Ayame 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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