢤⣰⠟⠁⠀⠀⢀⡴⢿⠀⠸⣆⢻⡄⠀⠈⢛⣦⡀⠀⠀⠀⠳⣄⠈⠳⢦⣀⠀ ⠀⠀⠀⠀⠈⣧⠀⡇⢣⢻⢸⠷⣄⡀⠀⠀⠀⠀⠀⢀⣴⠟⠀⢸⠀⢠⣿⠀⢷⠀⠀⠀⠻⣝⢦⡀⠀⠀⠀⠑⢦⡀⠉⠁ ⠀⠀⠀⠀⠀⢸⡆⢹⢸⡼⣸⠀⢹⡏⠓⡦⣄⣀⣴⡿⢁⣀⡤⣾⣠⢸⢿⣇⠈⢧⠀⠀⠀⠹⣦⠉⠳⢄⡀⠀⠀⠙⠦⡄ ⠀⠀⠀⠀⢀⡟⢹⡸⡈⣧⡇⠀⢸⡇⢠⢹⡼⣿⣿⠞⠉⠀⠀⣼⠇⢸⠞⢯⣷⣻⣷⣀⠀⠀⠹⣷⣄⠀⠈⠙⠶⣤⣀⡀ ⠀⠀⠀⠀⣼⠃⠀⣇⡇⡟⠀⢰⢻⠇⣸⣌⡇⠨⡏⠀⠀⠀⠀⡟⠀⡾⣆⠙⠿⠛⠁⠉⢹⡿⠋⢉⣽⣿⣿⣦⡀⠙⢮⡁ ⠀⠀⠀⣰⠃⠀⠀⢸⡄⡇⢀⣼⢼⡖⠟⣰⠃⣸⢷⠀⠀⠀⣸⠁⡄⡇⠈⠛⢲⣤⣤⣐⣮⠁⢀⣿⣿⣿⣿⣿⣷⡀⠀⠁ ⠀⠀⣰⠃⠀⢀⣴⠚⡷⡯⠏⢁⣀⡤⠞⠁⢠⠃⠈⢧⠀⢀⣧⠀⡇⡇⠀⢀⣿⣿⣿⢻⡏⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⣰⠋⡸⠁⣾⡟⠀⡇⣶⣾⣿⠁⠀⠀⠀⣸⠀⢠⠟⠀⣼⣿⠀⣷⡇⠀⣸⣿⣿⡇⣼⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⠸⠃⢰⠃⣼⣿⡇⠀⠄⣿⣿⣿⠀⠀⠀⣰⠃⠀⠘⡇⠀⡟⣿⡄⢸⢧⢠⠿⣿⣿⢇⡿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⢀⡏⢠⣿⣿⡇⢸⠀⣿⣿⠿⡀⠀⢠⠏⢰⠀⠀⢹⡀⡇⣿⣷⡈⣿⣞⠦⣌⣉⢠⠐⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⢸⠁⣼⣿⡿⠇⡞⠀⣯⡥⠚⡧⠴⢏⠀⢸⣤⣤⢴⣷⡿⣿⣿⣷⡽⣻⣷⣤⣴⢰⣾⣿⠀⡿⠿⡿⡿⠿⡿⡿⡿⢿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠁⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⢸⡀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠔⠒⠒⠲⠤⠤⢄⣀⡇⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡇⠀⣇⠀⢀⡠⠖⠋⠁⠄⠒⠤⣄⣀⠀⠒⠂⠀⠀⠀⠈⡟⠀⠀⢺⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⢆⠘⣖⠋⠀⠀⠀⠠⡊⠋⠀⠀⠀⠉⠲⡦⣄⡀⠀⠘⢁⠀⠀⠘⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡜⡄⠘⢆⠀⠀⠀⡰⠁⢸⠀⠀⠀⠈⢦⡈⢢⡁⠀⠀⠀⠱⡄⠀⠐⡟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠃⢇⠑⠄⠈⢢⡀⣰⠁⠀⡜⢆⠀⠀⠀⠀⢳⠀⣷⡀⠀⠀⠀⠈⢢⣸⠁⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⢡⠀⠘⡄⠀⠀⠀⠹⠃⠀⠰⠁⢸⣆⡄⠀⠀⠀⢇⠸⣣⠀⠀⣀⠐⣦⡹⠲⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠇⢻⡀⠀⠸⡄⠀⠀⢠⡶⡄⠁⠀⢸⢿⡸⡄⠀⠀⡼⡄⢻⢇⠀⢩⣆⢜⠃⢳⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⡜⡄⠀⡉⠁⡰⡙⣄⠀⡚⠿⠁⣷⡜⣼⢸⢳⣱⣶⣣⠛⡇⢸⣜⠑⢤⡀⠈⢆⠈⠆⢠⠀⠀⠹⡄⠀⠀⠀⠀ ⠀⢠⢷⠀⢰⠁⠀⠙⠿⣜⡷⠃⣠⠘⠙⠗⣿⢸⠀⢹⡆⠈⠀⢸⠀⢿⠀⠀⠈⠢⣼⠀⠘⡀⢆⠀⠐⡻⡀⠀⠀⠀ ⠀⢸⡆⠀⣾⠀⠀⠀⠀⠀⡇⡄⠇⠀⠀⢰⣝⡆⠈⠈⣾⡄⠀⠸⡀⢸⣪⡷⢟⠉⢻⡇⠀⢧⠘⡀⠀⢻⣣⠀⠀⠀ ⠀⣏⠃⠀⡇⠀⠀⠀⠀⠀⢳⣿⠀⠀⠀⡷⣿⠠⠤⠀⢰⣧⠀⠀⠇⡘⡟⠈⠈⡇⠘⣷⠀⠘⡄⠃⠀⠈⣟⡆⠀⠀ ⠀⣿⠀⡎⠀⠀⣸⠀⠀⠀⢸⢹⠀⢀⣸⣾⠶⢾⡓⠦⣈⣿⠀⢀⣇⠃⢳⡈⣇⣟⠀⡿⠀⠀⡇⠀⠀⠀⠇⣱⠀⠀ ⢠⠻⠀⠃⠀⠀⢻⡄⠀⠀⠀⣿⠴⣿⡻⡇⠀⡠⢰⡆⠀⡸⠀⢸⡼⠀⠀⠙⠛⠋⠀⡇⡀⠀⢸⠀⠀⠀⠀⢉⡇⠀ ⢸⢸⢸⡄⠀⠀⠈⣇⠀⠀⠀⠸⣶⠀⠀⢷⣙⠓⣹⢇⠞⠁⠀⣸⡇⠀⠀⠀⠀⠀⢀⡇⢹⠀⢸⠀⠀⠀⠀⠀⢳⠀ ⢸⣨⠸⡇⡇⠀⠀⠹⡄⠀⠀⠀⠹⣆⠀⠀⠈⠉⠉⠁⠀⡄⠀⡟⠀⣀⡀⠀⠀⢠⠞⠀⡸⠀⠀⢆⠀⠀⠀⠀⢸⡄ ⠀⣿⢠⢱⢻⠀⠀⠀⠹⡄⠀⠀⠀⠙⡦⢀⡀⠀⠀⠀⢰⠇⡸⠁⠉⠁⠀⣀⠔⠁⠀⢀⠇⠀⠀⣺⠀⠀⠀⡆⢸⡇ ⠀⡏⡾⠈⡎⡆⠀⠀⠀⠱⡄⠀⠀⢀⠘⣍⠈⢉⠲⢤⡎⡰⠥⠤⣀⣠⠚⠁⠀⠀⣸⣾⣤⣄⣀⠇⠀⡼⠟⠀⣾⠃ ⠀⢳⡸⢣⠙⡽⡀⠀⠲⡀⠹⡄⡀⠈⢇⠘⢾⣶⣶⣧⣉⠀⠀⠀⠀⠹⡄⠀⢀⡴⣿⡝⢿⡿⠋⣀⡌⢀⣠⡾⠋⠀ ⠀⢸⠙⢤⡀⠀⠱⡄⠳⣝⢄⡸⢾⡀⠈⢳⣄⠙⠿⠟⣹⣿⣦⣄⡀⠀⠈⠶⣉⣀⣹⣿⣷⣶⣾⣿⣿⣯⠁⠀⠀⠀ ⠀⠈⢧⡀⠨⢗⣢⣬⠙⢮⣛⣛⣿⣿⣦⡀⠡⠉⠒⢢⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⣿⣿⣿⡿⣫⣾⣿⣿⣷⠀⠀⠀ ⠀⠀⠀⠙⠒⠒⠒⢒⣶⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣾⣿⣿⣿⣿⣿⠿⠿⠿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⡟⠋⠀⢀⣴⠾⠻⣿⢿⡍⠻⢿⣛⢿⣿⠿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠉⠀⢀⣾⠟⠁⠀⣼⡿⠀⣿⡄⠈⢻⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠸⣷⣦⣤⣼⣿⠃⠀⢸⠻⣦⣸⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣾⠏⠀⠀⢸⡆⠈⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠲⢈⣡⡼⠇⠭⠐⠂⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⠔⠁⢔⢁⡼⢉⡄⠈⠁⠢⠑⢄⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠡⡂⢀⠜⡡⠎⢠⡻⡐⠀⢀⠆⢀⠢⢣⣧⠄ ⠀⠀⠀⠀⠀⠀⡀⢤⣰⣶⠞⣰⠑⠀⣮⣮⣏⢰⣿⣡⠀⢀⢮⠁⢆⠂⣿⠙⠀ ⠀⠀⠀⠀⡠⠹⡼⣿⡿⠁⣼⠣⠑⣸⠛⠜⡿⡟⢦⢻⢀⣾⣇⢌⢎⠎⣸⠀⠆ ⠀⠀⢀⠌⠀⠀⣺⠊⡐⣸⣼⠂⢂⠃⠀⠀⠀⠀⠀⡘⠷⢵⣤⣟⠎⡐⠇⢠⠀ ⠀⠀⡂⠄⠒⠐⣻⣠⠁⡿⡟⢰⠈⠀⠀⠀⠀⠀⠐⠀⠀⠻⢟⠻⡘⣈⠀⡌⠀ ⠀⠈⠀⡠⠈⠀⠀⠀⠑⣿⠁⣼⡿⡄⠀⢙⠁⣢⠀⠀⠈⠂⢀⡞⢠⠇⣼⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⠀⢿⣿⡜⣆⠀⠉⠈⢀⣀⡠⢶⡽⠁⡞⠐⢹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⡄⠙⢷⣿⠿⢿⣿⢰⢰⢸⠇⢰⢁⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡟⠗⡾⠀⠉⢉⡼⠇⢸⣿⠀⠀⣸⠈⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⡃⡜⠁⠀⣔⣩⠴⢣⠈⠿⠀⠀⡟⠆⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⢙⡀⢠⠞⢇⠀⡠⠃⠑⢔⣇⠀⢓⣰⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠋⠀⠀⠀⠈⢠⠊⠀⠀⢡⠀⡼⡏⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡖⠱⠱⡀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠐⠀⠀⠀⠀⠀⠀⠱⢔⠋⠀⠀⠀⢰⣷⡀⢀⣤⣖⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⢀⡠⠊⠀⠀⠀⠀⠈⡆⠀⠀⠀⢼⠟⠋⠁⠀⠀⠀⠉⠑⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⡠⣾⡇⠀⠀⠀⠀⠀⠀⢠⠀⠀⣰⠗⠊⠉⠉⠉⠁⠒⠤⢄⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢸⣤⣤⣤⠖ ⠥⠴⢏⣰⡀⠀⠀⠀⠀⢠⠃⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠈⠢⡀⣠⣴⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⣸⣿⣿⡟⠀ ⠀⠀⠀⠈⠳⡀⠀⠀⢀⣤⣼⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⣿⣿⣿⠇⠀ ⠀⠀⠀⠀⠀⠱⣀⠞⢡⢿⠃⠀⣠⠃⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣾⣟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣭⠀⠀ ⠀⠀⠀⠀⠀⠀⢱⣰⠃⡎⠀⢠⠃⠀⢰⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⡍⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣇⢹⠀⠀ ⠀⠀⠀⠀⠀⠀⢨⠇⡼⠀⢀⡇⢠⠀⠏⠀⢠⠀⢰⠃⠀⠀⣀⡇⠀⠀⢰⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠒⠛⢇⠀⡀ ⠀⠀⠀⠀⠀⠀⣼⣤⡇⠀⡸⠀⡆⢸⠀⠀⡎⠀⡌⠀⠀⣜⡿⠁⠀⢀⡇⡰⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⠀⠀⠀⠈⠀⠁ ⠀⠀⠀⠀⠀⠀⡟⣿⡇⠀⣇⢰⠑⢼⠀⢰⠃⢰⠁⠀⣰⣿⠃⠀⢀⡎⡼⠃⢀⠆⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⣼⣿⣷⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⢿⠀⣿⣿⢷⣍⠀⣾⠀⣸⡀⢠⣿⡏⠀⠀⡜⡼⡛⠀⣿⠆⠀⠀⡰⠁⠀⢠⠆⠀⠀⠀⢰⣿⣟⢿⣿⡀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠈⣷⣿⠸⣾⢹⣿⠃⠀⡟⠉⣽⠟⠠⠤⣼⣾⠷⠇⢰⡽⠀⠀⢠⠃⢀⢀⡏⠀⠀⢠⠃⢸⣿⣿⠛⠿⢿⢶⣦⣵⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⡆⡏⡇⠀⠉⠙⠉⠀⠊⠇⠠⡿⢦⣀⣼⠋⡏⠁⣇⣾⠃⠀⢀⠃⢀⣾⣾⠀⠀⢀⠏⠀⣾⣿⡿⠀⠀⠀⠀⠈⠛⢧ ⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠙⡗⣦⢤⣿⡏⠀⢠⠏⢀⡾⢿⣿⠀⠀⣼⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⢠⡿⠀⢠⠃⠀⠎⠀⣼⠃⠀⣸⠋⠀⣿⢟⣇⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡭⠀⡾⠞⢧⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⡰⠁⢀⣞⣷⣾⠏⠀⢠⣃⡀⣴⣻⠏⢸⠈⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⢸⢁⡆⠈⢧⠀⠉⢶⣤⡀⠀⠀⠀⠀⠀⢀⣾⠃⡰⠁⢠⣿⡿⠐⡟⢀⡴⠉⠀⠀⠀⠈⢦⠎⣠⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⣧⣧⠊⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⠃⡔⠁⣠⢿⡿⠀⢸⢿⡏⠀⠀⠀⠀⠀⠀⢸⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠋⣿⡎⠀⠄⠀⢸⡏⢙⣶⡖⢻⣾⣿⣿⣿⡾⠁⠈⠀⣰⡟⣿⠁⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢀⡀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⡌⢠⡿⠀⠀⠀⠀⠸⡄⠘⣿⠀⣸⣿⣿⣿⠏⠀⠀⢀⣾⠏⢰⠇⠀⠘⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡏⢁⣀⠀⢠⣤⣄⠀⠀ ⠀⠀⠀⢀⡜⠀⣸⡇⠀⠀⠃⠀⠀⡇⠀⠘⣴⠃⣿⢋⠏⠀⠀⡠⢿⡟⠀⡘⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠛⢿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⢀⠏⠁⠀⠀⢆⠀⠀⢳⠀⣰⠋⣠⡿⠃⠀⢀⡴⠗⣺⠃⣴⠃⠀⠀⢀⡾⡇⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠹⣿⣿⣇⠀ ⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⢸⢆⠀⠈⣧⡁⣰⠟⠁⠀⣠⠋⡠⠖⢹⠀⡟⠀⠀⢠⣾⠼⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⢿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠘⡜⡄⠀⠸⡿⠋⠀⣠⠞⡓⠉⠀⠀⠈⣦⠃⠀⣰⢋⠀⠀⣇⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠈⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⢀⣤⣄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢤⡈⠙⢷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡴⠋⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⢳⣄⠀⠀⠀⠀⠙⣆⠈⢻⣷⣜⢿⣿⣭⣯⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹⣆⠀⠀⠀⠀⠈⢧⠀⠹⣟⠷⡝⢿⣷⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠞⠁⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⣿⡄⠀⠀⠈⣇⠀⢣⡀⢻⣖⢻⣎⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⢀⠀⠀⢾⢸⠀⠀⢠⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⣧⠀⠀⠀⠸⡀⠈⢳⡈⢿⣼⣿⣎⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣴⠆⠀⢸⡆⡏⠀⠀⢸⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⢲⠄⠀⠀⠀⠘⣧⠀⠀⠀⢿⠀⠀⠀⠀⣷⢠⠈⣧⡈⣿⢻⣿⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣰⡏⠀⠀⣹⡀⡇⠀⠀⢸⣸⠄⠀⢸⣄⠀⣦⠀⠀⠀⠀⣾⠀⠀⠀⡀⠀⡿⠀⠀⢠⣼⡄⠀⠀⠀⢹⠘⡇⢹⣳⣹⡿⠟⢋⣿⣿⣿⣿ ⠀⢠⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡿⠀⠀⢰⣿⠄⡇⠀⠀⠀⣿⡇⠀⢸⡼⡀⢹⠀⠀⠀⠀⣿⡇⠀⠀⡇⠀⣷⡇⢀⣨⡧⡇⠀⡄⠀⠈⡆⢣⢸⣷⣿⡳⣶⣯⣿⣿⣿⣿ ⠀⢸⠀⣟⣷⡇⠀⠀⠀⠀⠀⠀⠀⢸⣤⣿⠃⠀⢀⡟⢸⣾⡇⠀⠀⠀⡇⡇⠀⠀⣷⡇⠸⡀⠀⠀⢀⣷⡇⠀⢀⣇⠀⣷⡟⠉⠀⡇⣷⠀⡇⠀⠀⡇⢸⠀⡏⣼⣷⡙⣿⣛⣿⣿⣿ ⠀⢸⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⣤⢸⣿⠏⠀⠀⡼⠁⠙⣿⢻⠒⠚⠒⢿⣷⠒⠲⣿⣽⠶⡧⠖⠒⢺⡌⡇⠀⢸⣿⠀⣿⣁⣠⠄⣷⣿⠀⣿⠀⢀⡇⣸⠀⡇⣿⣿⣿⡜⢿⣿⣿⣿ ⢰⢸⢠⣿⣹⢻⡀⠀⠀⠀⠀⠀⠹⡄⢻⠀⠀⡼⠃⠀⠀⣟⣿⡀⠀⠀⠸⣿⡀⣀⣻⡟⣧⣇⠀⠀⢸⡇⡇⠀⣸⡏⢸⣿⣿⣿⣿⣿⡏⢰⣿⠀⣼⣷⣧⣷⣿⣿⣿⣿⣷⡈⢳⣿⣿ ⢸⢸⢸⠗⠛⡇⡇⠀⠀⠀⠀⠀⠀⢳⠈⣇⣼⠁⠀⠀⣀⣻⣇⣗⣠⣯⣽⣿⣿⣿⣾⣿⣽⣾⣄⠀⣼⣷⠃⠀⣿⡵⠟⣽⣿⢫⣿⣿⢃⣾⣯⣰⣿⣿⣿⣼⣿⣿⣿⣿⣿⣷⡈⢻⣿ ⣿⣸⣾⢰⠛⣧⢹⡀⠀⠀⠀⠀⠀⠘⣆⢹⣿⠺⣿⢿⡟⠛⠛⠉⠉⣿⢟⣿⡟⠻⠇⠉⠙⠋⠃⠀⠀⠉⠀⠀⣸⠁⠀⣿⢛⣿⠏⢸⣾⡏⠟⠉⠃⢸⣟⣿⣿⣿⣿⣿⣿⣿⣧⠀⢿ ⣿⣿⣿⣈⣠⢾⡈⣇⠀⠀⠀⠀⠀⠀⠹⡄⣿⠀⠈⠻⣿⣦⡀⠀⠀⣷⡘⠿⢿⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠤⠿⠾⠏⠀⣾⣿⣇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⣿⣿⣿⣿⣿⣿⣧⣼⡄⠀⠀⠀⠀⠀⠀⢻⡘⡆⠀⠀⠈⠙⠛⠲⠤⣬⣷⣶⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣽⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣿⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢷⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢿⣯⣷⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⡀⠀⠀⠀⠀⠀⠀⢧⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⢸⣿⠈⢻⣾⣇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢷⡀⠀⠀⠀⠀⠀⠈⢯⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠀⠀⠀⠀⣾⣧⢷⠀⠙⣾⣆⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣄⢳⡀⠀⠀⠀⠀⠀⠈⢿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣏⢧⠀⠘⢿⡄⠀⠀⠀⢿⣻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⢦⣻⡄⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣄⣀⣀⣾⣿⣿⣿⣿⣯⠣⠀⠈⢻⣆⠀⠀⠈⢣⠻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⣿⣿⣆⠀⠀⠀⠀⠀⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠴⠤⠤⠶⠒⠉⠉⠀⠀⠉⠉⠓⣶⣿⣭⣭⣽⣿⣿⣿⣷⡀⠀⠀⠹⣆⠀⠀⠈⢷⠘⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⢈⢯⣿⣧⡀⠀⠀⠀⠘⣆⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⠋⠀⣠⠞⠁⠙⢿⣿⣿⣿⣿⣿⣿⢿⣄⠀⠀⠙⢇⠀⠀⠀⢳⡀⠹⢿⡏ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⠀⠈⣿⣯⢟⢷⡀⠀⠀⠀⠘⢆⠈⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡳⣄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⢷⡀⠀⠀⠹⡄⠈⠳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⡞⣎⢳⡄⠀⠀⢀⠘⢧⠈⢿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠙⠛⣱⣶⡀⠀⠘⣿⣿⣿⣿⣿⣿⣯⣿⣦⣄⠀⠙⠀⠀⠀⠙⣆⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⡜⣦⡙⣆⠀⠈⣆⠈⢣⡀⢻⣿⣿⣿⡿⠓⠒⠢⠤⠴⠞⠁⠀⢀⣤⣾⣿⣿⣧⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠈⢳ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣷⠸⣷⣜⢧⠀⠸⡄⠀⠳⡀⠙⣯⣿⣿⣶⡈⠛⣶⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣧⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⡆⢹⣿⣿⣷⡀⢻⡀⠀⠹⣄⠈⢻⡋⢁⣧⠶⠋⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠸⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⠁⠙⠳⣄⠀ ⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣧⠈⣿⣿⣿⣷⡀⢧⠀⠀⠘⣆⠀⠙⣾⣥⣤⣶⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢿⣿⣿⣿⡏⠀⣼⣿⣿⢿⣧⡀⠀⠈⠳ ⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⡆⢸⣿⣿⣿⣷⠸⡄⠀⠀⠘⢧⠀⠘⢯⠛⢥⡈⡿⠀⡼⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⣿⣿⡏⠀⢰⣿⡏⠈⢳⡙⢷⣄⠀⠀ ⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⡀⠙⢿⣿⣇⠈⣿⣿⣿⣷⢇⣷⠀⠀⠀⠈⢧⡀⠀⢳⡀⢻⠇⡼⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣘⣿⠀⢠⣿⣿⠻⡄⠀⠙⢦⡙⢧⡀ ⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⡇⠀⣏⠙⣆⠀⠻⣿⠀⢸⣿⣿⣿⡾⡼⡄⠀⠀⠀⠀⢳⠀⠀⢳⣸⡀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⡄⣼⣿⣇⠀⠹⣄⠀⠀⠙⢦⡉ ⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⠃⣸⣿⣦⠈⠳⡄⢸⡄⢸⣿⡿⠋⢳⣷⡇⠀⠀⠀⠀⠀⢷⡀⠀⢿⡓⢦⣀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⠀⡾⢳⣿⣿⡟⢧⡀⠘⢦⠀⠀⠀⠉ ⠈⢻⣿⣿⡆⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣷⣄⡘⢦⡇⢠⣏⢀⡴⠻⡽⣷⠀⠀⠀⠀⠀⠀⢻⡄⠈⣧⠀⠈⠳⢦⣤⣀⢙⡤⠄⣀⣉⣉⠉⠁⠠⠃⢸⣟⡿⠥⣄⡙⠶⣌⢳⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠑⢉⠝⢉⣁⣠⣤⣿⣟⣛⠻⣶⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⢀⡔⠁⠉⠉⠉⠙⣿⣿⠛⠻⠿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢠⠀⡠⠊⠀⢀⠃⠀⡠⣰⡏⢀⠀⠀⢠⠀⢹⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡷⡣⡊⠔⣤⠀⢸⢀⠔⣵⡟⠇⡘⠆⠀⢸⠀⣸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⡫⢊⢞⣲⡇⠀⢸⣡⠞⣉⡿⣠⡝⠀⠀⠇⢀⡟⢸ ⠀⠀⠀⠀⠀⠀⠀⣼⢟⠕⠊⢠⣏⠘⢤⣷⠀⢹⠻⣿⣾⣷⣏⠆⣠⡎⢀⣾⠁⣼ ⠀⠀⠀⠀⢀⣠⡾⠕⢁⢀⣴⣿⣿⣌⡈⢸⡀⢸⣤⠉⠃⠌⠛⠫⣟⣤⣟⡹⡿⣹ ⠀⠀⢀⢔⡵⠋⣠⡖⣡⡟⡫⣿⣿⣿⣿⡌⣧⠈⡿⠉⠀⠀⠀⠀⠀⢿⢟⣿⣿⣿ ⠀⣠⡶⠋⡰⢊⣼⡾⠋⣔⣽⣿⣿⣿⣿⠐⢅⢂⢡⠀⣢⡀⠀⠀⠐⠀⣨⣿⣿⣿ ⡾⠋⡠⠊⢀⣾⠋⣠⣮⣾⣿⣿⣿⣿⡟⠀⠈⡯⣆⡆⠈⠂⠓⠂⢀⣴⣿⣿⣿⣿ ⡤⠊⡠⣪⠟⢁⣜⣽⡿⢫⣿⣿⣿⣿⣿⣶⣤⣈⣌⢳⣄⣤⣴⣾⡿⠋⡉⢜⣽⣿ ⠀⢈⡾⢁⣴⣿⣿⡟⣠⣿⣿⣿⡟⡏⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣕⣬⣶⣿⡿⠃ ⣠⢟⣴⣿⣿⡟⡝⣰⡿⢫⡿⠋⠰⠀⠀⡀⠄⠂⠉⠁⠈⠙⢿⣿⣿⠿⢛⠟⠑⢒ ⣻⣾⠟⡹⠋⡜⣰⡟⠁⣾⠁⢠⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣧⣶⣾⣿⣿ ⠟⣡⠞⣥⡼⢸⡟⠀⢸⣿⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⡠⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢌⠳⣕⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⠔⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢇⠀⢠⠡⢡⠙⡂⠀⡜ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡆⠀⠀⢀⠀⠀⠀⡄⠀⠈⡄⠘⠀⠀⣆⢣⣛⣡⡞⠀ ⠀⢀⠀⠀⠀⠀⠀⡜⠀⢾⡇⠀⡇⠘⡆⡀⠀⣇⠀⠀⡇⢴⡇⡄⠁⡼⣿⣖⠁⠀ ⢠⢸⣧⠀⠀⠀⢸⠁⡌⢸⣇⠀⢻⠘⣷⡃⠀⣿⢰⢧⣧⡴⡇⡇⣄⣧⣽⢱⣣⠀ ⣌⡮⢟⡀⠀⠀⢃⣾⢤⡴⠟⢲⢿⠿⠛⠓⠘⠃⢸⠈⣿⠟⣿⠗⢻⠛⡟⢸⢡⠡ ⢹⡕⠺⣥⠀⠀⠈⢞⡀⠙⠢⠬⠬⠛⠀⠀⠀⠀⠀⠈⠉⢸⣿⡀⠀⣶⠁⡆⠀⢃ ⠘⡇⠀⠘⣧⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⡝⣧⠀⠸⡀⡇⢀⣼ ⠀⢻⠀⠀⠓⡣⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⠋⢷⠈⢧⠀⠹⢷⣿⣿ ⠀⠸⡄⠀⢰⠘⣷⡀⠀⢊⢂⠀⠀⠀⠀⠀⢀⡠⢉⠝⢟⠛⠀⠣⡀⠣⠀⠡⡻⡿ ⡀⠀⡇⠀⠈⡀⣿⣟⠄⠀⠣⠳⣤⣀⠀⠀⠀⡰⠋⢢⡀⢣⠀⠀⡗⢄⠑⠀⠑⡌ ⣧⠀⢸⠀⠀⡇⢹⣯⢮⣂⢀⠑⡙⢿⣭⢩⠉⢀⣶⣿⣷⡀⢡⣰⢃⡿⣿⣦⡀⠈ ⣟⡆⠀⡆⠀⡇⢸⣿⡜⣿⣆⠆⠐⠌⢺⣥⢴⢻⣿⣿⣿⣷⡄⢻⣼⢁⡿⡷⡀⠑ ⣿⣽⡀⠘⠀⡇⡏⠻⣇⢹⣿⣾⠀⠈⢄⠡⡙⠈⠘⢿⣿⣿⣿⡮⡇⣾⠓⡈⠪⡢ ⠻⣷⢧⠀⠀⢰⠳⣑⢼⢸⢋⢿⡆⠀⠈⢆⢩⠂⢄⡈⣟⠛⠻⠃⢹⡿⡑⢔⢄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠀⢀⢰⣿⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⠀⠌⠀⠔⡃⡀⠋⠉⠉⠐⠱⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡐⢀⠃⡌⠀⡌⣌⢌⢡⠀⡄⠂⠀⢠⠈⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠀⡌⢰⠀⠀⢸⡡⢹⡾⡤⣷⠀⣶⢸⠀⣼⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡌⠰⢠⣏⠀⠀⠙⠙⠿⡟⠻⣿⡄⡯⢼⠀⢿⡽⡀⠀⠀⠀⠀⠀ ⢀⣠⠴⠓⠇⢆⢟⣺⠀⡀⢠⠀⠀⠀⠀⠀⢱⡿⣿⣱⣼⣧⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⡘⡈⡌⡼⢹⡀⢃⠈⡄⠀⠄⣀⠀⠈⠰⠉⡏⢠⠎⢆⠀⠀⠀⠀⠀ ⠀⠀⠠⠋⡰⠀⠁⡎⣷⡈⢆⠐⡀⠀⠙⢕⠔⣁⣀⣰⣸⡀⠘⡄⠀⠀⠀⠀ ⠐⠢⣀⡔⠇⠀⢠⢠⣙⢿⣶⣷⣾⣶⣂⡧⣃⢲⠤⠀⠀⢀⣽⣗⢶⠲⣤⠀ ⠀⠀⠈⡞⠀⢠⠀⡦⢠⡟⠁⠘⠟⠉⠛⣞⢨⢔⡦⢠⡴⢻⣸⠊⠉⠉⣿⠀ ⠀⠀⠀⢀⠀⠸⣶⡇⡼⠁⠀⠀⠀⠀⠀⢘⣮⠁⢠⠎⠿⢀⣿⡇⠀⠀⣿⠀ ⠀⠀⠀⢸⢀⠐⡿⣣⢳⣤⣤⠤⠀⠐⠚⠑⠰⠓⠧⡜⡦⠋⠀⣿⠀⢰⡿⠀ ⠀⠀⠀⢸⠀⠢⠩⡜⢜⣿⣿⣿⣶⣖⠒⠒⠒⠓⠀⠭⠷⢄⣀⣟⠱⣨⣎⠇ ⠀⠀⠀⠸⡯⠀⠑⠑⢄⠉⠛⠛⣻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠙⢗⡜⢿⡄ ⠀⠀⠀⢸⢁⣷⡀⠀⠢⣑⢶⣖⡉⠀⠈⠛⣿⣦⣄⡀⠀⠀⠀⠀⠈⢳⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠒⠉⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣑⣢⣤⣀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⢠⣿⣄⠀⠀⣠⠔⠂⠉⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄⣴⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⡯⠖⠉⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠤⠤⢄⣀⡙⢿⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣦⡄⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⣄⠉⠙⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣆⣀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠳⡀⠀⠀⠙⡟⠷⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⣷⣬⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢆⢀⠀⠀⠈⢄⠀⠀⢎⢢⡈⠙⢷⣄⠀ ⠈⠁⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠟⡰⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠸⣆⠣⡀⠀⠈⢆⠀⠈⢣⡱⡄⠀⠙⢇ ⠀⠀⠀⠀⠲⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⡠⢸⠀⠀⡆⢦⠀⠀⢇⠰⠀⠀⠀⡀⠀⠀⢻⣆⢳⠀⠀⠈⢆⠀⠈⢷⡌⢆⠀⠈ ⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠸⡴⠁⣼⠀⠀⣧⢸⡄⠀⠸⡄⢃⠀⠀⢳⡆⠀⠘⣿⢆⢧⠀⠀⡘⡄⠀⠘⡌⡎⡆⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠸⡰⠁⠰⣿⠀⠀⢹⠘⣧⠀⠀⣷⠸⡀⠀⠈⡇⠀⠀⣿⠈⣬⣧⠄⢰⣡⠀⢣⢣⠘⣿⠀ ⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⣇⠀⠀⢃⠀⠀⠃⠀⠘⢩⡀⠀⢸⣆⣧⣧⠀⢼⣧⣷⢰⡀⣇⠆⠀⢸⡏⢹⢿⡀⠘⣿⠀⢸⣼⡀⢹⡇ ⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣄⢀⢿⠀⠀⠸⡀⠀⠀⡿⠀⣤⣿⡏⢹⣿⣤⠘⣄⠀⡿⣿⣧⣧⣿⡀⢀⣸⣧⣀⣽⣇⢠⣿⠀⢰⣏⠁⠈⠃ ⠀⠀⠀⠀⠀⠀⠀⢣⡆⠀⣇⡌⢸⡀⠸⠀⢣⡀⠀⢡⣼⠏⠸⣟⣨⣿⣿⣿⣿⣆⣸⡘⣏⢿⣧⣀⢸⣿⣿⠟⠹⠋⣽⡟⢀⡾⡿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢹⣇⣿⡇⠰⠀⠈⣷⠀⢸⣟⣤⣶⣿⣿⢿⠟⠁⠈⠉⠁⠀⢈⠞⠃⠻⢻⠿⢟⡆⠀⣴⡟⣡⡼⠽⠁⠹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⣉⣛⢳⠀⡆⠀⠹⣧⠀⡟⢅⣠⡙⠛⠉⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠛⠀⢸⡿⠋⢧⡀⠀⠀⢂⠘ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠃⠀⣽⡆⢡⠀⠀⢣⠳⣸⠀⠈⠉⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⢸⡇⠀⠸⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⠀⠸⠀⡃⠈⠀⢡⠘⡀⠀⠈⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⢸⣿⠀⠀⢹⠱⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡤⠀⢀⡇⢷⡀⠐⢾⡄⢇⠀⠀⠘⡄⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣿⠀⢰⠀⣇⠱⠀⠀ ⠀⠀⠀⠀⠀⣠⠋⠀⠀⢸⡇⢸⠻⣶⣄⣣⠸⡀⠀⠀⠹⡀⢩⢳⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⣲⠖⠀⢀⡾⡇⢸⠀⡈⠀⢸⡄⢱⠀ ⠀⠀⠀⣠⡔⠁⠀⠀⠀⣼⡇⠈⡇⣿⡇⠘⡆⢇⠀⠀⠀⠱⡀⡄⠹⣦⠀⠀⠀⠀⠸⣿⠛⠒⠈⣩⠋⠀⣠⣾⠀⡇⢸⠀⡗⠦⢼⣧⠀⢣ ⠠⠐⠈⡼⠁⠀⠀⠀⢀⡟⢠⠀⢻⡟⠛⠤⣸⠸⡀⠀⠀⠀⠱⡰⡀⠘⢷⡄⠀⠀⠀⠀⠉⠉⠩⠴⢀⣴⠋⠈⡇⢸⣼⠀⠙⢦⠀⣿⠀⠈ ⠀⠀⡔⠁⠀⠀⠀⠀⢸⠃⡜⡇⠈⡇⠀⠀⠈⢣⢣⠀⠀⠀⠀⠳⡹⡶⣮⣽⣆⡀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⢱⠀⣯⢸⠀⠀⠳⣿⠀⠀ ⢀⠌⠀⠀⠀⠀⠀⠀⡎⡰⢡⣿⡀⠘⡄⠀⠀⠈⡎⣦⠀⠀⠀⠀⠹⣷⡈⢻⣿⡻⣷⣖⠢⠤⠴⣞⢻⡀⠀⠀⠈⠀⢹⠸⠀⠀⠀⡟⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⣷⢃⣾⣿⠷⡀⠱⡀⠀⠀⢹⡸⡷⡀⠀⠀⠀⠘⢷⣾⣿⣿⡜⢮⣦⠀⠀⠘⣧⢣⡀⠀⠀⠀⡎⠀⣦⣀⢠⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣣⢎⣿⡿⠖⠳⡀⠙⡦⢄⣀⣧⣱⡈⢢⡀⠀⠀⠈⢻⣿⣿⣿⣌⢿⢷⣤⡀⠈⢷⣵⡀⠀⠀⡇⠀⠏⠹⣟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠖⠒⠒⠒⠒⠈⠉⠉⠉⠙⠓⠒⠒⠦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⣠⣴⣚⣉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠉⠉⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢋⣤⠤⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠞⠋⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⢤⡀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀ ⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⠀⠀⠀⠉⠷⣄⠀⠀⣠⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀ ⠀⠀⠀⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠘⣦⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⣠⣿⡿⠀⠀⢀⡴⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⣴⣿⡞⠀⠀⢀⡞⠁⠀⠀⣼⠁⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⣴⣿⡿⢛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⢀⣾⡻⡾⠁⠀⠀⡼⠁⠀⠀⣰⠁⠀⠀⢠⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣗⣛⡛⠷⢛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣼⢳⣻⠁⠀⠀⣼⠃⠀⠀⣰⡟⠀⠀⢀⡏⠀⢰⠇⠀⠀⠀⢠⠆⡤⠀⠀⠀⠀⠀⠘⠛⠒⢶⣔⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠇⣿⡇⠀⠀⣰⠇⠀⡀⢀⣿⠇⠀⠀⡾⠀⠀⡞⠀⠀⠀⠀⡎⡼⡁⠀⠀⠀⢀⡆⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⣾⠁⠀⢠⡿⠀⢰⠁⣸⣿⠀⠀⢸⠁⠀⢸⠁⠀⠀⠀⡾⣸⡿⠀⠀⠀⠀⡞⠀⣠⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⠘⣿⠀⠀⣸⡇⢀⡟⢠⣿⡏⠀⠀⡏⠀⢠⡏⠀⢠⠀⡸⣠⡿⠁⠀⠀⠀⣼⢃⢤⠏⠀⢀⠆⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⣿⡆⠀⣿⠀⢸⡗⣾⣧⠃⠀⣰⠇⠀⢸⠃⢠⠃⢠⢧⣿⠃⠀⠀⠀⣸⠃⡾⡜⠀⠀⣾⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣼⣿⣷⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⡀⣿⡇⠀⣿⣶⣾⡆⢸⣿⠀⠀⣿⠀⠀⡏⢠⡏⠀⣿⣾⠏⠀⠀⠀⢰⠇⣼⢡⠃⢀⣾⢳⠁⠀⠀⠀⢀⡞⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢾⡇⢹⣇⠀⣿⣟⣿⢻⣿⣿⠀⢸⢿⠀⢠⣧⡞⠀⡸⣾⣿⠀⠀⠀⢠⡟⣸⣇⡟⠀⣸⣏⡟⠀⠀⠀⠀⡼⠁⠀⠀⣠⡾⠁⠀⠀⠀⢀⠀⣸⣿⣟⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⢿⣸⢿⡏⢻⣸⠙⣿⣦⡼⢸⠀⢸⡟⠙⢻⣷⣿⣇⣀⡀⢀⡞⣰⣿⡿⡇⠀⣿⢻⠁⠀⠀⠀⣸⠃⠀⣀⢀⣿⠃⠀⠀⠀⢰⠇⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡿⢸⠻⣼⠃⠘⠿⣯⣛⡿⡇⢸⣤⣿⠀⠀⣼⡿⣥⠀⠀⢉⡿⣻⢿⣿⣁⡇⢠⠏⡇⠀⠀⠀⣰⠇⠀⢠⡇⣸⠃⠀⠀⠀⢀⡏⠀⢀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⢸⠀⡿⠀⠀⠀⠀⠉⠀⠁⠀⠏⢻⠀⢠⣿⠷⣿⣶⣦⣼⣰⢃⣿⠃⢸⣷⡼⣾⠁⠀⠀⣠⠃⠀⢠⣿⣧⣿⡰⠀⠀⢀⡼⠁⠀⢢⡿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⠇⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠉⣿⠿⣿⣿⣅⣀⢸⣿⢳⠃⠀⠀⢰⠏⠀⢠⣿⠿⣿⢷⠃⠀⠀⣸⢧⠀⢸⣼⣿⣻⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⣧⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣌⣻⣤⣿⠿⢟⠿⡏⠀⠀⣠⠇⠀⢀⣾⡉⢹⣿⡏⠀⠀⢰⣿⠏⠀⣼⣿⡿⣟⢿⣿⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠀⠀⣿⡿⣆⠀⠀⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡼⠀⠀⣰⠃⠀⢀⡞⠀⠉⣿⡿⠀⠀⢀⣾⠃⠀⢠⣿⡿⣣⣿⠘⣿⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⢰⡟⡼⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣳⠁⠀⣴⠃⠀⢠⡾⢷⣣⣾⡻⠁⠀⠀⣼⠏⠀⠀⣼⢟⣵⣿⣿⡇⢸⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡏⠀⡼⠰⢳⡏⢳⡀⠀⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⠃⠀⡴⠁⠀⢠⣿⣶⡟⢹⢻⠇⠀⠀⣰⠿⠒⠛⠛⠛⠿⣿⣿⣿⠇⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡇⢠⠇⣠⢿⠃⠀⢳⡀⠀⠘⢮⣙⡶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⠇⢀⡾⠁⠀⢰⣿⣿⡟⠀⢎⡏⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⡿⠋⢀⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣇⡿⣰⠃⡞⠀⠀⢸⣷⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⢀⡞⠀⠀⣴⣿⣿⡿⠁⠐⣾⣶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣴⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⣿⢻⠇⠀⡇⠀⠀⠀⣿⡿⣦⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡶⢾⣿⠇⢠⠏⠀⠀⣼⡟⣿⣿⠁⠀⢰⠇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣸⡞⡟⠀⠀⡇⠀⠀⠀⣿⠇⠀⣯⣿⣿⠉⣿⣿⣟⣽⣿⣿⣿⣿⠃⣰⠋⠀⢀⣾⡟⠀⣿⠃⠀⢀⡏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣿⢹⠁⠀⠀⡆⠀⠀⠀⡏⠀⢠⢻⣿⠈⠀⣿⣿⣿⣿⣿⣿⡿⠁⠀⠁⠀⣰⣿⡟⠀⣼⡏⠀⠀⣸⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣏⡇⠀⠀⠀⡇⠀⠀⠀⣇⠀⢸⠸⣿⠀⣰⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣴⣿⡿⠀⠀⣿⠀⠀⠐⠃⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀ ⠀⠀⠀⠀⠀⠀⠜⠁⠀⢸⢹⠃⠀⠀⠀⡇⠀⠀⠀⢸⡀⡟⠀⢻⣶⡿⣿⣿⠋⣹⠏⠀⠀⠀⢀⠾⢿⡿⠁⠀⢠⠇⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠙ ⠀⠀⣀⣀⠄⠀⠀⠀⢀⡏⣼⠀⠀⠀⠀⣇⠀⠀⠀⠘⠇⣿⠀⣰⣿⣶⣾⣿⡿⠃⠀⠀⢀⣴⣋⣤⣾⡇⠀⢆⡞⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀
⠀⠀⠀⢀⠄⠒⠈⣵⠒⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣦⡼⡡⠝⠒⠐⢽⣆⠱⡈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢾⠏⠀⠀⡄⢱⠒⡈⢂⠱⣂⡐⡀⠀⠀⠀⠀⠀⠀⠀ ⢰⢸⡄⡆⡀⢡⡘⣟⠏⢔⡄⢩⡔⠐⠀⠀⠀⠀⠀⠀⠀ ⠸⡆⣠⡸⡑⣘⡧⣥⣺⡟⠱⠸⣋⣐⢄⠀⠀⠀⠀⠀⠀ ⠀⠇⠡⡳⢶⠏⠁⠀⠉⠁⠀⡀⣿⡄⠨⣧⡀⠀⠀⠀⠀ ⠀⠘⡀⡏⡌⠀⠁⢀⡄⠀⢀⠇⡷⠘⣄⠈⠙⡒⢄⠀⠀ ⠀⠀⢡⢀⣼⠦⣄⡉⢀⡔⠁⠀⣆⢁⠈⢕⢄⠈⠂⢍⠀ ⠀⠀⡘⠾⡷⢀⣧⡞⡯⠈⢠⢃⡻⣶⠤⣌⢧⣌⡐⢤⠀ ⠀⡰⠀⣸⣤⠜⡋⢃⠳⠀⡈⣼⠈⣶⣴⠁⣾⣿⣿⡄⠁ ⠰⡙⣼⠀⢶⡏⠀⡘⠰⠀⣇⢉⢠⣿⣾⢀⣿⣿⣿⣷⠀ ⢠⢡⣿⠸⣼⣫⡐⢰⣀⣾⢿⣞⢦⣂⣠⢸⣿⣿⣿⣿⠀
⢸⣷⣄⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⣷⠖⠒⠢⠤⠤⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠃⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠋⠉⠀⠀⢰⣿⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠾⠗⠒⠒⠛⠛⠛⠛⢻⣿⡆⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢠⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣜⡟⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡆⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣟⠦⣄⣀⠖⠁⠀⠀⠀⢀⣀⠤⠴⠖⠒⠚⠛⠛⢲⡈⢻⣧⠥⢤⣀⣙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡇⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⣿⣶⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⡾⠋⠀⠀⢠⠉⠉⠓⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣡⠶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢻⢆⢸⠀⠀⢧⢀⠀⠀⠀⠀⢰⢷⡀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⢰⠀⠀⠀⢸⠀⠀⠀⢸⣼⢸⡄⢦⡘⣿⠀⠀⠀⠀⢸⡎⢇⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠐⠀⣸⠁⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⡜⠀⠀⢠⠀⠀⠀⢸⡀⠀⠀⢸⡆⠀⠀⢸⣻⡄⡇⠀⣷⣸⡄⠀⠀⠀⠘⡽⣼⡆⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣥⠀⡟⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠀⢠⡇⠀⠀⢸⠀⢠⠀⢸⡇⠀⠀⢸⢱⠀⠀⢸⣿⣧⢳⠀⠘⣞⡇⠀⠀⠀⠰⣧⢳⣷⠀⠀⠀⠀⡄⠀⢠⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠋⡇⠀⠀⠀⠀⡼⢃⠏⢸⠃⠀⠀⠀⢸⠁⠀⠀⢸⠀⢸⡀⠀⣇⠀⢠⢼⣿⡗⠀⠘⡏⢻⢸⢧⠀⠸⣿⠀⠀⠀⠀⣿⡄⢳⠀⢧⠀⠀⠸⡀⠀⢧⢳⡀⠀⠀⠀⠀⠀⠀⠈ ⢺⣿⣿⣼⠇⠀⠀⢀⡼⠀⡼⣼⡇⠀⠀⠀⠀⡜⡄⡇⠀⢸⠀⠈⣇⡆⣿⠀⠀⠀⣏⣃⣀⣀⣇⣸⣼⠀⢧⡀⣿⣸⠀⠀⠀⢹⢱⣄⡆⢸⡀⠀⠀⢷⠀⠘⡎⢇⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⠀⠀⠀⡼⠁⢠⣇⡏⡇⠀⠀⠀⠀⡇⣷⣷⠀⢸⢸⠀⣿⣱⣏⣇⢴⣾⣿⣿⣿⣿⣿⣿⣿⣤⣈⢻⡟⢸⠀⠀⠀⢸⣏⢿⣽⡀⣧⠀⠀⠈⡆⠀⠹⣞⡄⠀⠀⠀⣀⣠⣤ ⠀⠈⣿⣿⠀⠀⢰⡇⠀⢸⡎⢣⠀⠀⠀⡀⠀⣧⣿⣸⠀⢸⢸⠀⣷⢻⣿⢻⣿⠟⠹⣿⢿⣿⣮⠉⣧⢙⠋⠉⡇⢸⠀⠀⠀⠸⣯⣣⣹⣧⣿⠀⠀⠀⢳⠀⠀⠘⣿⡀⠀⠀⢻⣿⣿ ⠀⠀⢸⡧⠀⠀⣿⠀⠀⢸⡇⣼⠀⠀⠀⠁⠀⣿⡅⣷⡇⢸⣾⡆⣿⠀⢻⡉⠀⠀⠀⢁⡀⠻⠛⢠⡯⠊⠀⠀⡧⢸⠀⠀⠀⠠⣿⣿⠤⣜⣿⠀⠀⠀⠸⡇⠀⠀⠘⣇⠀⣀⡈⠿⣻ ⠀⠀⠈⠇⠀⠀⣿⠀⠀⢸⡇⢿⠀⢰⠀⠀⠀⣿⣿⣿⣽⣾⡹⢳⡏⠆⠀⠉⠀⠀⠀⢀⣳⣴⠖⠚⠁⠀⠀⠀⣿⢸⠀⠀⠀⠀⡿⢤⠀⢸⣿⠀⠀⠀⠀⡇⠀⡆⠀⠘⣮⡭⠖⠋⠉ ⠀⠀⠀⠀⠀⠀⢹⠀⠀⠘⡇⠘⡇⢸⣆⠀⠀⣿⡏⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⠀⠀⠀⠀⡇⠀⠓⠸⣿⠀⠀⠀⠀⣿⡀⡇⠀⠀⠘⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣐⣧⣻⣿⣢⠀⢻⣇⠀⢤⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⣇⣠⠆⣠⡟⠀⠀⠀⠀⣿⣇⡇⠀⠀⠀⢹⡆⠀⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠉⡯⣿⣿⣷⡘⣿⠀⠾⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡟⢁⣴⣷⠃⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⠀⣟⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡇⠹⣏⣿⣿⣦⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣷⣿⣿⡟⠀⠀⢸⠀⠀⣾⣿⠇⠀⠀⡼⢰⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡇⠀⣿⣿⡇⢻⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⡿⠁⠀⢠⡏⠀⠀⡿⡏⠀⠀⣸⣧⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠇⠀⡿⣿⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⠀⠀⡆⢀⣿⡿⠁⠀⠀⡜⠀⠀⢰⡇⡇⠀⣠⣿⠟⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⡇⡇⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢧⠁⠀⢠⡇⢸⡟⠁⠀⠀⣰⠁⠀⢀⣿⠁⡇⢠⡿⠃⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⡄⠀⣿⠁⠀⠀⢸⣹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⢺⣾⠀⠀⢸⠁⢸⠀⢀⡄⢠⠃⠀⢀⡞⡜⠀⣷⡿⠁⢠⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣻⠀⠀⠀⠀⡇⠀⡟⠀⠀⠀⠈⣾⣿⣿⡟⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⣸⡿⠀⠀⡜⠀⣎⣴⡟⢀⡏⠀⢀⡞⢀⡇⠀⡟⠀⠀⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣯⡇⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⠀⣻⣿⣿⢰⣿⢿⢳⣄⠀⠀⢀⣤⣶⣿⠟⠁⠀⠀⣠⣷⡇⠀⠀⡇⠀⢻⡎⠀⡞⠀⢀⠎⢠⣿⡁⢸⠁⠀⢀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⢻⠁⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⣾⣿⡟⣸⡟⡷⣾⣿⣷⣾⣿⣿⣿⣷⣄⣠⠴⠚⣹⣿⠀⠀⢸⠀⠀⣿⠀⡼⠀⠀⠀⣠⣿⣿⠀⣾⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⡏⠀⠀⠀⠀⠀⡇⢸⠁⠀⠀⠀⠀⣿⣿⣿⣿⣹⢷⣿⣿⣿⣿⣿⣿⠽⠚⠉⠀⢀⠔⢻⡏⠀⠀⡟⠀⢰⠃⣸⠃⠀⠀⢐⣽⠏⠃⠀⡟⠀⠀⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢸⠀⣼⠀⠀⠀⠀⣰⣻⣏⣿⢃⣿⡿⢻⡿⠛⠉⠁⠀⠀⠀⢀⠖⠁⠀⣾⠇⠀⢰⠃⠀⢸⣰⠇⠀⠀⣠⣾⡟⠀⠀⢠⡇⠀⠀⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠘⠀⡿⠀⠀⠀⠀⡿⣻⡟⢁⡾⠛⣴⠏⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⡟⠀⠀⡞⠀⠀⣧⠏⠀⠀⣾⣿⣿⡇⠀⠀⣸⡁⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡿⣡⠞⢡⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣰⠃⠀⢸⡏⠀⢀⣼⡿⠋⠉⢛⠃⢠⠏⠉⠒⢦⣅⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣾⡝⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠏⠀⢀⣞⡀⢀⣾⠏⠀⠀⠀⠀⠀⠋⠀⠀⠀⢀⡿⠋⠁⠀⠀⠀⠼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡼⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⢸⣿⣄⠀⠈⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣷⡹⣿⠟⠁⠀⠀⠀⣀⣀⡀⢾⣿⣋⡷⢄⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⢃⠤⠒⠊⠉⠀⠀⠀⠈⢻⣻⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⡷⡄⠰⣥⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⢀⠀⠀⠀⡇⠀⡇⠀⢸⡇⣇⠘⢆⠘⠀⠀⠀⠀⠐⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢠⠀⢸⠀⠀⠀⡄⡄⢰⠀⠸⡇⡟⢶⡈⠣⠀⠀⠀⠀⠀⡇⠀⠀⠈⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡀⠀⠀⢸⠀⠸⡆⠀⠀⡇⡇⢸⣄⠤⡗⡇⠀⠸⡄⠀⠀⠀⠀⣷⣶⠀⠀⠀⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⡇⠀⠀⢸⠀⢨⡟⠀⡀⢷⡗⢺⣧⣶⣷⠷⡤⣤⣽⠀⠀⠀⠘⣿⣿⠀⠀⠀⢺⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⡆⢀⢸⣇⢺⣷⣧⢣⠘⠀⠚⠉⣧⠼⠷⠛⠁⢸⠀⢠⠀⢠⣿⠿⣿⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣃⣇⢸⡌⣿⠿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⠀⢸⢤⠀⢿⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⡍⡄⠳⣷⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⢀⠀⡼⠀⠀⠙⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⣿⠏⠘⣇⠀⢹⡀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢠⠟⢻⣾⣇⠀⢠⣤⠹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⠋⡊⠀⢸⣿⠀⠸⢧⠀⠀⠀⢠⡄⠢⡤⠀⠀⠀⠀⢰⡇⠸⠀⠘⢲⣿⣿⢷⠀⠈⣿⣧⠹⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠚⢁⡜⠀⢀⣿⢾⠀⠀⢾⣷⡀⠀⠀⠀⠄⠀⠀⠀⠀⢀⢿⠀⡆⠀⠀⢸⡿⣿⣸⠀⠀⠏⢻⣧⢹⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣰⡿⠀⢀⣾⠃⠸⠀⠀⣸⡏⠈⠲⣄⠀⠀⠀⠀⢀⣠⠞⢻⢠⠁⠀⠀⢸⣧⡟⠙⡀⠀⠰⡛⣿⣧⠹⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢠⣾⡟⠁⠀⣾⠃⢀⡇⠀⠀⠛⡃⢠⠃⠈⢳⡤⢴⣶⠋⠹⠀⡆⡆⢀⠗⠊⠉⢹⡇⠀⡇⠀⠀⡇⠸⣿⣧⠙ ⣿⣿⣿⣿⣿⣿⡿⠃⢀⡄⣼⠟⠀⠀⡔⠁⠀⣼⠀⡀⠀⣾⠁⡞⠀⠀⣸⠁⢠⣿⣆⡤⢲⡿⠀⡌⠀⠀⠀⢸⡇⢠⢷⠀⠀⢸⠀⢹⣿⣆ ⣿⣿⣿⣿⣿⠏⠀⣠⣿⡅⠏⠀⣠⠊⠉⠀⣼⠇⣸⡇⢀⡟⣸⡇⠀⠀⣿⠀⣸⡏⣿⠇⡌⠁⢠⠁⠀⠀⢀⣸⡇⠘⡿⡇⠀⠀⢇⠀⣿⣿ ⣿⣿⣿⡿⠁⢀⣴⣿⡟⠀⠀⡰⠛⣄⣠⡼⢋⡔⠁⠁⢸⡗⢹⠀⡀⢸⢿⠀⣿⡧⠟⠠⠁⠀⡎⡠⠒⢩⣖⣲⢶⠀⣿⣧⣀⠀⠘⡄⠙⣿ ⣿⣿⡟⠀⢠⡾⡿⠋⢀⣤⡜⠉⢢⡤⢎⣴⠎⠀⣸⠀⢸⠀⡇⢠⢃⡆⡘⣰⡟⠀⢰⡄⠀⣼⠛⢃⣀⡀⠀⡠⠞⢦⠀⣁⡤⠬⢉⣙⣄⠘ ⣿⡟⠀⢠⡟⠀⠀⠀⠇⠀⠁⢀⠋⢀⣾⠃⢀⠜⣿⠀⡜⠸⢀⠆⣼⣀⠜⠋⠀⣠⣼⠃⢰⠏⢩⣿⣿⢿⡷⢀⡴⠊⠑⠢⠶⠤⠒⠀⠙⢦ ⡟⠀⢠⠟⠉⠀⢸⡀⢠⢀⠞⠚⡠⡛⠁⣠⣪⠞⠘⠀⣇⣥⢎⣴⡟⠁⠀⠐⠋⣠⠊⢠⣃⣶⣿⡿⢃⠞⣠⠊⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢰⣄⡠⠔⠂⠉⠁⠀⠀⠀⠀⠈⠉⠀⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢼⢿⡤⠄⠒⠂⠈⠉⠉⠉⠁⠀⠒⠠⢀⡀⣼⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠁⣨⡟⢀⡠⠄⠐⠒⠀⠀⠐⠒⠂⠠⢀⠀⠘⣟⡇⠈⠢⠀⠀⠀⠀ ⠀⠀⢠⠊⢀⠜⡣⡠⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠛⠗⡀⠀⠡⠀⠀⠀ ⠀⢀⢇⠀⠞⠁⠀⠀⠀⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⠑⢽⠀⠄⠇⠀⠀ ⠀⠌⠌⠀⢠⠀⡜⠀⠃⠃⠀⢸⡄⡇⠀⠀⡞⠀⡇⠀⠀⠀⢰⠀⠀⠃⠀⠀⠀⠀ ⠀⠀⠁⠀⡆⢠⠀⣼⢠⠀⠀⣴⢣⡇⠀⢰⠋⢰⡇⠀⢀⡄⠸⠀⠠⠀⢸⠀⠀⠀ ⠀⠀⠀⢀⠃⡞⢠⡟⢰⠀⠠⣿⡿⡇⠀⢸⡇⣼⡧⢀⣸⡅⢰⢀⡄⠀⢸⢰⠀⠀ ⠀⠀⠀⢸⡞⡇⡸⠁⢸⠀⠀⣿⡃⡇⠀⣾⢠⢁⡇⠀⣾⡏⢸⣼⠃⠀⠈⠸⠀⠀ ⠀⠀⠀⢸⠁⢀⡙⠘⠸⣀⣄⠿⠇⠃⠀⠇⣤⣼⠇⢀⣿⡇⡜⣿⠀⠀⠀⠀⡄⠀ ⠀⠀⠀⢸⠀⠉⠉⠛⠋⠉⠀⠀⠀⠂⠀⠀⠀⠉⠙⠛⠛⠛⠁⡘⠀⠀⡇⠀⢁⠀ ⢠⠈⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠇⠀⢠⡅⡆⠈⡄ ⢸⠀⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠆⣸⠁⡇⢡⡐ ⠸⠀⢃⠀⢸⣄⠀⠀⠀⠀⠞⠉⠀⠀⠀⠉⡆⠀⠀⠀⠀⢠⠇⡘⢠⠉⠀⢷⠀⡗ ⠀⠀⠸⠀⠘⡈⣦⣀⠀⠀⠈⠆⠀⠀⣀⠔⠁⠀⠀⢀⢤⡿⠠⢀⢻⠀⠃⠸⡆⢰ ⠀⠀⠀⡇⠀⢃⢧⡏⠱⣤⡀⠀⠀⠀⠀⠀⢀⠠⢲⣿⢨⢡⠁⡌⠈⣧⠀⠀⢧⠀ ⠀⠇⠀⠟⠀⠘⣸⢁⠀⣿⣿⣷⣦⢤⠔⢊⡁⠄⠊⢻⣾⠁⡰⢳⠀⠹⠢⣀⡘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡒⠋⠉⢀⣼⣿⣋⠉⠑⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⢁⠔⠁⢀⠴⠾⣿⣿⠥⠤⠄⣁⠁⠀⠀⡉⠲⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⠖⠁⠀⡔⢁⠤⣠⠏⠀⡠⠀⠀⠀⠉⠓⠤⡈⠢⡀⠡⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⡔⠁⠀⢀⣾⠖⣡⡾⠋⢀⣾⡝⢀⠀⠀⠀⢀⠀⠈⠢⡈⢢⠘⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⢀⠎⡀⠀⢠⠟⢁⣴⡿⠁⢠⣞⡞⢠⠃⠀⠀⢀⡞⡄⠀⠀⠘⡆⢳⣾⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⢤⡾⠋⣰⠇⡜⠀⢠⣋⡴⢻⡟⠁⢠⣿⡿⢀⡏⠀⠀⢀⡞⡐⠀⡜⢀⠆⢸⣾⠟⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣋⣭⣶⣾⣿⠟⠁⣼⡏⡜⢀⠀⣾⣿⠓⣿⣷⣤⣯⡝⠛⣾⡤⠤⢀⡞⣰⠁⠰⢁⡎⢀⠟⢿⠆⢸ ⠀⠀⠀⠀⠀⠀⠀⡰⠋⠹⣌⢿⣿⣿⡟⠁⠀⣼⡿⡰⢀⠇⣸⡏⠙⢼⡹⡿⣿⠟⣿⡄⣿⡇⢀⣞⣾⡇⠀⠀⡞⣰⡟⠀⣯⠀⢸ ⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⣹⣦⣻⠋⠀⠀⡜⢨⣧⠁⡈⢠⡟⠀⠀⠀⠈⠙⠉⠀⠘⠃⢿⣡⣮⠞⠉⠈⢳⣞⣰⡟⠀⣸⡏⠀⢸ ⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⣸⡿⠁⢀⠂⣸⣧⡿⡏⢀⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠑⢺⣿⣷⣿⣩⠿⢀⡔⡛⠀⠀⡆ ⠀⠀⠀⠰⠃⠀⣀⠤⠄⠤⢽⣇⠀⡌⠀⣿⣿⣿⠁⠸⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠘⣯⠿⣿⠿⣏⢠⠎⢠⠁⠀⢰⠁ ⠀⠀⢀⡴⠊⠁⠀⢀⡠⠤⠄⠹⠾⣄⢸⡟⣸⠇⠀⡆⢸⡄⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠛⠚⣉⠏⢀⣧⠃⢀⡇⠀ ⠀⠀⠈⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠈⠹⣿⡿⠀⢠⡧⣾⣷⡄⠀⠀⠈⡣⠈⠓⢄⠀⠀⠀⠀⠀⠓⠀⠀⣨⡏⠀⣾⠇⢠⣿⡇⠀ ⠄⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⢸⣧⣿⣎⢻⡄⠀⠀⠙⠂⠈⠟⠁⠀⠀⠀⠀⢀⣴⢚⡿⠀⢸⡏⠀⣾⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠘⣿⠿⣿⣆⢻⣆⠀⠀⠀⠀⠀⣀⣀⡠⣤⠶⢻⣶⣿⠁⠀⡿⠀⠀⠁⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢿⡀⠙⠻⣷⣯⣿⣿⣿⣿⣿⣿⡏⢀⠇⢰⢺⣿⡇⠀⢸⠃⢰⠀⡄⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢸⣷⣤⣀⠀⣿⠟⢯⣀⣩⣿⠿⣧⡼⠀⡆⢸⣿⠀⠀⡎⠀⡇⢀⠀⡾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠘⣿⡻⠟⢷⣾⠀⠀⠀⠁⢀⣴⠿⠇⠀⣿⣾⣿⠀⠀⠃⠸⡇⢰⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⠀⡏⠀⢀⡞⠁⠀⠀⢀⣴⠟⠁⣀⣇⠀⢹⣿⣿⠀⠀⠀⢣⡇⡈⢀⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⢁⢠⡞⠀⠀⠀⢠⢎⣡⡶⠟⠛⢹⣄⠀⡟⢿⠀⠀⠀⣿⢡⠃⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⠟⠀⠀⢀⣴⡷⡏⠀⠀⠀⣠⠃⠈⠢⡘⣬⡆⡀⠀⢹⡞⢀⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠸⣶⣤⡤⠞⠋⠈⠑⠤⣀⡴⠁⢀⠀⠀⠈⢮⡳⡅⠀⠘⣆⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⢣⠀⠀⣀⢿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⢇⢀⠏⡼⢣⠀⠀⠀⠀ ⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠁⠀⠀⠀⠀⠀⠀⢸⠃⠸⢣⠈⢆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠄⠒⠒⠒⢲⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⡤⠀⠀⢀⠴⠒⡿⣿⣃⣉⣉⡙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⢀⠞⠀⠀⡰⠛⡋⠉⠉⠛⠁⠀⠀⠈⠙⠒⢝⣦⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠂⢠⠎⠀⠀⡜⢀⡜⢁⣾⢁⠀⠀⠄⠀⠀⢀⠀⠀⠈⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢀⠆⠀⡎⠀⠀⢰⠁⣾⡴⢁⡇⣼⠀⠀⡇⡎⠀⢸⠀⢰⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡜⠀⣸⠀⠀⠀⠃⣸⠏⡰⠛⣡⣿⣄⣀⣷⡇⠀⢸⡄⢈⡆⠀⡈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⠁⢠⣇⡀⠀⠀⢀⣿⣾⣤⣼⣿⣇⣦⣹⣿⡇⠀⢸⡇⢸⡇⠀⡗⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡆⢠⣾⣿⠁⠀⠀⠈⡇⠈⢿⣿⣿⠋⠻⢿⣿⣧⠀⣾⣄⣼⠇⠀⡇⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⢖⣹⠁⢸⠀⣾⢉⣿⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠉⠻⢰⣿⣴⣿⡰⢠⢇⣿⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⡶⠛⠋⠉⡜⢀⠇⡜⢻⢠⣿⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢿⣿⣣⣾⣿⢿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠚⠉⠀⠀⠀⠀⢰⠃⡜⢰⠁⣼⠓⣿⡀⠈⡇⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⡜⠙⣿⠉⢸⠀⡎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⢃⠜⢀⠇⠀⡏⠀⣿⣧⠀⠸⡀⠀⢳⠀⠀⠈⠑⣶⣤⡤⠀⠀⡰⠁⠀⠘⡇⠀⡇⠇⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠋⢀⡜⠀⢰⠁⢸⠙⣿⣦⠀⠱⡄⠀⢳⡀⠀⠀⠈⠻⡐⠦⣎⠁⠀⠀⠀⢹⠀⡇⡀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⠠⢄⣀⡠⠊⠀⢠⢾⠃⠀⢸⠀⡎⢀⠿⣷⣧⣀⣈⣦⣤⣵⣤⣀⣀⣴⡟⣲⢤⣉⠉⠉⠉⠉⠑⠓⠛⠂⢸⣿⣤⣄⣀⡀⠀⠀⠀ ⠀⠀⠈⠑⢆⣠⠃⡜⠀⠀⢸⢰⠀⣸⣠⡬⢛⣽⣿⣿⣿⣿⣿⣷⣇⣜⣒⣋⡡⠤⡿⠞⠁⠀⠀⠀⢀⣴⣿⣿⣽⢿⡏⠿⣿⡆⠀ ⠀⠀⠀⠀⠀⢻⣼⠁⠀⠀⣸⠘⢠⡁⠀⣰⣿⠋⠁⠐⣿⣿⠛⠋⠿⣷⡾⠗⠊⣉⢤⣤⣀⣀⣠⣴⢿⡏⢩⡼⠛⠛⠛⠒⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡇⡀⣾⠇⢀⣟⠋⠀⠀⠀⠈⠑⠀⠀⠀⠘⢿⡅⢹⣣⠾⠋⠀⡼⢻⣽⠈⣿⣿⡆⠀⠀⠀⠀⢹⡇⠀ ⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢿⣧⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣮⡀⠀⢀⡼⠃⡞⡇⠀⣼⣿⣧⠀⠀⠀⠀⣸⡇⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⣾⣿⡆⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠚⠉⢩⣧⣤⡟⠁⣰⢱⢀⣼⠋⢹⣿⡆⠀⠀⢀⣿⣇⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⢹⡟⢁⢧⢸⣿⣿⣶⣶⠒⠚⠉⠉⠉⠉⠉⠉⠉⠚⠋⠉⠳⣴⣁⣦⠞⠁⠀⠀⣿⣧⠀⠀⣸⣧⣻⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⢣⠈⢷⠁⡼⡄⢿⣿⣿⣿⣿⣶⣤⡤⠤⠤⠤⠤⠤⠤⣶⣆⣐⣋⣛⣳⣄⠀⠀⢀⣿⡏⢧⡀⢈⣇⠹⡄ ⠀⠀⠀⠀⠀⠀⢸⣆⣀⠀⠳⡈⢿⡄⠘⢌⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠢⠼⣿⣆⠀⠱⣟⢾⣾⠀ ⠀⠀⠀⠀⠀⠀⠸⢾⣏⠀⠀⠙⢄⠳⣄⠀⠈⠉⠙⠛⠛⠿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⣶⡘⣾⣿⠀ ⠀⠀⠀⠀⠀⠀⢠⠟⡈⣧⠀⠀⠀⠱⡌⠳⢄⣀⠀⠀⣠⠶⠛⠉⠛⢿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⢸⣿⡇ ⠀⠀⠀⠀⠀⠀⢸⡀⣇⣿⣷⣄⠀⠀⠈⠲⣄⡙⠿⣿⣄⡀⠀⠀⠀⠀⠈⢛⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠤⠒⠒⠒⠒⠢⠤⢤⣤⣀⠈⣷⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣽⠀⠀⢻⠀⠀⠀⢀⣠⠴⠞⠛⢉⠁⠤⣀⡀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠈⠙⣿⠀⠀⠀⣶⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣇⡀⠈⣧⣠⡶⠛⠁⠀⠀⠀⢀⣴⣶⠌⠉⠙⠲⠦⣄⣀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢻⠀⠙⣇⠀⠀⠀⠀⠀⠐⣣⠀⣇⠀⠀⠀⠀⢀⠀⠙⣟⠦⣄⠀⠀⠈⠠⣄⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡌⣧⠀⠙⢆⠀⠀⠀⠀⣰⠃⠀⢹⡄⠀⠀⠀⠀⠱⣄⠈⢳⡀⠀⠀⠀⠀⠈⠳⡀⠀⠀⢹⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⠉⣷⠈⢆⠀⠘⢧⡀⠀⣰⠃⠀⠀⡼⣇⠀⠀⠀⠀⠀⠙⣄⠀⢳⡄⠀⠀⠀⠀⠀⠙⣄⠀⡏⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠁⠀⠘⡆⠀⠀⠀⠀⠙⢲⡟⠀⠀⣰⠁⠸⡆⠀⠀⠀⠀⠀⠹⡀⠸⣿⡄⠀⠀⠀⠀⢄⡈⢿⣣⡄⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⢣⡏⠀⠀⠻⡄⠀⠀⠀⠀⠈⠀⠀⢠⠃⠀⢰⣿⡜⡆⠀⠀⠀⠀⢷⡀⢱⣧⠀⠀⢰⣄⠀⢻⡆⢣⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡇⠈⣧⡀⣀⠀⢳⡄⠀⠀⠀⣦⣟⡆⠀⠀⠀⢸⣿⣧⢸⣄⠀⠀⠠⡜⡇⠈⡿⣧⡀⠀⣽⡆⢮⠃⠈⢇⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⡀⠀⠈⠉⠉⠀⣶⢷⡄⠀⠀⠺⡿⠁⣼⣦⡸⣾⡏⡿⣇⢹⢤⡴⣴⡻⢣⠀⢡⠋⠙⢦⡀⠀⠈⢧⠀⠘⡆⢠⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀ ⠀⢸⣧⠇⠀⣸⠀⠀⠹⣾⣧⡹⣦⣼⠀⠀⠀⡿⣯⡧⢻⣿⡇⠘⢷⣏⠛⠃⠁⢸⡄⢸⡟⠀⠀⠙⠢⣄⠘⡇⠀⢰⡈⢧⠀⠀⠀⡿⡆⠀⠀⠀⠀ ⠀⣸⡸⠀⠀⡟⠀⢰⠀⠀⠙⠿⢾⠀⠀⡾⠀⠀⠀⢀⣿⣿⢃⣠⠘⡽⡄⠀⠀⠀⡇⠈⣇⣀⣤⣀⣀⣬⣽⣧⠀⠀⢧⠈⣆⠀⠀⢳⣽⡀⠀⠀⠀ ⢀⣇⡇⠀⢸⡇⠀⢸⠀⠀⠀⠀⢸⢰⢸⠃⠀⠀⠀⣼⣻⡝⠀⠀⠀⢻⣷⠀⠀⠀⢣⠀⡞⣡⣾⡛⣯⡀⠘⣿⡆⠀⢸⡀⢹⠀⠀⠈⣏⣇⠀⠀⠀ ⢸⣿⠃⠀⢸⠀⠀⢸⠀⠀⠀⠀⢸⣼⣾⠀⠀⠀⢠⣷⣳⣇⡤⠤⠀⠀⣞⡄⠀⠀⠸⠀⣿⡟⠁⠈⠙⣆⠀⢿⡇⠀⠈⣇⠀⡇⠀⠀⢸⣼⡆⠀⠀ ⣾⠛⠀⢰⠋⠀⠀⠸⠀⠀⠀⠀⠸⡿⡇⠀⠀⢀⣾⣹⣧⣤⣶⣦⣄⠀⢻⣷⠀⠀⢸⢸⠋⢿⠀⠺⠀⡿⠀⢸⢠⠀⠀⢻⠀⠀⠀⠀⢸⣁⢷⠀⠀ ⣿⡆⠀⡆⠀⠀⠀⣦⡇⠀⠀⠀⠀⢳⡇⠀⣠⣶⣿⠏⠉⠈⠹⣂⡉⠓⠙⡿⠀⠀⡟⡐⠀⠈⠳⣌⣶⡷⠃⢸⢸⠀⠀⠘⡆⠀⠀⠀⠈⠃⢾⡇⠀ ⡇⡇⠀⠁⠀⠀⠀⠸⣷⠀⠀⠀⠀⠸⣿⠊⡿⣧⢹⡄⠀⣰⢃⢸⣧⠀⢠⠃⠀⢀⣷⡇⠀⠀⠀⠈⠉⠀⠀⢸⣸⣄⠀⠀⣧⠀⠀⠀⠀⠄⢰⢳⠀ ⡇⡇⢸⢠⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⢹⣿⠀⠀⠀⣿⣜⠒⢋⣿⢏⡾⠁⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⣸⠋⣹⡄⠀⣿⠀⠀⠀⠀⠀⠀⢸⣇ ⡇⡇⢸⢸⢰⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠉⠙⠛⠛⠉⠀⢀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⢸⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿ ⣷⠀⠀⢸⣸⡆⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢠⡏⠠⡴⠗⠂⠀⠀⣠⠞⠁⠀⢀⡏⠀⠀⢸⢸⠀⠀⠀⠀⡀⠀⣿ ⣿⢠⢸⠘⡏⣷⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠻⣗⣶⢤⣄⡀⠀⠀⠀⡟⢠⠟⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⡀⡼⠁⠀⠀⢸⡿⠀⠀⣠⣰⠇⠀⣿ ⣿⡼⡾⡄⢹⡸⡀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⡀⠻⣄⠀⠠⡉⢻⠶⣾⣠⠯⠤⠤⢄⣀⡴⠋⠀⠀⠀⠀⢠⣽⣿⣶⣤⣀⣸⠁⠀⣰⠿⠋⠀⣼⡿ ⠸⣇⢱⣱⡈⢧⢳⡀⠀⠀⣆⠀⠘⣆⢀⠀⠀⢳⡀⠙⣶⣶⣷⣼⣅⣙⠉⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⣠⣿⣏⠻⣿⣿⡿⠉⢀⡀⠁⠀⣀⣼⠟⠁ ⠀⣟⢧⡁⠁⠀⠃⢷⠀⠀⡌⢳⡀⠈⣧⣣⠀⠀⠻⣄⠘⢻⣿⣿⣿⠿⣷⣤⡀⠀⠀⠀⠀⠻⣤⣠⠞⠁⢹⣿⣷⣬⣭⣤⣴⣿⣷⣖⠚⠋⠁⠀⠀ ⠀⢻⡀⠙⠳⣤⣀⠀⠻⣀⣈⠢⣙⣦⣽⣻⣦⡀⠀⠹⡗⢠⣈⠉⠉⣰⣿⣿⣿⣿⣦⣤⡀⠀⠈⠛⠒⠲⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀ ⠀⠈⢳⣀⠀⠲⠭⢽⣒⣆⡉⢳⣎⣉⣡⣿⣿⣿⣆⡀⠈⠆⠈⠉⢁⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⣼⣿⣿⣿⣿⣻⣼⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⠀⠀⠉⠓⠶⠶⠶⠶⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠟⠋⠁⠀⣀⣤⣾⢿⣿⣿⣟⠻⢿⣿⡿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣫⣿⣾⠟⠁⠀⠀⣠⣾⠿⠋⠁⣨⣿⠋⢻⣆⠀⠙⢿⣎⠙⠛⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣾⡟⠁⠀⠀⣰⣿⡿⠀⢸⣿⣆⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠘⢿⣷⣤⣤⣴⣿⣿⠃⠀⠀⣿⢻⣶⣄⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⣩⣿⠏⠀⠀⠀⣿⡄⠈⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⢠⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⡈⣺⣤⠁⠀⢀⡀⠤⠄⠀⠀⠀⠠⠤⢰⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⡀ ⣿⣿⡟⠉⠲⠈⠀⠀⣀⣀⠀⠀⢀⣀⣀⠈⡆⠸⢢⢀⠀⠀⠀⠀⠀⠀⠈⣧⣀⡇ ⣿⣿⣿⡢⠆⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠃⠆⠄⡑⢄⠀⠀⠀⠀⠀⢹⠏⢡ ⠈⢻⣿⠰⡌⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠉⠃⡀⠀⠀⠀⠸⠀⢸ ⠀⠚⢻⠰⠀⢠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢂⠀⠀⠀⠁⠀⠀⡀⠀⣆⣸ ⠒⠒⢺⢀⠀⠎⡌⠀⠀⠀⠀⠀⣔⠀⠀⠐⣠⠀⡄⠈⠀⠀⠀⣤⠀⠀⠃⠀⢡⣀ ⠀⠀⢸⢸⠘⢺⡿⣤⣘⠀⢠⠀⣿⡤⠥⠆⡇⢣⢵⡄⠀⠀⠀⡿⢃⡔⡼⡀⠘⡀ ⠀⠀⠈⣼⣧⡀⣇⢰⠸⡜⠈⡄⠉⠇⢸⠈⠃⠀⠑⢎⡇⠀⡀⣷⠃⢰⢠⢳⡀⠰ ⣦⣄⡀⡇⣿⣟⠯⣻⠿⡷⣹⡐⠄⠺⡾⡷⢿⡓⢒⡿⡇⠀⠇⣯⡀⢌⢞⣾⣗⠒ ⠘⠸⢻⣃⢹⢻⡆⠀⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⣇⡔⠁⠛⠐⠊⠀ ⠀⠀⠀⢸⢸⢸⢱⡀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⡇⠐⢠⢀⣀⣀⢤ ⡑⠲⢿⠿⠘⠈⢸⣿⠢⡀⠀⢀⣀⣀⡄⠤⠀⠀⠀⣠⡇⠀⠀⠀⢀⠆⢸⣿⡻⢸ ⠈⠑⠄⡈⡆⠀⠈⠹⠀⠋⣶⠄⡀⠀⠀⠀⡀⠴⠾⡏⣇⠀⠀⡠⠂⠀⣼⣿⣽⣾ ⠀⠀⠀⠈⡇⠀⢸⠀⢃⣿⡗⣠⣾⣶⠒⠉⠢⢀⢰⣘⠘⢘⢸⢀⡠⠊⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠟⠛⠛⠛⠛⠻⡶⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⠟⡫⠡⠤⠀⣀⣆⠀⠀⠀⠀⠀⠑⠀⠉⠻⢶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡾⠋⢹⠮⠀⠀⠀⠀⠄⢿⡣⡀⠀⠀⠀⠀⠀⡀⠀⠀⠙⢷⣄⠀⠀⠀ ⠀⠀⣴⠟⠀⢀⠂⠀⠀⠀⠀⠀⠀⠓⠑⢼⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠙⣧⡀⠀ ⠀⣼⠏⠀⠀⢨⠰⠀⠀⢰⢠⠀⢠⡀⢰⡀⠃⠀⠀⠠⠀⠘⣆⠀⠀⠀⠀⠘⣷⠀ ⢰⡏⠀⠀⠀⡇⠀⡆⣇⢸⢸⣀⡤⡇⢸⠹⡆⠀⡂⣧⠰⡀⠡⣢⠀⠀⢠⣶⢸⣇ ⣾⠁⡠⢄⢠⣝⣶⠰⠻⣍⠾⠀⠗⢟⣾⠖⡇⢀⠀⣽⠀⢡⠀⠙⡦⠤⢾⢿⠀⣿ ⣿⠊⠘⣼⣧⣸⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⡈⣘⡿⠀⡞⢀⠠⣒⠅⠊⠁⠁⣿ ⢿⡄⠌⠐⡞⠛⠛⠻⣿⢄⠠⠀⠀⠀⠀⡸⢀⢣⣹⣿⠀⢩⠔⢈⠔⠂⠉⠉⠘⣿ ⠸⣿⠒⠂⠵⢄⣠⡤⢻⠀⠇⢠⣀⣤⣾⠃⢌⢺⠃⢸⡆⢸⡤⠁⠀⠀⠀⠀⢸⡏ ⠀⢻⣆⠀⠀⡘⢿⠀⠆⡘⠀⣿⣏⢋⠄⠚⠪⢁⠀⠐⣥⢤⠁⠀⠀⠀⠀⢠⡿⠀ ⠀⠀⠻⣶⠠⠤⢼⠀⠠⠁⠊⡔⠁⡆⠀⠀⠀⠀⢳⡀⠟⡈⠀⠀⠀⠀⣠⡟⠁⠀ ⠀⠀⠀⠙⢷⣄⠀⠠⠇⢀⢆⠀⡐⣅⠀⠀⠀⠀⠀⡞⣾⡇⠀⠀⣠⡾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣶⣄⡆⠜⠋⡰⠉⣆⠀⢀⡀⠤⠴⣿⣃⣴⠾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⢧⣤⣼⣦⣧⣴⠶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⣠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢶⣝⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠱⡄⠻⡷⣿⣦⡀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⢻⡀⠀⠀⢄⠙⡄⢱⡈⠋⠓⠀⠀⢠⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⡄⠀⠈⣧⠀⠀⠘⡄⠘⣆⢣⣼⠃⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⡇⡇⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣷⠀⠀⢹⠀⠀⠀⢧⢀⢹⣎⣇⣀⡾⡟⠀⠀ ⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣼⣿⡇⠀⠀⣾⠀⠀⣧⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⢀⣼⡇⢀⠀⢸⢸⠀⣿⣿⣥⠔⠃⠀⠀ ⠀⠀⢠⣧⡀⠀⠀⠀⠀⠀⢰⣴⠇⠀⢰⠉⣿⡇⠀⠀⣿⡀⠀⣿⡄⣇⠀⠀⣸⡇⠀⢸⡀⣿⡏⠁⢾⡇⢸⠀⢸⢸⡀⣿⣿⣎⢧⠀⠀⠀ ⠀⡄⣸⣿⠇⠀⠀⠀⠀⢀⠸⡟⠀⢠⠃⠀⣿⣏⠉⠉⢻⡇⠈⢿⣿⢻⠉⠀⣿⡇⠀⣾⢁⣿⣤⣦⣾⡇⣸⠀⣸⣸⣇⣴⣿⠈⣎⢳⡀⠀ ⢠⢃⡿⠿⣽⠀⠀⠀⠀⠀⢇⢣⢠⠏⠀⠀⠹⢻⣄⣠⣾⣷⣶⣿⣿⣿⡀⠀⣿⡇⠀⣿⠼⢿⣿⣯⣼⢃⣿⢠⣿⣿⣿⣿⡿⠀⡟⣆⢳⡀ ⣾⣼⡇⠛⣇⡇⠀⠀⠀⠀⠘⡌⣿⠒⢶⣿⠛⠉⠉⣿⢻⣿⢛⠋⠉⠉⠁⠀⠉⠀⠀⡇⠀⣼⣻⡟⢹⣿⠘⠉⠁⣿⠈⢸⠃⢸⡇⠘⡄⢳ ⢻⣟⠧⢴⣳⠘⡀⠀⠀⠀⠀⢱⡹⡀⠈⠛⢷⣄⡀⠹⣌⣋⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠀⣿⣿⡄⠀⠀⢸⡄⡞⠀⢸⠀⠀⠹⡄ ⠘⣿⡆⠀⠈⠻⣧⠀⠀⠀⠀⠀⢳⣳⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣷⠀⠀⠀⢿⡇⠀⣿⠀⠀⠀⢳ ⠀⢹⣇⠀⠀⠀⢻⢧⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⢠⣿⡘⣿⣇⠀⠀⠘⣇⢀⡇⠀⠀⣰⣿ ⠀⠘⣿⠀⠀⠀⠸⣎⢣⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⢿⣣⠈⢻⣆⠀⠀⠹⣾⡇⢠⣾⣿⣿ ⠀⠀⢿⡆⠀⠀⠀⣏⢦⢳⡀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⡼⠁⠀⢳⡣⠀⠹⣆⠀⠀⢹⡳⣿⣿⣿⣿ ⠀⠀⢸⡇⠀⠀⠀⢻⠀⢻⣷⡄⠀⠀⠀⢨⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⠉⠉⠛⣿⣿⠿⠷⠦⠀⠱⡄⠀⠘⢆⠀⠀⠱⡙⢿⣿⣿ ⠀⠀⠀⣿⠀⠀⠀⠸⡆⠠⣿⣿⣄⠀⠀⠀⢣⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⣠⡞⠁⠈⠢⡀⠀⠀⠀⠘⢦⠀⠈⢣⡀⠀⠙⡄⠹⣏ ⡀⠀⠀⢸⡆⠀⠀⠀⡇⠀⣿⣿⢟⢆⠀⠀⠀⠳⡈⢶⣤⣀⠀⠀⠀⠀⠀⠀⢀⡴⠑⠿⢂⣄⠀⠹⡄⠀⠀⠀⣼⠑⣄⠀⠑⠀⠀⠘⢆⠈ ⣇⠀⠀⠈⣇⠀⠀⠀⢻⠀⢸⣿⣞⣦⠳⡀⠀⠀⠱⡈⢻⣿⣿⡗⠒⠦⠤⠴⠋⠀⢀⣤⣿⣿⣆⠀⠙⣄⠀⢠⡏⢀⣿⣷⣤⡀⠀⠀⠈⢣ ⣿⡆⠀⠀⢹⠀⠀⠀⢸⠀⢸⣿⣿⡘⣷⣵⡄⠘⡀⠘⣄⠙⢿⣿⢦⠉⡷⠀⠀⣰⣿⣿⣿⣿⣿⣆⠀⠸⣦⣾⠃⣼⡿⢹⣿⣿⡶⢄⠀⠀ ⣧⢿⡀⠀⠈⣇⠀⠀⢸⠀⢸⣿⣿⣇⢹⣿⣿⣆⢠⠀⠈⢆⠈⢣⣞⣉⣀⣠⣾⢿⣿⣿⣿⣿⣿⣿⣆⠀⢹⡿⢰⣿⠃⣸⣿⣿⣄⠀⠙⠦ ⣿⡞⣇⠀⠀⢹⡀⠀⢸⠀⢸⣿⣿⣿⡀⣿⣿⣿⡆⡄⠀⠈⢣⠀⠹⡟⢏⣹⠇⣸⢻⣿⣿⣿⣿⣿⣿⣦⠀⢿⣿⠃⢀⣿⡋⠳⡟⣦⡀⠀ ⣿⣿⢹⡄⠀⠈⠃⠀⢸⠀⣦⡈⠻⣿⡇⢸⣿⣿⣿⣧⠀⠀⠀⢡⡀⠘⡄⡟⠀⠁⠀⠻⣿⣿⣿⣿⣿⣿⣷⣬⣇⢀⣿⡟⢣⡀⠈⠢⡙⢄ ⣿⣿⣇⢿⡀⠀⠀⠀⡜⢀⣧⡘⢦⡈⠃⠈⣿⣿⢿⣿⡆⠀⠀⠀⠱⡀⠘⣿⣄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠁⠻⣼⣿⡧⡀⠱⡀⠀⠈⠢ ⠘⢿⣿⡜⣷⠀⠀⠀⡧⡼⠉⠳⣄⠑⣾⠀⡏⢁⠼⣿⡇⠀⠀⠀⠀⠱⡄⢰⡄⠙⠢⣄⡀⢹⣍⠉⠉⠙⠋⠀⠀⣿⡿⢧⣈⠲⣌⢦⡀⠀
⠀⠀⠀⠀⠀⠀⢀⡤⠤⠒⠒⢲⡖⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠚⣁⠤⠤⠤⠤⢼⣷⠀⢀⡈⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢷⣤⣪⢖⡥⠒⠊⠉⢉⠉⠺⣿⣇⡀⠱⡀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡿⠋⠀⠀⠀⠀⠀⣧⢠⢠⠀⢣⠀⠹⡀⡀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡯⡿⠁⡄⠀⠀⢰⣄⠀⢹⡆⢎⣆⠀⢣⠀⢱⢹⣆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⡗⡄⢡⠸⡀⠀⡞⡄⠘⣿⡸⣯⠳⡵⣄⠀⢇⡏⢆⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡀⢱⢇⠘⣆⢳⡀⢹⣇⠀⢻⡑⣸⣤⣬⣿⡀⢸⢸⡌⢦⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣧⠸⡜⣦⠹⡆⢳⣄⣿⡄⢺⢿⣽⣾⡈⠀⣧⠈⣾⣼⠄⢣⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⠀⢣⠙⣧⣿⣾⡏⠉⠀⠀⠀⠙⠉⠀⠀⢸⠀⢹⣿⡄⠀⠳⡹⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠘⡇⠀⣿⣍⠙⠿⠁⠠⣄⠀⠀⠀⠀⠀⠀⢸⠀⢸⡏⢻⡄⠀⠘⢾⣗⢦⡀⠀⠀⠀⠀ ⠀⠀⢹⠀⢸⠘⣆⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⣼⠀⣞⢧⠀⠹⣦⡀⠀⠈⠳⡉⠢⣄⠀⠀ ⠀⠀⠈⢇⠸⡄⢻⢳⣄⠀⠈⠑⠋⠀⠀⣠⠎⢹⠀⣹⡘⣆⠀⠀⢿⢦⡀⠀⠈⠢⣄⠙⠦ ⠀⠀⠀⢸⡄⡇⣿⢸⠈⣿⠒⣤⣀⣠⡞⣁⡠⣼⡄⣿⣇⠘⡄⠀⠀⢳⡉⠢⢄⡀⠈⠑⠤ ⠀⠀⠀⡞⢱⢠⣿⠇⢀⣿⢠⢴⠻⣿⠊⠀⠀⣾⠁⡟⢻⣷⣿⠦⢀⣀⡿⣦⣀⣈⠑⢦⣄ ⠀⠀⣸⠁⠀⣏⡟⠀⣌⣯⣼⢻⠀⣭⠀⠀⢠⠇⢸⠙⠦⣍⣀⡀⡸⠃⢠⣿⣿⣿⣧⠈⠓ ⠀⣰⠃⠀⡤⢺⡿⠟⢁⡨⠔⠋⡸⠈⢧⠀⣼⠀⣿⠀⢀⣾⣿⡿⡏⠀⣿⣿⣿⣿⣿⣆⠀ ⡰⢁⠆⣼⡇⠈⢶⣿⡏⠀⠀⢀⡇⠰⡏⠀⣿⠀⣿⠀⣸⣿⣿⢸⡇⠀⣿⣿⣿⣿⣿⣿⡆ ⠁⡜⢰⣿⡇⡘⢸⣿⡧⠀⠀⡞⠀⠀⢣⢸⢸⣇⢹⣦⣏⠛⠋⠋⠁⢸⣿⣿⣿⣿⣿⣿⡇ ⢰⠁⣿⣿⠇⡇⢾⡫⢾⣀⡾⠀⣧⣀⣸⣾⢾⣿⣾⢿⣦⣉⣭⣤⣦⢸⣿⣿⣿⣿⣿⣿⡇
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⠟⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⡠ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡅⢀⡤⠔⠛⢿⣿⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠴⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣆⡹⠻⢿⣿⣆⣀⣤⣶⣾⡻⢿⡒⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀ ⠿⣿⣿⣿⠿⠛⠛⢿⡟⠹⣿⡀⠤⠐⠒⠾⠿⣿⡿⣿⣿⣿⣿⣿⣧⡀⠀⠉⣿⣿⣤⣿⣿⣿⡆⠳⡀⠸⢿⣿⣿⣿⣿⣿⣿⡿⡼⠀⠀⠀ ⠀⠈⣿⡇⠀⠀⠀⠀⢳⠚⣿⣁⣤⣤⡴⢦⣄⠘⢷⡌⠛⢿⣿⣿⣿⣿⣄⠀⠈⠘⣿⣿⠿⢻⠇⢀⠖⠀⠘⣿⣿⣿⣿⢿⡏⡇⠹⡀⠀⠀ ⠀⠀⢹⠀⣆⢰⢊⡉⠽⢿⣿⣅⣽⣿⣿⡄⠈⢟⠊⠻⣆⠈⠙⢿⣿⡟⠻⣷⣦⡀⠀⠙⠚⠗⠒⠁⠀⠀⠀⢹⣿⣿⢿⢈⣿⣿⣆⣣⡀⠀ ⣀⠤⠚⢦⠻⢏⠁⠀⢀⠜⢹⣿⣿⣿⢿⡟⢀⡀⠀⠀⠈⢷⡄⠀⠙⠫⣢⡉⠫⡙⠦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠃⡼⠿⠿⠿⠟⠛⠶ ⡁⠀⢀⠼⠗⠤⡉⣿⣿⡀⠘⠬⣽⠶⡋⠐⠉⠀⠀⠀⠀⠀⠈⠂⠀⣇⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⢠⠎⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡿⠤⣆⠀⠀⣿⣿⣧⣀⠎⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⡤⠋⠀⢠⠞⠁⠀⢸⣿⣿⠃⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⡰⠁⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⢀⠜⠋⠀⢀⠐⠂⢈⣻⣽⠷⢄⣀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⠋⠀⠀⡴⠁⠀⠀⠀⢀⡁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⠄⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀ ⠀⢀⠎⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⢉⣁⠀⠀⠀⠀⠀⢀⡴⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢾⡲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⢰⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⡀⢙⢦⡈⠉⠒⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠏⢸⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⣇⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣦⡁⠌⡓⢤⣀⠀⠀⠈⠉⠒⠢⠤⣤⠔⠉⢠⠎⢠⢃⣄⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀ ⠈⢣⡀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⡒⠌⢙⠒⠤⠄⣀⣀⣀⠀⢀⣴⢧⣠⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠙⠛⣻⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣬⣁⣒⠂⠤⢀⣹⣛⡟⠀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⢠⠖⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⢀⣠⠃⠀⠀⠀⠀⢠⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⢿⣿⠏⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⡴⠟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠶⠛⠉⠉⠻⢿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣧⡀⣤⠶⠚⠉⠙⢿⣿⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⣿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⠴⠶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢈⡟⢿⣿⣿⣷⡃⢀⣠⣤⣶⣞⠻⢿⣗⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢿⣿⠁⠀⣀⣀⣠⣤⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠛⢿⣿⣟⠉⣹⣿⣿⣿⣌⠹⣄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⠀⠀⠀⠀ ⠉⠻⣿⣿⡟⠉⠁⠀⠀⠙⢿⡀⣨⣿⡷⠊⠉⠀⠀⠈⠉⠛⢻⣷⡙⠿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠰⡟⢻⣿⣿⣿⣿⣿⣿⠀⠘⢧⠀⠉⣿⣿⣿⣿⣿⣿⣿⡿⢹⠈⣏⠀⠀⠀⠀ ⠀⠀⠸⣿⡇⠀⠀⠀⢀⣀⣈⣏⠀⣿⣅⣴⣶⣶⣾⠿⠿⣦⡀⠙⣿⣄⠈⠙⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠈⢿⣿⠟⠋⣹⠏⠀⡠⠏⠀⠀⠙⣿⣿⣿⣿⡿⠃⣇⢸⡀⠸⡄⠀⠀⠀ ⠀⠀⠀⣿⠀⣾⡀⡼⠋⢀⣈⣿⣿⣿⣅⣀⣿⣿⣿⣷⡀⠈⣻⠓⠊⠻⣦⡀⠈⠻⣽⣿⣯⠛⠿⣿⣶⣀⠀⠀⠨⠝⠛⠵⠞⠋⠀⠀⠀⠀⠀⢻⣿⣿⣿⣳⠀⣿⣿⣿⡀⢻⣀⠀⠀ ⠀⠀⣀⡿⣄⢯⣧⠳⠋⠁⠀⠀⣼⠸⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠈⢳⣄⠀⠈⠛⢿⡳⣄⠛⠮⡛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⡿⡱⠃⣰⣿⣿⣿⣿⣿⣿⣷⣤ ⠖⠉⠁⠀⢹⣎⠉⠓⠤⣤⣤⡞⠁⠀⡟⢿⣯⣛⣡⡿⣁⡴⠂⠀⠀⠀⠀⠈⠚⢦⡀⠀⢠⠙⢮⣣⡄⠙⠂⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠞⠁⡴⠋⠉⠉⠉⠉⠁⠀⠀⠈ ⣤⣀⣀⣠⠟⡏⠑⠦⠄⢸⣿⣷⠀⠀⣗⢲⠞⠛⢇⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠸⣆⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⡷⠦⣧⡀⠀⠀⣾⣿⣿⣧⠀⡴⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣾⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡼⠁⠀⠀⣠⠟⠀⠀⠘⣿⣿⣿⡟⠁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⢀⡜⠁⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣵⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣞⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⠋⠁⠀⠀⡀⠖⠂⠀⠙⢧⣽⠿⢦⡀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣽⡀⠀⠀⠀⠀⠀⠀ ⠞⠀⠀⠀⢠⠏⠀⠀⠀⠈⠉⠹⠃⠀⠀⠈⠉⠑⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣠⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⢀⣜⠁⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠂⠀⠀⠀⠀⠀⠀⣠⢾⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀ ⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢿⡗⠢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⡞⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣆⠂⡙⢦⡀⠉⠙⠲⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣹⠏⢠⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀ ⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⣌⠢⠈⠳⣄⡀⠀⠀⠈⠉⠓⠶⠤⣀⣀⠀⠀⠀⠀⣠⠞⠁⢠⠏⢀⡞⠀⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠓⢤⡉⠳⢤⣀⡀⠀⠀⠀⠀⠈⠙⠛⠒⠚⠁⠀⣴⠋⠀⡼⢀⣷⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⡀⠀⠀⣠⣴⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⠒⠦⣌⡉⠒⠢⢤⣤⣀⣀⣀⡀⠀⣠⣾⡷⣄⡾⢡⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠷⠟⡟⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣈⠙⠒⠢⢤⣀⡈⠉⢉⡽⢳⡞⠀⣼⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠐⠁⠀⠀⣀⠞⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣭⣉⣉⣺⡅⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇⠀⠀⠀⠀⠀⠀ ⢀⣀⡞⠀⠀⠀⠀⠀⠀⠈⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⢿⣧⣨⣷⠾⠟⠛⠛⠉⢉⠉⠛⠙⢻⣿⣽⣿⣾⣳⢶⣄⠀⠀⠀⠀ ⠀⠀⠀⢸⡿⢯⣿⠋⢀⡤⠴⠒⡜⣌⠣⡍⢛⠲⣄⠻⢋⢠⣈⠙⢷⣮⡳⣄⠀⢠ ⠀⢠⣤⣾⠿⢿⠏⢠⡞⠬⣑⢣⠒⡬⠱⣌⢃⢣⠘⠢⣿⠐⡬⠙⡤⡙⢷⡝⣿⢳ ⣿⢿⡿⢑⠲⢤⡰⢋⠔⡡⠢⠅⢊⠔⡁⢆⢈⠒⣦⠷⢾⣧⡐⢣⡐⣡⠊⣿⣎⢿ ⣿⣿⠃⠎⡅⣺⣅⣬⢶⣡⠈⣑⢊⠜⡐⡊⣄⠃⣿⠐⢺⡏⠻⣮⣷⡰⢩⠌⣿⣎ ⣿⡟⢈⡱⢢⡿⣟⠐⢢⣹⣧⠠⣉⠢⣕⠰⠠⣡⣾⣼⡾⣷⣶⣬⣟⣧⣇⠚⡼⣿ ⣿⡇⡜⣷⡿⢡⣿⣮⣴⣼⣾⣧⡄⢂⣿⣿⣤⣽⠟⣣⣶⡶⠌⠙⢿⣿⡇⢣⣹⣽ ⣿⠥⣘⣿⢸⣿⠟⣻⣿⣿⣍⡉⡉⠉⠀⠀⠈⠈⣸⣿⣿⣧⣨⣶⠸⣿⣧⠣⠜⣧ ⣿⢆⡱⢻⣿⡏⢰⣿⣿⣦⣸⣿⡀⢈⡐⡁⠆⢂⠸⢿⡿⠿⢫⣿⣳⣿⢿⡇⣍⢻ ⣿⢢⠱⣹⣿⣇⢸⣿⠿⣿⠛⣿⠁⢆⠰⣁⠎⡐⣢⡀⠴⠲⢿⡷⢛⠡⡘⣷⠌⡎ ⣿⢢⡹⢜⣿⢿⣆⡀⠡⠤⠘⣀⠜⣰⠛⡐⠎⡜⢡⠢⡵⢋⠆⢆⠣⢄⢡⣿⡣⢜ ⣿⠢⡝⡬⣻⣌⡙⢩⠃⣐⠣⢍⡸⢁⠎⣴⣷⣬⡀⢃⠰⢁⠎⡌⠑⣢⡿⢻⡧⢩ ⣿⢱⢪⡱⣙⣷⡘⢆⠱⢈⠒⡄⠒⠈⠸⢿⣿⣿⡇⠀⠂⠄⢀⣠⡽⢫⡔⢣⡟⣽ ⣿⠆⣧⠓⡼⢼⣷⣮⣒⣌⡀⣀⠈⡀⠀⠈⠛⢉⣀⣠⣤⡾⢟⠭⣜⢣⠞⡥⣿⣹ ⣿⡍⠶⣙⢬⠣⢿⣆⣏⣛⣛⢻⣛⡟⡿⣿⣿⣟⣿⣿⣱⢎⡭⣚⢬⡳⣙⠦⣿⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠳⢦⣤⠤⠴⠶⠶⠶⢖⣒⡒⠺⢻⣧⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣶⡻⠥⠤⠤⠤⠤⠤⢤⣈⠉⢧⢀⡱⣍⠓⣦⠀ ⢀⣠⠔⠯⠩⣲⡄⠀⣠⡞⠛⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⡘⣦⣈⡿⢦⣘⣦⠈⢷ ⢨⠀⠀⠀⠀⢠⠇⣰⡏⠀⢀⡏⠀⠀⠀⢠⡇⠀⠀⠀⠀⣷⠈⠁⠀⠀⠙⢾⡆⠘ ⢭⣢⣤⣤⣪⠞⠀⣿⢰⠀⢸⣇⡀⠀⢀⠗⠀⠀⠀⠀⠀⠏⢧⠀⡆⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠀⠀⠀⣿⣿⠴⡎⠈⠉⠁⠈⠀⠒⠒⠢⠤⠄⠇⠈⢆⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠇⣠⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠋⣰⠋⠉⠛⠻⠆⠀⠀⠀⠀⣠⣤⣦⣄⡀⠁⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⠿⠤⠧⣄⡀⠀⠀⢀⠀⠀⣀⣀⡉⠉⠛⠛⠿⠄⡇⠀⡀⠀⠀⠀ ⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⢙⢦⢀⡼⠖⢋⠉⠉⠉⠓⢢⣄⠀⢸⠁⢰⠃⠀⠀⠀ ⠀⠀⢰⡏⣤⠀⠀⠀⠀⠀⠘⠞⠋⠔⠊⠁⠀⠀⠀⠀⠀⠘⣦⡜⢠⡏⠀⠀⠀⠀ ⠀⠀⢸⡇⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢹⡇⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⢷⡘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⢾⠇⣿⢱⡷⢦⡀⠀⠀⠀ ⠀⠀⠀⠈⢻⡶⠔⣷⣄⡄⠀⠀⠀⠀⣠⣼⠟⠶⠟⡏⢈⣼⣿⡘⠁⠈⢷⠐⠀⠀ ⠀⠀⠀⠀⣾⣇⠀⠉⠸⣅⠀⠀⠀⠀⣼⠃⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢰⡟⠙⢦⣤⣾⣁⠀⠀⠀⠀⢈⢙⣶⠶⡚⠁⠈⢿⣿⣷⠀⢀⠟⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠛⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠈ ⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⣿⣿⣿⣿⣿⣿⡇⢈⣿⣿⣿⣿⣿⣟⢿⣿⣧⠐⢊⣻⣯⣻⣿⣿⣿⣿⣿⡟⡄⠀ ⠿⣿⠿⠛⠻⢛⣯⠄⠐⠻⢿⠿⣿⣿⣷⡀⠙⣿⣽⣿⣮⠢⠹⣿⣿⣿⣿⣧⠃⠀ ⠀⢹⢀⡠⢒⣧⣗⣺⣿⡙⠮⠳⡈⠻⣿⡿⣦⡀⠛⠭⠧⠊⠀⢸⣿⣏⣣⣧⢆⠀ ⠔⠊⣞⠫⢤⡜⢹⢿⡻⠣⠀⠀⠘⠢⡈⡋⡎⠋⠂⠀⠀⠀⠀⠸⡞⡡⠛⠛⠋⠑ ⢁⠮⢤⠈⢼⣧⡠⠁⠐⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⢰⣰⣆⠀⠀⠀⠀ ⠀⠠⠂⠀⢸⣿⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡆⠀⠀⠀ ⠔⠁⡠⠀⠨⠿⠓⠤⢸⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠀⠀⠀ ⠀⠌⠀⠀⠀⠣⠀⠀⡆⠀⠀⠀⠀⠀⠐⠋⠩⠁⠀⠀⣰⢹⣿⣿⣿⣿⣷⠀⠀⠀ ⠘⠀⠀⠀⠀⠀⣴⣎⢫⢑⠀⠄⣀⠀⠀⠀⠀⠀⡠⡞⡄⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⢇⠀⠀⢀⣠⣾⣿⣿⣷⣕⡡⡢⠄⡈⠁⠒⠒⢈⡜⡐⣤⣬⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠑⠲⠋⢿⣿⣿⣿⣿⣿⣿⣶⣥⣔⣈⣍⠰⡛⢸⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⢀⠌⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⣾⠹⣆⣀⣵⠶⠟⠋⠉⠉⠉⠉⠉⠉⢻⣇⣠⠿⣎⣲⠦⣄⠀⠀⠀⠀ ⠀⠀⠀⢸⡿⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠉⠀⠈⠙⢷⣌⠳⣄⠀⢀ ⠀⠀⢠⡼⠛⢶⠏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢦⠀⠀⠀⠀⠙⢷⡜⢟⠃ ⣸⢻⡟⠁⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠴⠾⢦⠀⠀⠀⠀⠀⢻⡌⢯ ⣏⣾⠃⠀⠀⢸⠀⣠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡌⠻⣤⣷⠀⠀⠀⢻⡆ ⢹⡏⠀⠀⠀⡟⣏⠀⠀⠸⣄⠀⠀⠀⡀⠀⠀⢠⣼⣤⠴⠷⣦⣤⡝⣆⡄⠀⠈⢿ ⣸⠇⠀⣧⠞⠀⣻⣄⣀⣠⣾⣆⠀⠀⢹⡶⣄⣠⠟⣡⣶⡶⠀⠉⢿⣿⡇⠀⢰⡸ ⣿⠀⠀⣿⢀⣾⠟⢙⣽⡿⣍⠉⠁⠀⠀⠀⠈⠀⢸⣿⣿⣇⣀⣄⠸⢻⣇⠀⠀⠇ ⣿⠀⠀⢸⢿⡏⢀⣿⣿⣀⣨⣷⡀⠀⠀⠀⠀⠀⠘⠧⠽⠿⠁⣿⣠⣿⢻⡄⠀⠸ ⣿⠀⠀⢸⣇⡇⠘⣏⠻⠿⠋⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡷⠛⠁⠈⣇⠀⠀ ⣿⠀⠀⠈⣿⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀ ⢹⠀⠀⠀⢻⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⠞⠙⡇⠀ ⢸⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣻⠇⠀⠀⠀⠀⣀⠔⠁⠀⠀⠇⠰ ⢸⠀⠀⠀⠀⠸⡷⣄⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⢻⡀⠈⠉⠙⠒⠒⠒⠲⣶⣶⣚⣙⣯⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀
⣠⣤⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀ ⣿⣿⣿⣿⠿⠟⠃⣾⣿⣶⣄⣾⣿⣄⣸⣿⣷⣁⣤⣁⣶⣶⡆⢰⣿⣿⣤⣾⣿⠇ ⣿⣿⣿⣧⣤⡄⢠⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⡇⠀⠻⣿⣿⡿⠃⠀ ⢹⣿⣿⣿⠛⠃⢸⣿⡿⣿⣿⣾⣿⡟⠟⣿⣿⢸⣿⣿⢿⣿⣷⣶⠀⣿⣿⡇⠀⠀ ⠸⣿⣿⣿⠀⠀⠸⠿⠇⠸⠛⠉⠛⠁⠀⠘⠛⠈⠉⠉⠾⠿⠿⠛⠀⠛⠛⠋⠀⠀ ⠀⠉⠉⠉⠀⠀⣠⣴⣶⣶⣶⣤⣤⡆⠀⣤⣤⣴⣶⣄⢠⣶⣦⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⠟⠛⠛⢻⣿⣷⣀⣿⣿⡿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣀⣛⣿⡿⣿⣿⣿⣿⡿⠁⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⡿⠇⠈⠉⠛⠉⠀⠀⠘⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⣤⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡔⢰⣿⣿⣶⣿⣾⡟⣯⣿⡸⣶⣿⣶⣄⠀ ⠀⠀⠀⠀⢠⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡆ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠿⣿⣿⣿⣿⣯⡆⠟ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⣿⠹⠇⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀ ⠀⠀⠀⠘⡀⠿⣿⡏⠀⠀⠠⠶⢶⣦⣤⠀⠀⣰⣿⣧⠀⠀ ⠀⠀⠀⠀⣧⡀⣽⡇⠀⠀⠀⠉⠉⠛⠀⠀⣼⣿⡟⠁⠀⠀ ⠀⠀⣴⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀ ⠀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠐⠦⣷⡟⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠀⠀⠀⠂⡀⠀⠀⠈⢀⣉⣹⡟⠀⠀⠀⠀⠀ ⠸⠿⠿⣿⣿⡇⠀⠀⠀⠈⢦⣀⠀⢀⣀⣩⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣧⠀⠀⠀⢀⣾⣿⣿⣿⣿⠛⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⠿⡄⠀⠀⠘⠛⣽⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⬜⬜⬜⬛⬜⬜⬛⬜⬛⬜⬜⬛⬜⬜⬜ ⬜⬛⬜⬛⬛⬜⬛⬛⬛⬜⬛⬛⬜⬛⬜ ⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜ ⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜ ⬛⬛⬛⬜⬜🟦🟦⬜🟦🟦⬜⬜⬛⬛⬛ ⬛⬛⬜⬜⬜🟦🟦⬜🟦🟦⬜⬜⬜⬛⬛ ⬜⬛⬜⬜⬜🟦🟦⬜🟦🟦⬜⬜⬜⬛⬜ ⬜⬜⬛⬜⬜⬜🟦🟦🟦⬜⬜⬜⬛⬜⬜ ⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬛⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜🟨🟨⬜⬛⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛🟨🟨⬜🟨🟨🟨🟨🟨⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬛⬛🟨🟨🟨🟨🟨⬜⬜⬜🟨⬛🟨⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜🟨⬜⬜🟨⬜⬜⬜⬜🟨⬛🟨🟨 ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨 ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨🟨⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬛⬛⬜⬛⬛⬜🟨🟨⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬛⬜⬜⬜⬛⬛⬜⬛⬛🟨🟨🟨⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛🟫🟫⬜🟫🟫🟫🟨🟨🟨🟨🟨🟨⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨⬛⬛🟨🟨🟫🟫🟨🟨🟫🟨⬛⬛🟨🟨🟨 ⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟫🟨🟨🟨⬛🟨🟨🟨🟨 ⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜🟨🟨🟫🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛🟨🟨🟨⬜ ⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜🟫🟨🟫🟨🟨🟨🟨🟨🟨⬛⬛⬛🟨🟨⬜⬜ ⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜🟫🟫🟫🟫⬛⬛⬛🟥🟥🟨⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟩🟥⬛🟥🟥🟨⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟩🟩🟥⬛🟥🟥🟨🟩⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜🟩🟩🟥🟥🟥🟥🟨🟩🟩⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟩🟩🟥🟥🟩🟩🟩🟩⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨🟩🟩🟩🟩🟩🟩🟩⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟩🟩🟩🟩⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟫⬜ ⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟫⬜ ⬛⬛⬜⬜⬜🟨🟨🟨🟨⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟫⬜ ⬛⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟫⬜ ⬛⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟫⬜⬜ ⬛⬛⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟫🟨🟨🟨🟨🟫🟨🟨🟨🟫⬜⬜⬜ ⬜⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟫🟨🟨🟨🟨🟫🟨🟨🟨🟫⬜⬜⬜⬜ ⬜⬜⬜🟨🟨🟨🟨🟨🟫🟨🟨🟨🟨🟫🟨🟨🟨🟨🟫🟨🟨🟫🟫⬜⬜⬜⬜ ⬜⬜⬜🟨🟨🟨🟨🟨🟫🟨🟨🟨🟫🟨🟨🟨🟨🟫🟨🟨🟫🟨🟫⬜⬜⬜⬜ ⬜⬜⬜🟨🟨🟨🟨🟨🟨🟫🟨🟨🟫🟨🟨🟨🟨🟫🟨🟫🟨🟫⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟨🟨🟨🟨🟨🟫🟨🟨🟫🟨🟨🟨🟨🟫🟫🟨🟨🟫⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟫🟨🟫🟨🟨🟨🟨🟫🟨🟨🟨🟫⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟫🟨🟫🟨🟨🟨🟨🟫🟨🟨🟫⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟫🟨🟫🟨🟨🟨🟫🟨🟨🟫⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟫🟨🟫🟨🟨🟨🟫🟨🟨🟫⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟫🟫🟨🟨🟨🟫🟨🟨🟨🟫🟫🟫🟫⬜⬜ ⬜⬜⬜⬜⬜🟫🟫🟫🟨🟨🟨🟨🟨🟫🟨🟨🟨🟨🟫🟨🟨🟨🟨🟨🟨🟫⬜ ⬜⬜⬜⬜🟫🟨🟨🟨🟨🟨🟨🟨🟨🟫🟨🟨🟨🟫🟫🟫🟫🟨🟨🟨🟨🟨🟫 ⬜⬜⬜🟫🟨🟨🟨🟨🟨🟨🟨🟨🟨🟫🟨🟨🟫🟨🟨🟨🟨🟫🟨🟨🟨🟨🟫 ⬜⬜⬜🟫🟫🟨🟨🟨🟨🟨🟨🟨🟫🟫🟨🟨🟨🟨🟨🟨🟨🟨🟫🟨🟫🟨🟫 ⬜⬜⬜⬜🟫🟨🟨🟫🟨🟨🟫🟫⬜🟫🟨🟨🟨🟫🟨🟨🟫🟨🟫🟫🟫🟫⬜ ⬜⬜⬜⬜⬜🟫🟫🟫🟫🟫⬜⬜⬜⬜🟫🟨🟨🟫🟨🟨🟫🟨🟫⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟫🟫🟫🟫🟫🟫🟫⬜⬜⬜⬜⬜
⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬛🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬛🟩🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬛🟩🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜ ⬛🟨🟥🟥🟨⬛⬜⬜⬜⬜⬜⬜ ⬛🟨🟥🟥🟨🟥⬛⬜⬜⬜⬜⬜ ⬛🟨🟨🟨🟨🟥🟥⬛⬜⬜⬜⬜ ⬛🟨🟨🟨🟩🟩🟨🟨⬛⬜⬜⬜ ⬛🟥🟥🟨🟩🟩🟨🟨🟥⬛⬜⬜ ⬛🟥🟥🟨🟨🟨🟨🟨🟥🟥⬛⬜ ⬛🟨🟨🟨🟥🟥🟨🟨🟨🟨🟨⬛ ⬛🟩🟩🟨🟥🟥🟨⬛⬛⬛⬛⬛ ⬛🟩🟩🟨🟨🟨🟨⬛⬜⬜⬜⬜ ⬛🟨🟨🟨⬛🏾🏾⬛⬜⬜⬜⬜ ⬛🟥🟥⬛⬜⬛🏾🏾⬛⬜⬜⬜ ⬛🟥⬛⬜⬜⬛🏾🏾⬛⬜⬜⬜ ⬛⬛⬜⬜⬜⬜⬛🏾🏾⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🏾🏾⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬜⬜⬛⬛⬛⬜⬜⬛⬛⬛⬜⬜⬛⬛⬜⬜⬜ ⬜⬜⬛⬛⬛⬛⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬛⬛⬛⬛⬜⬜ ⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬛⬛⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜ ⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜ ⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛ ⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬛ ⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜ ⬜⬜⬜⬛⬛⬛⬜⬛⬛⬛⬜⬜⬛⬛⬛⬜⬛⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬛⬜⬜⬜⬜⬜
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⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟩🟩⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟩🟩🟩🟩⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟩🟩🟩🟩🟩🟩⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟩🟩🟩🟦🟩🟩🟩🟩⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟩🟦🟦🟩🟩🟩🟩🟦🟩🟩⬛⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟩🟩🟦🟦🟩🟩🟩🟩🟩🟩🟩🟩⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟦🟦🟩🟩⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛🟩🟩🟩🟩🟩🟩🟩🟦🟦🟩🟩🟦🟦🟩⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟦🟩🟦🟩🟦🟩🟩🟩🟩🟦🟦🟩🟩🟩🟩⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛🟦🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛⬜⬜⬜⬜⬜ ⬜⬜⬛🟦🟦🟦🟦🟩🟩🟩🟩🟩🟦🟩🟩🟩🟩🟩🟩⬛⬜⬜⬜⬜⬜⬜ ⬜⬛🟦🟦🟦⬛🟩🟩🟦🟩🟦🟩🟩🟩🟩🟩🟩🟩⬛⬜⬜⬜⬜⬜⬜⬜ ⬛🟦🟦🟦⬛🟦🟩🟦🟩🟩🟩🟩🟦🟩🟦🟩🟩⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬛🟦🟦⬛🟦🟦🟦🟦🟦🟩🟩🟩🟩🟩🟩🟩🟩⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛⬛⬜⬛🟦🟦🟦🟩🟦🟩🟦🟩🟩🟩🟦⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟦🟦🟦🟦🟦🟦🟦🟩🟩🟦🟩⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟦🟦⬛🟦🟦🟦🟩🟩🟩🟩🟦⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛🟦🟦🟦🟦🟦🟦🟦🟦⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟦🟦⬛🟦⬛🟦🟦⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬜⬛🟦🟦🟦⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛🟦🟦🟦⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛🟦🟦⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛🟨🟨🟨🟨⬛⬜⬜ ⬜⬜⬜⬜⬛🟨🟨🟨🟨🟧🟧🟨⬛⬜ ⬜⬜⬜⬛🟨🟥🟨🟥🟥🟧🟨🟨🟨⬛ ⬜⬜⬛🟨🟥🟥🟨🟥🟧🟧🟧🟨🟨⬛ ⬜⬛🟨🟥🟥🟥🟥🟥🟧🟧🟧🟧🟨⬛ ⬜⬛🟨🟥🟥🟥🟥🟧🟧🟧🟨🟨🟨⬛ ⬛🟨🟥🟥🟥🟧🟧🟧🟧🟧🟧🟨⬛⬜ ⬛🟨🟥🟥🟥🟧🟧🟥🟧🟧🟧🟨⬛⬜ ⬛🟨🟥🟥🟥🟥🟥🟥🟧🟨🟨⬛⬜⬜ ⬛🟨🟥🟥🟥🟥🟥🟧🟨🟨⬛⬜⬜⬜ ⬜⬛🟨🟥🟥🟧🟧🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬛🟨🟨🟨🟨⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜
⠀⠀⣀⣤⣤⣤⡀⢀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⣠⣤⣀⣤⠄⠀⠀ ⢀⣾⣿⡟⠋⠙⣿⣿⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢸⣿⣿⣿⠀⠀⠀ ⢸⣿⣿⡄⠀⠀⢸⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⡄⠀⠀ ⠘⢿⣿⣿⣦⣤⡈⠉⠘⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⠃⣸⣿⡏⢻⣿⣇⠀⠀ ⠀⠈⠻⣿⣿⣿⣷⣄⠀⢸⣿⠀⠀⢀⣿⣯⠀⠀⠀⣿⡇⠸⣿⣿⠀⢸⣿⣿⡇⠀ ⢤⣤⣤⠉⠉⢿⣿⣿⡇⢸⣿⣦⣴⣾⡿⢿⣷⣦⣴⣿⡇⢰⣿⣿⣶⣾⣿⣿⡇⠀ ⢸⣿⡇⠀⠀⠀⣿⣿⡇⠈⠛⠿⣿⣿⠁⠈⣿⣿⠿⠛⠁⣼⣿⠇⠀⠀⣿⣿⣇⠀ ⠀⢻⣿⣦⣀⣴⣿⡿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⠀⢰⣿⣿⠀⠀⠀⢸⣿⣿⡀ ⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠐⠛⠛⠛⠀⠀⠀⠘⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⡿⢹⣿⣏⠉⠉⠉⠉⠉⢿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣿⡿⠁⠀⣿⣿⣧⠀⠀⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⡟⠁⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀ ⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⢹⣿⠟⠻⣷⡀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀ ⠀⢀⣿⣿⡟⠀⠀⠀⠀⣠⣿⠋⠀⠀⠙⣿⣿⣶⣦⣤⣀⣻⣿⣿⡀⠀ ⢠⣿⣿⡏⠀⠀⠀⠀⣰⣿⣷⣶⡶⠶⠶⠾⠿⠿⠿⠿⠿⠿⢿⣿⣿⡄ ⠀⢻⣿⣷⡀⠀⢀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀ ⠀⠀⢻⣿⣷⣀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀
⬜⬛⬛⬛⬜⬛⬛⬛⬜ ⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛🌫️🌫️🌫️🌫️🌫️🌫️🌫️⬛ ⬛⬜⬜⬜⬜⬜⬜⬜⬛ ⬜⬛⬜⬜⬜⬜⬜⬛⬜ ⬜⬜⬛🟪🟪🟪⬛⬜⬜ ⬜⬜⬜⬛🟪⬛⬜⬜⬜ ⬜⬜⬜⬜⬛⬜⬜⬜⬜
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⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜ ⬜⬛🟥🟥🟥🟥🟥⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛🟧🟧🟧🟥⬛ ⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬛🟧🟧🟧🟧🟧🟥⬛ ⬛🟥🟥🟥⬛⬛⬛🟥🟥🟥⬛⬛⬜⬜⬜⬛🟧🟧🟧🟧🟧🟥⬛⬜ ⬜⬛⬛⬛🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬛🟧🟧🟧🟧🟧🟥⬛⬜⬜ ⬜⬜⬛🟥🟥🟥⬛⬛🟥🟥🟥⬛⬜⬜⬛🟧🟧🟧🟧🟥⬛⬜⬜⬜ ⬜⬜⬛🟥⬛⬛🟥🟥🟥🟥⬛⬜⬜⬜⬛🟧🟧🟧🟥⬛⬛⬛⬛⬜ ⬜⬜⬜⬛⬛🟥⬛⬛🟥🟥⬛⬜⬜⬜⬜⬛🟧🟧🟥⬛🟧🟧🟥⬛ ⬜⬜⬜⬜⬛⬛⬜⬜⬛🟥⬛⬜⬜⬜⬜⬛🟧🟧🟧🟧🟧🟥⬛⬜ ⬜⬜⬜⬜⬜⬜⬛⬛🟥🟥⬛⬜⬜⬜⬜⬜⬛🟧🟧🟥🟥⬛⬜⬜ ⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬛🟧🟧🟧⬛⬛⬛⬜ ⬜⬜⬜⬜⬛🟪🟥🟪🟪🟪🟥⬛⬜⬜⬜⬜⬜⬛🟧🟧🟧🟧🟥⬛ ⬜⬜⬜⬜⬛⬜🟪⬜⬜⬜🟪🟥⬛⬜⬜⬜⬜⬛🟧🟧🟥⬛⬛⬜ ⬜⬜⬜⬛⬜⬛🟪⬛⬜⬜⬜⬛⬛⬛⬜⬜⬜⬛🟧🟧🟥⬛⬜⬜ ⬜⬜⬜⬛⬜⬛🟪⬛⬜⬜⬜⬛🟨🟨⬛⬜⬜⬛🟧🟥🟥🟥⬛⬜ ⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬛🟨🟨🟨🟨⬛⬛⬛🟧🟥⬛⬛⬜⬜ ⬜⬜⬛🟨🟨🟨🟨⬛⬛⬛🟨⬛⬛🟨🟨⬛⬜⬛🟧🟥⬛⬜⬜⬜ ⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛🟨🟨⬛⬛⬜⬜⬛🟧⬛⬜⬜⬜⬜ ⬜⬛🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛⬛⬜⬜⬜⬜⬛🟧⬛⬜⬜⬜⬜ ⬜⬜⬛🟨🟨🟨⬛⬛⬜⬛🟥⬛⬜⬜⬛⬛⬛🟥⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬛⬜⬜⬜⬛🟥🟥⬛⬛🟥⬛⬛⬛⬛⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟧🟥🟥🟥⬛🟥🟥🟥🟥🟥⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟧🟥⬛🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟧🟥🟥⬛🟥🟥🟥⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟧🟥🟥🟥⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬛🟨⬛🟨⬛⬜⬛⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟦🟦🟦⬛⬛⬜⬛🟨⬛🟨⬛⬛🟦🟦🟦⬛⬜⬜ ⬜⬜⬜⬜⬛⬜⬜🟦🟦🟦🟦⬛⬛⬛⬛⬛⬛🟦🟦🟦⬜⬜⬛⬜ ⬜⬜⬜⬜⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛🟦🟦🟦🟦🟦🟦🟦⬛⬜ ⬜⬜⬜⬜⬛⬛⬛🟦🟦🟦🟦⬛⬛⬛⬛⬛🟦🟦🟦🟦🟦⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠉⠛⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡎⡇⠀⠀⠀⠀⠀⠹⡿⣧⣀⣀⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠇⢓⣒⠢⢄⠀⠀⠀⠉⠻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣞⣬⣂⣼⣿⣿⣷⡀⠀⠀⢠⠛⠛⢛⠃⢀⣀⣠⣤⣶⣶⣶⣶⣤⡀ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⡦⡠⠞⣒⠋⠋⠉⣿⣿⣿⡿⠋⠁⠉⠙⣿⣷ ⠀⡠⠟⠛⠋⠉⠉⠀⠀⠀⠀⠘⠿⢃⣀⠤⠿⢿⣿⡇⠀⠀⠀⢀⣾⣿ ⠞⠄⠤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣷⣦⣄⣀⡈⠻⣿⣷⣶⣶⣿⠿⠃ ⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠂⢀⡀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣠⣀⠀⠘⠋⠉⠉⠁⠀⠺⣿⡷⣿⣿⣿⡿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣛⠛⠉⠀⠀⠀⠀⠺⣷⣦⠀⠀⠀⠙⠛⠉⠀⠀⠈⣿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣆⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⢸⣦⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀ ⢠⣾⣷⣦⡀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠟⠛⠋⠁⣀⣠⣤⣄⣀⠀ ⠘⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣶⣿⣿⣿⣿⣿⣿⣟⠘⣿⣷⡀⠀⠀⠘⠿⡿⠉⠀⠀⣀⣴⣾⣿⣿⣿⣿⡿⡂ ⠀⠈⠿⢟⣿⣿⣆⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⣿⣿⣎⠛⢫⣿⣿⣿⣷⡘⢿⣿⣆⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠛⠋⠁ ⠀⠀⠀⢺⣿⣿⣿⣷⡄⠀⢰⣿⣿⣿⣯⠹⣿⣿⣿⣷⣶⡜⢿⣿⣿⣿⣷⡄⠹⣿⣷⣄⠀⠀⣴⣼⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢻⣿⣿⣿⣦⡘⢿⣿⣿⣿⣃⠉⢿⣿⣿⣿⣿⡌⢻⣝⠻⠿⢃⡀⣿⣿⣿⣷⣶⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣄⠛⣿⣿⣿⣿⣄⠻⣿⣿⣿⣿⡆⠙⠷⠶⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠈⠻⣿⣿⣿⣷⠘⠧⣉⣁⡴⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣄⠙⠧⣍⣩⡜⢀⣀⣀⠄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣦⣄⣀⣤⣾⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠛⠛⠁⠉⠙⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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