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\______________/ __/__|______|__\__ /⭕⭕_______⭕⭕\ |__/__GTR-R34__\__| \©©__|_|_|_|_|__©©/
\____________________/ __/ |____________| \__ /⭕️⭕️__________⭕️⭕️\ |___/___GTR-R34___\___| \🔘🔘_|__|__|__|_🔘🔘/ |____| |____|
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢤⣶⣶⣶⣶⣶⣒⣒⣀⣺⣿⣿⠿⢶⣶⣶⣶⣦⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠒⠲⠦⢤⣉⠙⣿⣿⣿⣟⢿⣿⠿⠿⠿⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡦⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠈⠛⢿⣿⡀⠀⠀⠀⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⢴⣿⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠙⣿⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡶⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠒⠢⠤⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢠⠤⠤⠤⣤⣾⠀⠙⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣾⣛⣩⢴⣿⠿⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠒⠒⠤⠤⢤⣤⣾⢿⣴⢏⣀⣀⣤⡼⠻⡆⠀⠈⢷ ⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠙⠓⠲⠤⠬⠷⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⡞⠉⠀⠀⠹⡟⠀⠀⠀⠀⠀⢱⠀⢠⣼ ⠀⠀⠀⣀⡴⠋⠈⢙⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠢⠤⢄⣀⣠⠴⠛⣋⣠⠴⠒⠉⠉⢉⣲⠶⠀⣀⡠⠤⠒⠊⠉⠁⠀⠀⠀⠠⠀⡂⠐⢹⠂⠀⠀⠀⠀⣼⢰⣿⣿ ⡀⣠⣼⠏⠀⠀⣰⠟⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠋⣉⠤⠒⠋⠁⠀⠀⠀⠀⡀⠠⠀⠈⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⢀⣯⣼⣿⣿ ⡟⠋⠹⢤⣠⠞⠁⠀⠀⠀⠀⠈⠉⠐⠲⠤⢄⣀⡀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠤⣄⣀⣀⠀⢀⡠⠖⠋⠀⠀⠀⠄⡠⢐⠤⠀⠂⠀⣀⣀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢒⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⠀⠀⠀⠈⠈⠀⠀⠀⠀⢀⣴⣿⡿⣿⡝⣆⠀⠀⠀⠴⣽⠤⠞⣠⣵⠿⣻⣿⣿⠈ ⢿⣿⣿⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⣀⣀⣤⣤⣾⣿⢿⡆⢸⣧⢹⠀⠄⣪⣶⣿⣴⠟⢋⣥⠴⢻⣿⠏⠀ ⢸⣿⣿⡇⠀⠘⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣞⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⢻⢸⣿⣾⣿⣾⣤⣾⣿⠿⢋⡡⠞⠉⠉⠉⠉⠀⠀⠀ ⣼⡟⣿⡇⠀⠀⢹⣄⠈⠙⠒⠯⣽⣶⢶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠿⠛⠛⠛⢉⣉⣽⠶⣿⠟⣿⣿⣧⣿⣾⣿⣿⡇⢹⡿⠋⣡⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠳⣼⣧⠴⠛⠉⠉⠉⠒⣦⣤⣀⡀⠀⠀⠉⠙⢦⠀⠉⠉⢙⣷⣶⠒⠒⠒⠶⡶⠶⠶⢶⣤⠖⠚⠉⠁⠀⣰⣷⠾⣿⢿⢥⣼⣾⣿⣿⠃⣸⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠳⣌⣿⢦⣄⠀⢀⣴⣿⣿⣷⣿⡯⣗⠲⠤⣀⡈⣇⠀⠀⠻⡄⠈⣷⠀⠀⠀⡿⠒⠶⠾⢿⠀⠀⠀⢠⣾⡏⠁⣸⡇⢸⡸⢠⡌⢡⣿⠴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠳⢿⣙⠺⢽⣿⣮⣿⣿⠗⠋⠀⠀⠀⠉⡿⠀⠀⣀⣹⣿⣯⣤⣶⣚⣛⣒⣛⣓⣿⠀⠀⠀⢽⣿⣶⣶⡏⢧⣼⣷⡿⢁⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠢⢬⣙⠛⠧⢤⣀⣀⠀⢀⣴⠃⠀⢀⣹⢦⣤⣉⣉⣯⣍⣹⣿⣿⣿⡃⣀⡤⠴⠛⠋⠁⠀⡇⠘⣜⣏⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢤⣈⡉⠉⠙⠛⠛⠛⠲⠤⠤⠤⠴⣶⣶⣿⣿⢿⡿⣯⠀⠀⠀⠀⠀⢀⣠⡟⠤⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠤⢤⣄⣀⣀⣀⣤⣈⣤⣤⠤⣴⣿⣥⠤⠴⠒⠚⠋⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢠⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⣛⣋⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣀⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
AI Story Generator
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠠⠤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⡤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠞⠛⢉⣩⡭⠿⠛⠉⠁⣀⡠⠄⠒⣀⣨⣭⣿⡿⠿⠛⠛⠛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣴⡶⠟⠋⢁⣀⣤⠶⢚⣉⣥⣶⣾⡿⠟⠛⠉⠁⢀⣀⣤⣤⣶⣾⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣆⣈⡉⢷⢠⡶⠛⣉⣡⣤⣶⣟⣫⣭⣶⣿⣿⣛⣋⣉⣀⣤⣤⣶⣾⣿⣿⣟⣻⣭⣷⠚⠉⠉⠛⣆⢸⢉⡉⠨⡆⠀ ⠀⠀⠀⠀⠘⣾⠋⠉⠉⠉⠉⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠂⠈⢉⣉⠉⣻⢇⡀⠀⠀⠀ ⠀⠀⣠⠊⠁⢿⡍⠀⠀⠀⠀⠈⢻⣕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡟⠁⠀⣀⣀⠀⢲⡻⠀⠈⢠⠆⠀ ⠀⢀⡟⠶⢄⣾⣿⣿⣿⣿⣿⣿⣿⣯⣦⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⢤⣤⣤⣤⣤⣵⣿⣿⣿⣿⣿⣿⡿⣿⡤⠔⠛⡇⠀ ⠀⢸⣄⣀⢸⣿⣿⣿⣛⣻⣿⡿⢛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⣛⣻⣿⣟⣿⣯⣿⣷⣠⣠⣼⠀ ⠀⣼⠈⠉⢚⣛⣛⣛⣛⡛⠛⠙⠙⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⢛⣛⣛⣲⣭⣍⠉⢀⢿⠀ ⠀⡇⠉⠉⣿⣶⣶⣶⣿⠟⣽⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣝⡝⢻⣧⣶⣶⣾⡏⠁⢸⡆ ⢐⡇⠀⠀⢻⣿⣿⣿⣇⠀⣣⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⠇⣼⣿⣿⣿⣟⠇⠀⢸⡇ ⢸⡷⠖⠐⢤⠭⢿⡿⠟⣒⣑⣞⣉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣙⣟⣀⡙⠛⠯⠷⠵⢄⠶⠿⡇ ⣀⣧⣄⣀⣀⣁⠘⠿⣿⣯⡽⣍⡻⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡹⣋⢩⡋⣿⣿⡯⠃⣂⣁⣠⣼⣇ ⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠈⠉
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
__________ ___/ _|___|_ \___ |🔴\_____/⚫️⚫️\______🔴| |_______________________| | /_______|Ford GT|______\ | |/__|___|___|___|___|___|__\|
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣶⠌⣿⢈⡿⡁⣹⠇⣶⡤⣿⣯⣼⣭⣭⣽⣭⣭⣿⣭⣭⣯⣽⣿⣭⣽⣭⣭⣿⣭⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣾⣿⣷⣾⣷⣶⣶⣿⣷⣶⣷⣶⣾⣷⣶⣶⣾⣶⣶⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡿⣿⣿⡹⢏⣿⣻⣿⢿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣽⣻⢾⣵⣿⣾⣿⣽⣳⣯⣷⣿⢿⣻⣿⣟⣶⣻⢞⣶⣿⣿⣯⣗⡿⣞⣷⣻⢾⣻⠾⣝⢞⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣏⢷⣫⡟⣿⣿⣻⣿⣿⢯⡿⡽⢯⡻⢿⡝⣎⢳⡹⢎⠷⣫⢗⡫⢞⣽⣽⣶⠿⠟⠋⠁⠘⠈⠁⠉⠀⠁⠈⠀⠈⠀⠁⠀⠀⠀⠁⠈⠁⠉⠈⠉⠉⠑⠉⠙⠛⠻⠿⣿⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⢯⣷⣛⣿⣿⣧⣿⣿⢏⡞⣝⣣⣟⠷⣚⠬⢣⠓⣍⢚⡱⣾⡿⠛⠉⠁⣀⣀⣠⣤⣶⠶⢿⣿⢿⢿⠛⣛⠻⡛⢟⠿⡻⡟⢿⢻⢟⡻⢻⢿⣿⡿⠻⢶⣶⣤⣤⣀⣀⡈⠉⢻⣿⣿⣿⣿⣿⣳⣿⣽⣯⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡝⣞⠶⣽⣺⣿⣿⣿⣟⣮⡝⢦⡳⢎⡛⢬⠉⠇⠙⠄⠂⠕⣚⣶⣿⣿⣿⡿⠿⠟⠛⠛⠁⠊⣻⠙⠋⠘⠂⠃⠑⢊⠒⢁⡉⢊⡉⢊⠉⠁⠈⣿⠑⣉⣟⡛⠛⠻⠋⠽⣿⣿⣿⣿⣿⣿⣿⡿⣽⡾⣯⣟⡿⣿⣻⢿⡿⣿⣿⣿⣿⣾⣹⢿⣿ ⢯⡙⢯⢳⣹⣿⣿⣿⣿⣬⣙⠎⡝⢢⠑⣂⠡⡈⢀⠠⢈⣴⣿⣯⣥⣴⣶⡶⠶⢿⡿⠛⠛⠻⢿⣿⣟⣿⣛⣯⣽⣭⣭⣭⣭⣭⣽⣭⣛⣛⣛⣿⢿⡉⠙⠻⠿⠶⢶⣶⣤⡤⠙⢿⣿⣿⣿⡽⣷⢻⡷⣯⢿⣱⣏⡿⣽⡿⣟⣿⣻⢿⣿⣾⢿ ⢎⡝⢯⡳⣎⣿⣿⣿⣿⢎⠳⡹⠘⠅⠒⠤⢃⠐⣣⣶⣿⣿⡿⣿⣿⣯⠭⣿⣶⣛⣤⣄⣀⠤⠝⡿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠋⠈⠁⠉⠀⠐⣒⡞⠉⢿⣧⣶⣿⣟⡛⢿⣿⣖⢯⡞⡽⢯⣟⣾⣻⢽⣻⣟⣷⡿⣟⣾⡿⣿ ⠈⡘⢣⠝⡢⣿⣿⣿⣿⢎⡱⠄⡁⠠⢀⠐⣠⣴⣿⣻⣿⣿⣷⣿⡿⢃⣼⣿⠿⠋⢀⢿⣹⣞⠻⣹⢖⡶⣶⣺⣍⣻⣝⡳⠏⣙⠒⡐⠂⠀⠠⢀⠒⢀⣠⡤⠀⠲⠘⠣⣄⠹⣿⣿⣿⣷⣶⣿⣿⣮⠽⣹⢳⣛⢾⣽⣳⣿⣞⡷⣿⢿⣯⣟⣿ ⢀⠱⠃⠦⡑⣿⣿⣿⣿⢎⠐⡀⠀⠁⠀⠀⣨⣿⣿⣿⣿⣿⣿⠏⣠⣾⠟⠉⠀⠀⠈⠊⠉⠉⠳⠷⠛⠛⠉⠉⠉⠉⠉⠉⠛⠙⠛⠛⠓⠶⠶⠶⠶⠚⠛⠳⠿⣦⣄⡐⠋⠛⠻⣿⣿⣿⣿⣟⣿⣿⣷⣍⠣⡛⢎⡷⣽⡞⣭⢛⡭⢛⡼⣝⠾ ⠈⠂⠐⡀⢶⣹⣿⣿⣿⣇⡺⣐⠁⠂⠄⢠⣿⢻⣿⡿⣯⢿⣿⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⢶⣽⣯⣝⠿⣿⣌⢻⣿⡌⢡⢉⡚⠌⡱⢛⠴⡋⠜⡩⢉⠇⡞ ⢀⣐⣢⣘⢲⡿⣿⣿⢿⣛⣁⣀⣄⣀⣀⣼⣯⣿⣟⣳⣭⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣭⢻⣿⡆⢿⣿⣷⣶⣾⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿ ⣿⣳⡷⣯⣿⣻⣿⣾⢯⡿⣽⢯⡿⣽⣻⣿⣿⣟⡾⣵⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣏⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡾⣵⡿⢁⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣈⢿⣯⡽⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⡿⣯⢿⣽⣿⠏⣾⠵⠟⣰⡿⠋⠉⠉⢉⠉⠉⠉⠉⠉⡉⢝⠩⣉⠍⡩⢩⣙⣻⢯⡟⣿⣿⣿⣿⣿⢟⣿⣯⡙⢫⠝⣉⢏⠻⡍⡭⣉⠍⣭⣉⢯⣯⡹⣍⡛⣿⣧⠺⣽⣳⢿⣿⣳⣟⢾⣻⡞⣷⣫⡽⢧⣛⡼⣳ ⣿⣻⡾⣟⣾⣟⣾⡿⡽⢾⣝⣯⣻⣾⡏⢸⠧⠋⣼⡿⠁⢀⡒⢬⣌⡛⣿⣇⡉⢖⡩⢎⡱⡜⡬⢵⣶⣿⣿⣿⣷⣽⣿⣿⣿⣷⣮⣿⣷⣯⣓⢮⡝⣮⢳⡝⣶⡹⣞⣵⣿⣿⡷⣿⣳⡳⡜⣿⣧⢚⣽⡈⣿⣗⡎⢧⡳⡝⣧⢏⡽⣫⢽⣹⢳ ⡷⣯⣿⡽⣶⣻⣞⣷⣽⣳⡾⢳⢿⡿⠀⠌⠃⣼⣿⠁⠠⣎⡝⡶⣼⣹⣿⡧⣙⢦⠳⣍⠶⡹⣜⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣷⢾⣱⣿⣾⣧⣿⣞⣿⣿⣿⣿⣿⣿⣿⡽⣽⣿⣧⠚⡅⠸⣿⣽⣷⢻⣹⡜⣏⣻⣽⣣⢿⣜ ⢿⡙⣾⡿⠟⠛⠛⠿⠾⣷⣿⣿⣿⡇⠀⠌⣼⣿⠃⣄⢳⣮⣟⣷⣟⣾⣿⡷⣹⢎⡳⣎⢿⡱⣏⢶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⢿⣯⣷⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣧⢃⠀⢹⣿⣾⣿⡛⠛⠋⠉⠉⠉⠹⣿ ⣿⣽⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠘⢰⣿⡏⡜⢣⡟⣾⣿⣿⣿⣿⣿⡗⣯⡞⣵⢯⡷⣽⡞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢢⠀⢻⣿⣿⣥⠀⠀⠀⠄⠀⠀⢹ ⣿⣿⣯⣝⡳⣆⡄⡀⣼⣿⣿⣿⠃⡰⢋⣿⣿⣱⢯⡿⣽⣿⣿⣿⣿⣿⣿⡷⣯⢷⣻⣞⣷⣽⣻⣽⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠆⢘⣿⣿⣟⡆⠴⡑⢄⡣⣭⣾ ⣿⣿⣿⣿⣿⣷⣮⣵⣿⣿⣿⡿⣳⢥⣿⣿⣯⡿⠋⠈⠉⣿⣿⣿⣿⣿⣿⣿⢿⣻⣯⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠿⣿⣿⣿⣿⡜⣞⣻⣿⣾⣽⣶⣽⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡧⣾⣿⣿⡽⣧⣤⣤⣾⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⡸⡱⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡞⣽⣿⣿⣽⣻⡟⣿⣟⡿⣷⢿⡿⣿⣻⢿⣻⢿⡿⣿⣿⢿⡿⣿⣿⣟⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡱⠹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡜⣴⣿⣿⣿⣿⣷⣿⣾⣼⣿⣽⣳⣿⣷⣿⣻⣽⣿⢿⣿⣽⣿⣻⡿⣷⣿⣯⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢣⡍⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⢛⡱⢾⡇⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⢛⠀⠙⠣⢾⣻⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⣋⡔⢣⠜⣹⣇⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠁⠀⠀⠀⢀⡾⢐⠀⠀⠀⠹⢿⣽⣿⣿ ⣿⣿⣿⣿⠳⣡⢺⠧⣛⡼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠉⠁⠀⢀⠀⡀⠠⢀⠂⠠⠌⡀⣼⡇⠙⡀⠀⠀⠀⠈⠿⣿⣿ ⣿⣿⣿⣧⢛⡴⣿⠀⠉⣿⣽⣧⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠠⡀⠄⡀⢀⠀⠠⠀⠄⠠⠐⠠⠠⢸⣿⣿⠀⠀⠀⢿⣿⡇⠠⠐⡀⢂⠐⢠⠀⠂⠄⠠⡀⠆⡐⠤⢈⡐⠈⡄⢂⢁⠒⠠⢈⠔⢂⠰⣿⢁⠒⡠⠁⡄⠀⠀⠀⡽⣿ ⣿⣿⣿⢆⡻⢼⣿⠀⠀⠐⢿⣿⠎⣖⡀⢀⠀⠄⠂⡀⠂⠁⠌⡀⠂⠌⡐⠈⠐⠈⠠⢈⠁⠡⠈⡄⢁⠂⣁⢺⣿⣿⠀⢁⠂⣽⣿⣇⠡⠐⡠⢡⠘⡠⢉⠘⡈⢅⡐⠡⠐⡌⠠⢌⠡⡐⠨⢄⢊⡁⠆⡌⢂⣿⡇⢌⢢⠁⢎⠰⢡⠈⡰⢳⣿ ⣿⣿⣿⢎⡵⣻⣿⠀⠠⠀⢊⢿⣷⡸⣧⠀⢂⠈⡐⠠⠁⢌⠂⡔⠡⢘⠠⢁⠌⢠⠡⢈⠌⡐⢡⠐⡈⠄⢠⢺⣿⣿⠀⠢⠐⣸⣿⡷⢀⠡⢂⠅⢢⠁⡌⢢⠑⡄⢢⢁⡘⢄⠣⢌⠂⡅⠣⠌⠤⡘⠰⡈⣾⡟⢰⡈⢆⡉⢆⡑⢢⡁⢆⣹⣿ ⣿⣿⣟⣎⢶⣹⣿⠄⢡⠈⡄⢊⣿⣧⢻⣆⠂⠄⠱⢠⠉⡄⡘⢠⢁⠊⡔⠡⡈⢄⠢⣁⠊⢄⠡⢂⠱⢈⠰⢸⣿⣿⠠⢑⠨⢸⣿⣿⢀⠒⡨⠘⠤⡑⢨⠐⡌⠰⡁⠆⡌⢢⠁⢎⠰⣈⠱⣈⠆⡉⢇⣰⣿⠑⣆⠩⢆⡩⢒⠬⡡⢆⠳⡼⣿ ⣿⣿⣿⡜⣦⡓⣿⣭⠐⢢⠐⣁⢚⣿⣏⢿⣄⠘⡠⢁⠎⡐⢌⠰⣈⠒⡌⡐⢡⠊⡔⢠⢉⠢⡘⠄⡃⠂⡍⢺⣿⣿⠠⢈⠔⣹⣿⣿⡀⢣⠰⡉⢆⡑⢢⠑⡌⠱⣈⠒⡌⢢⠉⢆⡱⢌⡑⢢⡙⡔⢎⣾⠏⡜⠤⣋⠴⣡⢃⢎⡱⢈⡱⢿⡽ ⣿⣿⣿⡜⣧⡹⣽⣿⣼⡂⢅⠢⠌⡒⣿⡾⣿⡤⢑⠂⡜⠰⣈⠒⡄⢣⠐⡁⢆⠱⡈⠆⡌⢢⠑⡌⠰⢡⠘⣹⣿⣿⢐⣈⠒⢸⣿⣿⢠⠃⣆⡑⢢⠜⢢⠱⣈⠕⣠⢣⡘⠤⣙⠢⡜⢢⡙⢦⠱⡘⣾⡟⡱⢌⡓⠤⡓⢤⣯⣾⣧⠣⣞⢯⣝ ⣿⣿⣿⡝⡶⣙⣿⣿⠸⣿⣬⣂⠱⡈⡝⢳⠹⣷⣈⠲⣈⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⢆⠱⣈⠑⢢⢉⢾⣿⣿⢠⢢⢉⢼⣿⣿⡡⢓⡰⢌⡃⢎⠥⠓⣌⠚⡤⢣⠜⢢⢅⠳⣌⠣⡜⢢⢣⣹⡿⣁⠳⡌⣜⢡⣹⣿⡟⢸⡷⢸⣝⡾⣭ ⣿⣿⣿⣽⢣⣏⢿⣿⡄⢿⣿⣷⣄⠱⡈⢥⠃⡽⣷⢢⢡⢒⡡⢒⡅⣊⠔⣡⠊⡴⢁⠧⡑⡌⡒⣄⢋⠴⡈⢾⣿⣿⠰⣈⢎⢸⣿⣿⡡⢣⠜⡢⢍⠎⡜⡱⢌⠳⣌⠣⢎⡡⢎⡱⢌⡓⣌⢣⢶⣿⠱⢌⡱⢰⣨⣶⣿⣿⠃⣾⡗⣟⣮⢿⣱ ⣿⣿⣿⣞⡷⣎⡻⣿⣧⠈⣿⣿⣿⡿⣿⡆⣍⠰⢻⣧⢊⠦⣑⠣⡔⠬⡘⣄⠳⢠⢋⡔⣡⢒⡱⡐⢎⠲⣉⢾⣿⣿⢰⠡⢎⢸⣿⣿⡥⢃⢎⡱⢊⡜⠴⡑⢎⡱⢢⡙⢦⡑⢎⡔⢣⡜⢢⢭⣿⠣⡝⢢⣽⡿⢿⣿⣿⠏⣸⣿⢯⡗⣯⢾⣽ ⣿⣿⣿⢿⡼⢧⣻⢹⣿⣧⠸⣿⣯⣄⢸⣿⣦⡡⣉⢿⣇⠚⡤⢓⡌⢣⡑⢦⡙⢢⢃⠖⡡⢎⠴⣉⢎⡱⢌⢾⣿⣿⢌⠳⣌⢺⣿⣿⡧⣉⠦⡱⢩⠜⣡⡙⢦⡑⣣⠜⣢⠙⣆⡚⢥⡚⢥⣾⣯⣵⣬⣿⡿⠂⣶⠻⡿⢰⣿⣿⢺⡽⣏⡷⣾ ⣿⣿⣿⣯⣟⣯⢳⡍⣿⣿⣇⣉⠹⣿⡈⢿⣿⡿⢿⣯⢿⡱⣌⠧⡘⡥⢚⠤⡙⢦⡉⢎⡱⢊⠖⣡⢎⡱⢊⣽⣿⣿⢌⠣⡜⣼⣿⣿⣷⠡⢎⡱⢃⠮⡱⡘⢦⡙⣤⠛⣔⠫⡴⡙⢦⡙⣾⢿⣿⠿⣿⣿⠃⣼⡟⢀⣡⣿⣿⡏⣿⡼⢯⣟⣿ ⣿⣿⣿⣿⡾⣭⢷⣆⠹⢿⣿⣿⣶⣿⣷⠀⠿⢁⣾⣿⣿⡷⣜⣢⡓⣌⢣⡙⡜⢢⡙⢦⠱⣉⠞⣰⠊⡵⣈⠾⣿⣿⣎⠧⡙⣿⣿⡿⢋⡵⢣⠱⣋⠖⣡⠝⣢⠕⣆⠛⡤⢛⠴⣙⣦⡽⢿⣿⣿⣧⠘⠏⢸⣿⣿⣾⣿⣿⠟⣱⡟⣾⢯⣿⣿ ⣿⣿⣿⣿⣿⣽⣳⣞⡐⠢⡙⠿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣷⡨⢝⠻⢟⡶⣷⣬⣇⣜⣆⠳⡡⢞⡡⣋⠴⣡⢚⣬⣿⣧⣊⣵⣿⣿⣵⡉⡖⣍⢣⡙⡜⡡⢞⡡⣞⣨⠧⡗⢏⡛⣍⠶⣱⣿⣿⣿⣿⣶⣶⣿⣿⣿⠟⣋⠥⣈⢷⣻⣭⣟⣿⣿ ⣿⣿⣿⣿⣿⣷⣻⣞⣥⠂⡐⠢⣄⡙⠻⢿⣿⣿⣿⣿⣿⣿⣷⡌⠳⣌⠲⡡⢍⡹⢋⢟⡻⠿⣶⣷⡼⣶⢷⡛⣍⢮⢱⣩⡜⣤⠫⣜⠳⡼⢤⡳⠞⠾⣙⢏⡱⣊⠴⡓⣜⢣⡓⡌⣶⣿⣿⣿⣿⣿⣿⡿⠟⡋⠤⡉⠄⠒⣬⣟⣷⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣯⣷⣦⡁⢆⡐⢨⠁⢆⠩⡙⠿⣿⣿⣿⣿⣷⡣⢌⠳⡑⢮⠱⣉⠦⣑⢣⠖⡤⢓⡬⢒⡱⢊⡖⣿⡿⢿⡷⢃⡎⢵⡘⢦⣑⢫⠱⣃⠎⡵⢨⢣⡙⣤⠣⡝⣰⣿⣿⣿⣿⠿⢛⡁⠒⠌⡁⠒⠠⣈⣴⣿⣿⣿⣤⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣂⣉⠄⠣⢘⠰⢠⢉⡛⠿⣿⣿⣌⢣⡙⢦⡙⢤⢋⡜⢆⡫⢜⡡⢎⢣⡙⢦⢩⡙⣿⡾⣛⠣⡜⢦⡙⢦⡘⢦⡙⢤⢋⡴⣉⠦⡑⢆⡓⣼⣿⡿⢛⠩⠄⡘⢠⠠⢉⡄⣔⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣘⡄⠢⢌⠡⢂⡙⠻⠇⡜⢢⡉⢦⠩⡜⢢⡑⣣⠱⣉⠦⡙⢆⡣⢜⢢⠱⣌⠳⡘⢦⡙⢢⡙⢤⡙⢆⢣⢒⡡⠎⠱⡈⠟⠋⠡⠀⡄⠁⣂⣄⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣦⣁⢆⡑⠨⡐⠡⠜⣂⠳⡈⢧⠘⡤⠓⢥⢊⡕⢪⠔⡩⢆⠳⣨⠱⣉⠦⡑⢣⠜⢢⠘⡌⢂⠆⡰⠉⠄⡁⠈⡀⣤⡴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣯⣟⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣤⣧⣌⣄⣂⣑⢢⣁⢒⡉⣆⢢⢌⡡⢊⡱⣈⠖⣁⢆⣁⢢⡑⣠⢊⣄⣡⣈⣄⣂⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⡿⢯⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣯⣞⡽⣯⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠻⠿⣿⠻⠿⢿⣿⠿⠿⠻⠿⠛⠿⠛⠻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣻⢣⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣝⡽⣳⢯⣟⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡻⢏⣯⣽⣿⣿⣿⣿⣿⡀⠰⠒⠟⠸⣯⢸⠏⠀⢤⠀⠤⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣭⣛⠿⣻⢿⡿⣿⢿⣿⣿⣿⣿⢿⣻⡽⣞⢯⣹⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣚⡽⢳⣯⠿⡽⣏⠷⢫⣹⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡤⢤⣤⢦⠸⣦⠋⣀⢀⡀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣧⣝⣩⠟⡞⣳⢟⡞⢯⣳⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣭⣵⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣀⣸⣃⣼⣠⣟⣀⣛⣘⣃⣀⣀⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠱⡖⠻⣁⡠⠔⠂⠉⠁⣀⡀⢀⡠⣖⣫⡁⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣹⡒⠉⠁⠈⠉⡑⡢⠿⣃⣸⣆⠑⠄⡇⡐⡒⠾⠶⠒⢠⡄⣀⠀⠀⠀⠀ ⠀⠀⡿⢃⡠⠤⠤⡀⠙⡤⢽⠑⠒⠬⢈⡉⠉⠁⠀⡠⠒⠒⠢⡈⠑⠫⣢⣄⠀ ⠀⠀⢱⠃⣴⣶⣦⠈⡆⢏⣉⣓⡂⠤⠄⣀⡁⠀⠘⢰⢾⡿⣢⢸⠀⠀⠀⢩⣧ ⠀⠀⠀⣄⠱⠿⠟⢠⠇⠀⠀⠀⠀⠈⠉⠉⠉⠛⠻⣄⠛⠟⢃⡼⠀⠀⠀⠠⠏ ⠀⠀⠀⠈⠑⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡿⠿⠛⠛⠉⠉⠉⢉⣭⣿⣿⣭⡉⠉⠉⠉⠛⠛⠻⢿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠙⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⣰⣿⣿⠋⠸⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⠇⠙⣿⣿⣦⠀⠀ ⠀⣰⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣶⣦⣤⣿⣿⣄⣀⣀⣀⣀⣠⣿⣿⣦⣤⣶⣾⣿⣿⣿⣿⣿⠟⠋⠀⠀⠘⣿⣿⣧⠀ ⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆ ⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇ ⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇ ⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀ ⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠀⠀ ⠀⠀⠀⠈⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⣄⣠⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣷⣶⣤⣤⣀⣀⡀⠻⣿⣿⣿⣿⠟⠀⣀⣀⣠⣤⣴⣾⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣩⣿⣷⣶⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠢⢄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣩⣭⣿⣿⡟⢛⣿⣶⣠⣿⡙⢦⡀⠀ ⠀⠀⠀⠀⠀⣠⣴⠞⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠟⢿⡟⠛⣛⣛⣛⠻⠛⠛⢋⣩⠭⢝⣻⡅⠈⢉⣻⣿⣿⣿⠿⠛⠋⠋⠀⣼⣿⡿⠁⠈⠉⣿⣷⠀ ⠀⠀⠀⣠⠞⢩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠉⠀⠀⣀⡤⠔⠊⠁⠈⣩⣋⣴⠟⣱⣻⣶⣾⣿⡿⠆⢀⣠⠖⠻⣿⣿⣧⠀⠀⢸⣿⣿⠀ ⠀⢀⣾⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⣱⣁⠤⠔⠒⠉⣁⣠⠤⠒⣲⢻⢟⠟⠁⢠⣿⣿⣿⣿⣿⡷⠟⠋⠁⢀⢼⣿⣿⣿⡀⠀⣾⣿⣿⡆ ⢠⣿⣻⣿⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣠⣤⣶⣾⣉⣉⣻⣧⢶⣿⠇⠁⠀⠀⢀⣿⣿⣿⣿⣿⠁⡄⠀⢀⠞⣾⣿⣿⣿⣷⣢⣿⣿⣿⡇ ⠸⣿⣿⣿⣄⡀⠀⠀⠀⡰⠿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠛⠛⠛⠛⠉⠉⠉⠙⢱⣟⠃⠀⠀⢾⠯⢿⣿⣿⣿⣿⣿⡀⠹⣤⣪⠶⠛⠻⣟⣿⣻⣾⣿⣿⣿⠁ ⠀⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣧⣄⣤⣤⣤⣤⣤⣤⣤⣌⠪⡿⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⢻⣡⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣙⣿⣷⡀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠁⠀ ⠻⢤⣽⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣠⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣙⣛⣛⣉⣉⣉⣉⣉⣉⣻⣯⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
_________________________ \____________________/ __/ |____________| \__ /⭕️⭕️__________⭕️⭕️\ |___/___GTR-R34___\___| \🔘🔘 | | | | 🔘🔘/ |____| |____|
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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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⠀⠀⠀⠀⠀⠀⢙⠯⣷⢻⡶⡄⠋⠷⠘⣷⣤⡲⢶⣕⢦⣾⣦⣔⣮⣶⡴⢦⠬⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⢉⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⠀⠰⠀⡼⠚⣱⣷⢿⣠⣾⣷⢿⢰⡜⢳⡌⣶⣻⡅⠁⢡⠀⠀⠀⠀⠀⢀⣴⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢀⢀⣐⣚⣋⠁⣠⠔⠁⠀⠜⢡⣷⣯⢞⡙⢻⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢪⣽⠾⣿⣧⣛⣉⡑⢶⣭⣻⡿⠿⣷⣿⣿⣭⣙⡻⠶⣄⠉⠀⠑⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢂⡐⡹⠟⡉⢾⣜⣏⢍⢿⡷⠳⡙⣷⠀⡏⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠄⠠⠬⠍⠀⠀⢈⣨⠷⠟⣱⠯⣀⠼⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣴⠿⣷⡾⢿⣿⣷⣿⣛⠷⣿⣿⣯⣷⣽⣾⣽⡻⠖⠒⢌⡀⠀⠀⠀⠸⣿⣿⣷⡙⢾⣽⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⡜⢛⢀⢊⢤⡟⣿⠇⡸⣼⣥⣤⣇⢈⡶⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠐⠃⢀⣨⣀⣀⣀⡨⠅⠂⣀⣴⠞⣩⣾⣥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣸⣿⣧⣿⣿⡷⣭⣻⢿⡿⢾⡼⠿⣿⣿⣿⣿⣿⣟⡛⠵⢶⡠⠀⠀⠀⠀⠹⣿⣷⡹⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠂⠀⢀⠜⠆⢊⣠⣠⣏⣽⢷⣹⣼⠟⢈⠈⠄⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣽⡳⣿⣿⣏⠐⠀⠈⠁⠶⠩⠴⠳⣆⣊⣐⣫⡿⢋⡭⢆⡀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⢿⣿⣽⣻⣿⣷⣗⡶⣽⣫⡝⣛⢿⣿⣻⣷⣮⣟⣯⣛⣓⢮⣍⠁⡈⠀⠀⠹⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠆⠀⠠⠀⠠⡰⢉⠄⢐⡜⠑⡆⠿⡖⡏⠂⣗⠌⠂⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣳⢀⠳⣿⣿⡧⠀⠀⠀⠀⠀⣀⣀⡨⣟⠋⣽⡿⣶⡏⣠⢯⠐⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢭⣿⣿⣿⣿⣞⣿⣻⡽⣭⠻⡭⢟⡻⣯⣿⣿⣾⣿⣆⣛⣝⠿⣕⢺⣦⡀⠀⠘⠿⣿⣷⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⢭⣻⣿⣿⣿⣿⡇⠀⠀⠀⠠⠐⢀⡵⢀⠾⠧⣜⡱⢮⠗⠏⢢⠀⠂⠀⠀⠀⠐⢿⣿⣿⣿⣿⡛⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣰⢊⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⣀⡠⢴⣿⣿⡿⣍⠤⣤⣦⣴⠟⢁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣘⣾⣿⣿⢿⡽⣳⣝⠶⣠⠳⡘⢧⡁⠣⢭⣳⣯⣽⣟⡒⠯⢽⣼⣧⣪⠝⠿⣄⠠⠄⠉⠓⠺⠷⢮⣭⣯⣽⣯⣭⠭⠿⠞⠛⢻⣿⣿⣿⣿⠄⢀⠀⢀⢐⡦⠁⢤⢔⠁⣹⣟⣉⡂⠟⢤⠂⠦⡀⠀⠀⠄⢈⣿⣿⣿⣿⣷⡌⢧⣹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⣱⣾⣿⠟⠁⠀⠀⡀⠤⠀⢂⡼⠳⣞⣯⣿⣿⣻⠟⣋⢱⢋⣳⣽⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡙⣿⣿⣿⡏⠾⠱⢎⣈⠁⠙⠻⠷⠞⡛⡟⢯⣿⣽⣞⣛⢟⡳⠶⣶⣿⣯⣶⠞⠖⢺⡱⣆⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⢋⡽⣯⣶⣃⣰⠀⢘⢰⢆⠊⠊⣴⣫⡯⠞⡯⣓⣴⡌⡬⢧⡁⠈⢀⢘⣿⣿⣭⣟⠿⠻⠿⢯⣟⣿⣿⣿⡿⠿⣿⣟⣫⣵⣻⠭⠟⠁⠀⢀⣠⣶⠶⠶⣭⡯⣹⣿⣿⣛⡯⡿⠵⣶⠶⠿⠻⣟⣧⡽⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣛⣯⣑⡀⠀⠀⠈⠉⠒⠒⠴⢾⢵⡚⠷⢊⣽⣿⣟⣿⣝⣭⣙⣷⣭⡽⠿⣿⢠⡜⣥⣲⡒⠒⠠⠄⠀⠀⠀⠀⠀⠤⢀⣠⣿⣿⣿⣿⣿⣿⡠⢠⡯⣿⣧⣈⣶⢏⣼⣴⠯⣾⡅⠤⢥⣍⢲⣇⢢⣞⣞⣿⣿⣿⡿⣇⡀⠀⠀⠀⠈⠉⠛⠛⠿⣛⠋⠉⠉⢁⣀⣀⣤⣶⣿⢛⣠⠶⣿⣷⠻⣽⠞⣩⠶⠚⣱⠞⠬⠞⣱⣻⣯⣷⡧⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢾⡶⣿⣿⣤⠀⠉⠀⠀⠀⠀⠀⠐⢊⠶⢭⣩⣴⣞⡩⢯⣿⣾⣍⡈⠻⠑⠶⣝⡿⣷⣷⣶⠏⣑⣲⠉⣒⡀⡐⠂⠀⠀⠀⢈⣳⣾⣿⣿⣿⣿⣼⢥⣺⡿⠿⡐⣡⡬⣼⣋⠼⣗⣩⣾⣖⠂⢤⠩⢷⣮⢻⣿⣿⣿⣿⣿⠄⠤⣀⠀⢀⠀⠈⠀⠐⠠⠀⢤⡴⣮⡽⢟⣽⠿⣫⣼⠿⣿⣿⣭⠞⠓⠚⠐⠀⠀⠄⠀⠀⠀⠸⠯⠵⢞⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⣾⣱⢶⣬⡛⡄⠰⠀⠀⠀⢀⠀⠒⠮⢧⡽⣴⣌⣛⣳⣤⡛⠿⣽⢿⣾⣻⠭⣝⡦⠵⠿⣋⡲⠬⣯⡔⢀⠀⠒⠀⠐⠊⢏⣩⣿⣿⣿⡿⣋⣿⣿⣿⣋⣶⣶⣻⣾⣯⢇⡘⢟⣻⣹⣟⡾⠹⡝⢨⢧⣷⣻⣿⣿⣿⡧⢄⠀⠀⠈⠐⢌⠒⠼⢷⣻⠿⣿⡿⢻⣾⣿⣵⣚⡯⣚⡟⠛⠛⡧⢄⡴⢖⣊⡴⠚⣀⡀⠀⡀⠔⠈⠀⠐⣚⣛⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢤⣽⣩⣛⢮⣷⡒⠲⠄⠐⠒⠀⠂⠑⠌⠰⠲⠽⣬⢍⡱⠬⠿⠷⢭⢶⣈⣩⢭⡿⣙⡉⣿⣶⡮⢍⣓⠶⡛⢛⠙⣓⣞⠻⣿⣾⢿⡿⣛⠨⣷⣿⣿⣿⣿⣧⣻⣿⡽⢷⣸⡟⣹⠾⣜⣝⢿⣿⣿⢯⣽⣿⣿⣦⢻⠯⣿⣿⣶⡦⣅⡈⠉⠤⠤⣬⠿⣿⣭⣺⡽⣻⣾⠟⢋⣥⡺⠥⠀⢔⠒⡐⠯⠄⠁⢠⣒⡉⠁⠀⠁⠀⢀⣀⡴⢞⡋⣉⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⢤⣽⣯⣟⣯⣽⣻⠽⣛⢻⣥⡒⠀⠐⠲⠭⣱⣫⣜⣫⢌⡅⣃⣼⡶⢛⢋⣛⡳⢾⡽⢿⣅⣬⠍⠓⡒⠛⠙⢄⡅⠠⣌⡿⠝⠫⡁⠤⠋⣲⣯⣻⣿⣿⣿⣿⣿⣟⡿⢟⣇⣞⢿⣿⣟⣾⣿⣿⣷⣿⣻⣿⣻⣿⣿⣄⢉⣛⣻⢻⣤⣑⠚⢙⣛⣩⡷⣆⣼⣫⢟⠵⣯⡭⢗⢊⣄⣤⡈⠒⠈⠐⠒⠒⢈⣁⠍⠀⠀⠀⢀⡤⠊⣠⠾⠛⠟⣻⡅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠨⢝⣳⠿⢶⣫⣿⢟⡻⣖⣶⡯⠷⠖⡲⢭⣵⣒⡾⠴⣟⣿⢍⡅⣒⡉⠍⠦⣴⣿⣛⠟⠂⠘⠒⡀⢉⣑⣐⠛⢟⣢⠀⠈⠉⠶⢡⠭⠖⣀⠾⣓⢻⣿⣿⣿⣿⣧⣿⣿⣻⣿⣿⣿⣿⣟⣯⣽⣿⣿⣿⣿⣿⣫⡷⠘⠑⠨⠽⣧⣄⣾⠛⠭⡉⠤⠬⠿⠿⣶⡾⢗⣺⠍⡤⠚⣁⠄⣐⠤⠐⠒⡀⣀⡀⠀⢒⣠⠔⠊⠁⠀⣼⡶⠾⠁⠊⣁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠠⣴⣾⣿⢿⣳⠶⡾⢯⡽⢛⡒⠢⠴⠶⢒⢦⣢⣱⡍⣟⡹⢞⠯⣝⣓⣳⠬⣬⣍⡉⠭⣷⠂⠄⣠⠴⠉⠤⠍⠗⢢⣬⡿⢷⠤⣔⠒⠦⢤⠀⠹⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠏⢀⣤⠀⠀⠀⠐⢨⡒⢯⣥⠖⠢⠄⠁⡾⢿⣻⣟⣉⣩⣤⠞⣂⣉⠤⠂⠀⠀⠀⢀⠒⠺⠥⠤⠀⠀⣠⠮⠁⠀⠀⠒⠛⠐⡂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣄⢳⣽⣿⣯⣷⣧⢿⡜⢫⠔⠂⡀⠄⣉⣍⣿⣖⣶⠲⡽⢮⠷⣯⢞⡻⣿⣣⣫⣵⠒⣬⠝⣁⠠⠤⢀⣉⣓⣤⣡⣤⠀⠀⠩⣀⣀⡀⢀⠔⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠄⠀⠐⠀⠐⠫⠨⡥⣶⡯⠞⡉⠷⣉⠑⠲⡤⢖⣰⣊⠴⡶⢖⡂⠀⣀⡈⠓⠔⡚⠉⠀⠀⠀⠀⢀⡠⠄⠊⠀⠀⢀⠐⠋⣙⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢞⣯⢿⣟⣿⣖⡱⢢⢼⣶⣯⠿⣝⣾⣿⠿⢛⠒⢚⢫⡝⣭⢻⣔⣫⠵⣣⢏⡗⠶⣋⡡⠈⠐⠛⢻⣷⡶⠿⠿⣑⡛⡿⢒⠳⣿⣷⠍⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠐⠒⠂⠁⣙⠿⢷⡚⣚⣗⣡⠒⠖⠈⠒⣚⡭⠛⠍⠑⢀⣁⡦⠽⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠯⣼⣻⣾⣯⣟⡇⠣⠶⢖⡯⠯⠭⠔⠦⢌⠁⢈⡬⠒⠭⢒⡱⢎⢧⣛⡴⣋⣞⣭⡗⠂⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠈⡑⠘⣥⣈⠉⣒⡀⠭⢁⣉⣁⣀⠀⠠⠌⢍⣒⡩⣬⡉⢖⣒⠊⠍⣉⠄⡌⡔⡈⠄⢉⠉⠁⠀⠀⠀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⢻⣞⣷⣻⢾⣿⢿⣿⣭⢿⡿⣿⣭⣭⠞⠉⢰⣊⠤⠥⠶⢒⣒⣛⣉⡭⢭⢭⠬⢤⠂⠐⠐⢀⡀⠀⠀⠀⠀⢀⡤⠒⠀⠀⠤⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠚⠛⠛⠉⠻⠷⠶⠒⠒⠂⠀⠀⢒⢛⣋⠿⠶⠤⣭⣘⡄⢫⠙⡴⣍⡒⢈⠈⠁⠀⠀⠀⠀⠀⢊⢁⢂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢌⣳⣻⡼⣭⡿⣿⣟⣦⣙⣦⠿⠿⢛⣒⣲⠭⢅⣒⣢⠭⠍⢁⢂⡶⣼⣶⣿⡾⣽⣒⣫⣥⠶⠑⢈⡋⠥⠄⠒⠁⠈⡀⠁⠁⠀⡠⠀⠔⠈⠀⠂⠀⠈⠠⠀⢀⠄⠂⡠⠚⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⠉⠀⠀⠠⡀⠀⠉⠁⠁⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠠⠩⠍⡝⡒⠒⠭⠭⠗⣒⡠⠤⣀⠀⠀⠀⠀⠀⠴⠌⠂⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢤⣳⢯⣿⣯⠿⢷⣚⣭⠥⢖⡺⠽⣏⣯⣶⣾⠟⣉⡑⠠⠄⢊⣵⣾⡿⢽⣞⣻⡭⠽⢓⠊⣄⡋⠁⢂⠀⠀⠀⡀⢀⠠⠀⠠⠀⡀⠄⠂⠀⠂⢀⣂⡀⡀⠎⣠⡴⢇⠖⠡⢀⢿⣿⣿⣿⣿⣿⠻⡉⢌⡈⠢⡀⠌⠢⠀⠀⠀⠀⠀⠐⠄⠒⠄⠤⢄⡐⠤⠄⣠⠀⣐⠒⠢⠭⢍⣓⣓⠾⠶⢵⣊⡕⠪⠰⠀⠀⠀⠉⠒⠊⠍⣑⡠⠴⢒⠃⠨⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⣘⡶⢿⣯⣿⣶⣿⣿⣿⣾⣛⣢⣤⠷⢾⣳⢗⡎⡱⠄⢀⡐⢚⡭⣕⠶⢛⣋⣭⠵⢒⣩⣴⠿⣋⠤⣲⠃⣠⢆⣪⡰⠁⣀⡠⠀⣈⣀⡠⣀⠤⠋⢁⡴⣪⠝⠝⡋⡠⣂⡼⣳⠊⣼⣿⣿⣿⣿⡟⣤⣌⡰⣍⠲⠪⡨⡠⢁⠀⠀⢄⠀⠀⠄⡀⠈⠁⠉⠉⠁⠑⠂⠀⠀⠳⢤⡒⢆⡲⢌⣋⠑⡒⠢⠭⢭⣓⠲⢤⣀⠀⠀⠀⠀⠀⠈⠑⠲⠽⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣿⣿⣿⣿⣿⣹⣾⢷⣏⣿⣱⣈⣁⡷⢏⠿⣰⠱⣎⢷⣸⠏⣁⠶⠈⣱⠎⣰⣎⡿⢏⡰⢏⣰⠾⢁⡎⠁⠈⡁⢰⠇⢎⡶⠏⡈⣰⠏⠆⠀⢀⡶⣉⣀⣆⠎⡰⣏⠏⡹⡁⣾⣿⣸⣿⣿⡿⣿⣹⡉⠰⡀⠹⡆⢱⢹⡷⡱⡀⡀⢰⡀⠀⠀⠰⠆⠀⠀⠰⠀⠀⠆⡀⠸⢶⡉⣀⠱⡈⢀⢉⡀⠁⠰⠀⠀⠀⠀⠆⡉⠶⢆⡀⠀⠹⠿⢉⠹⡈⠹⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⢿⣻⣟⣿⣻⢾⣟⡿⣯⣷⠿⡱⢆⠯⣹⡥⠟⣊⣵⠞⠉⣀⢔⡫⢖⡭⣒⡭⠞⣉⢞⠔⣡⢞⡡⠎⣠⢊⣴⢋⣔⠁⣠⢊⠔⢁⣤⣦⡚⣯⣶⣽⣵⣧⣦⣶⣷⣧⣾⣿⣿⣿⣿⣿⣿⣿⣯⣿⣈⣧⠫⡲⢌⢵⡀⠱⣔⢄⢻⢄⡈⢦⣀⠈⠒⠢⢤⡙⠶⡂⢤⡚⢍⠲⢽⣢⢤⣁⡈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠒⠨⢕⡢⢤⣁⠂⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣻⢿⣻⢿⡼⣯⣷⣾⣽⣿⡿⣟⢻⡩⣚⠥⠒⠩⣛⣥⠔⣪⠒⢉⣠⠔⠊⠅⠒⢌⡰⢋⢞⡕⢊⢔⠞⣡⠟⣡⠞⡡⡻⢣⢃⡾⢋⡔⠼⣹⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⡿⣿⡿⣿⣿⣷⡿⣿⣾⣿⣿⣷⣄⢫⢈⢆⢆⠻⢆⠹⡆⠄⡀⠄⡙⢄⡈⠒⢍⠢⣀⠀⠈⠁⠈⠉⠙⠆⡀⣀⠙⠂⡀⠀⠀⠠⠀⠀⢀⢢⠌⡑⠪⢝⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣭⠾⣽⢿⣿⣿⣿⣾⣿⣾⡿⢛⣥⣎⠁⠀⢀⡾⢛⠥⠊⠁⣰⠭⠶⢃⡭⡠⠌⡰⢁⡵⢃⠜⣠⢊⡼⢃⡾⢃⠎⡴⡳⢣⠏⡐⠣⠘⡌⠡⢒⡼⡛⢹⡵⢺⠿⣿⡱⢻⠿⢻⣿⣶⣷⣜⣿⠟⣻⢿⠭⣿⠷⣿⣿⡽⢛⠣⢸⢸⡎⡇⡆⠑⡔⢌⢆⠑⢜⢳⠈⠃⠀⠉⠂⠑⢄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡈⣉⠒⠀⢄⡁⣌⣘⠢⠔⣄⠢⢌⡓⠬⢑⠠⡀⠀⠀⠀⠀⠀ ⡳⢎⡿⣡⣏⡽⣯⣿⣿⢟⣩⣾⣿⣿⢿⡛⣡⣊⠖⠁⣀⠶⠟⠉⣀⣾⣫⠞⣁⡶⢡⠟⡘⢌⡲⢡⡾⣡⠟⡰⠁⡼⣱⢣⠃⡐⠌⡡⠡⠌⠠⠴⠋⣸⡵⢒⠥⠚⠉⡠⣿⣣⢻⣿⡷⢿⡯⣙⡙⢦⠭⡓⢜⠻⡮⣉⠑⠦⡌⢸⣸⢀⣇⠇⠀⢈⠢⣊⠳⡈⠢⡑⢄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠄⠀⠀⠢⠄⢑⣲⢶⣤⣌⠭⣛⡜⢄⠒⠠⠀⠀⠀⠁⠐⠄⠀⠀⠀⠀ ⣟⢦⡱⣏⢞⡙⣧⢛⣵⣿⣿⣿⣿⣽⡿⣫⢞⣡⣠⡴⠃⠀⢠⡼⣛⣥⠶⣩⠎⢠⠣⠞⡘⡴⡱⡟⡰⠟⡘⠀⡼⢱⢣⠃⠐⡐⢌⡐⠡⠈⠄⢠⠘⠕⠐⠁⠀⣴⢮⡞⣫⠂⡏⢰⡛⠜⢾⡑⠡⡑⠕⡌⣢⠑⠔⣌⠊⢧⡀⡞⡏⣸⠸⠀⢈⠀⠐⠘⢧⠑⡄⠈⠂⠣⡀⠀⠀⠀⠀⠐⠀⠠⡀⠀⠀⠀⣀⠀⠑⠠⣤⣏⣛⠛⠳⠌⠈⠂⠉⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠆⠳⢎⡿⣫⣶⠿⡽⣞⣷⣯⣿⣞⣽⣿⡿⢟⣁⡴⣢⢠⣾⣿⠫⠍⣻⢇⡔⠃⠁⢊⡜⡰⡝⡰⠹⡸⠁⠈⢠⢇⠇⠀⠡⠈⡄⢨⠁⢣⠘⠤⢀⡀⢀⠂⠘⣸⢋⡜⠃⠹⠅⣏⣆⢬⠠⡑⠔⣥⡘⡌⠆⡃⠀⠈⠁⠀⣱⡹⠀⡇⡆⠐⠀⡀⠄⠀⠀⠑⡘⠄⠀⠁⢀⠄⠀⠠⠀⠀⠀⠀⢀⠢⣀⠀⠀⠙⠻⣶⣄⡙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢂⢄⣠⢪⣾⣽⢧⣟⡳⣟⣾⢟⣵⣿⣿⣷⡿⣻⣿⣾⣿⣿⠟⣁⠤⢒⣥⡏⠀⠀⢀⠜⡔⠱⠰⢁⠇⡇⠀⡀⡞⠎⠀⠀⠠⠁⠄⡡⠊⠄⡼⣢⢦⠏⣰⢎⣼⢣⠋⠀⠀⣰⢸⢚⢸⡈⠀⠁⠈⠈⠂⠳⡑⣅⠠⢀⢂⣰⢣⠇⣸⢸⠀⠄⢀⠀⠀⠀⠀⢀⠘⠌⡄⠀⠀⠢⡑⡈⢄⡈⢂⡀⢀⠑⣍⢿⠿⣖⠧⣀⠉⠋⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠞⢊⡵⢫⠖⣭⢛⡾⣽⡾⣩⣿⣟⡾⣯⣿⣿⣿⡿⣿⣿⡿⢋⣵⣾⣿⢳⠁⠀⢀⢌⣜⢠⢡⠃⢘⢸⠀⠠⡼⣸⠁⠀⠠⢁⠈⡐⠤⢉⠰⠞⣁⡞⡼⢃⠿⣠⠏⣐⠂⣴⣳⠃⠞⡜⠀⡄⠰⠀⠄⠢⠄⢳⡈⢶⡡⢂⢦⢏⣒⡏⡇⢌⠰⢀⠂⠐⠀⠀⠈⠓⢶⡘⡄⣠⣀⠱⡘⣶⣬⣷⢯⣽⣷⣾⣦⡙⣎⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠋⡑⠫⠽⣵⣺⡴⣫⢞⡟⣶⢿⣻⣽⣷⣿⢯⣿⣿⢟⣴⣿⣿⣟⣽⢸⣫⣶⢏⡞⢡⢆⡇⣀⣎⣯⢈⢤⣇⡇⡠⣈⣑⡢⢰⣬⢒⡌⡐⣄⡞⣼⡑⣎⣱⢊⡔⣈⡶⣳⡧⣎⡽⢡⠣⣝⢢⡍⢆⣳⣌⣧⢻⡵⣷⢍⣋⠶⣼⣳⣍⢚⣶⣦⡘⣤⡁⢆⡐⡈⠤⢳⠹⣖⡿⣯⣽⡌⢿⡺⣿⣿⡿⠿⣷⡛⢌⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠒⡠⣫⠾⣳⣞⢾⡹⣞⣧⢿⣼⣽⣻⣻⣯⣾⣻⢯⡿⣽⣏⣾⣿⢋⣾⣽⡟⣾⣷⣿⣧⣿⢋⣼⣼⣳⣿⣴⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣴⣿⣷⣿⣿⣿⣿⣵⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣽⣿⣿⣿⣿⣶⣯⢧⢻⣿⡽⣯⡻⣌⢷⠠⠉⠁⠂⠀⠀⠀⠡⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠰⣚⠉⢩⢞⠥⠒⣄⠋⢖⡻⣵⣚⠿⣜⣣⢟⣵⠿⡽⣯⢿⣽⣷⡇⣿⢋⣾⣿⣿⣹⣿⣿⣿⡿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣳⢯⣟⡎⣷⣿⡙⠧⠜⠎⢆⠀⠀⠀⠀⠀⠀⠀⠀⢌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⣁⣀⣃⡲⠶⠶⠌⣈⠦⡹⣖⣯⣿⣺⡵⣏⢯⣛⡵⢏⣿⣹⣯⣷⢏⣾⡿⣽⣧⣿⡿⣿⡽⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣯⡿⣽⢷⣻⢳⢯⣿⡽⢣⢏⡳⢌⣳⢸⠡⣅⠲⠤⠈⡄⡍⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠀⠉⠉⠉⠡⣄⣴⣬⢂⠱⠤⣍⣚⣫⠝⡼⢳⣬⠳⣍⢮⡵⢺⢇⣾⣯⣿⡿⣽⡳⣟⢷⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⡿⣽⣾⣿⣿⣿⣿⣿⣻⣟⣿⢿⣿⣾⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣟⣯⢿⡿⣾⠿⣝⢿⣭⢷⡙⢷⣎⢼⡻⣧⡂⠁⠈⢁⡆⠓⠀⠁⠐⠶⠘⠐⡀⠑⠂⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢁⠂⠀⠀⠀⠈⠒⣱⣊⣟⣛⠿⣿⣿⡻⡝⢋⠳⢣⠖⣫⢜⣢⣝⢏⡎⣿⣼⣯⣧⣿⣻⣽⣾⣯⢿⣸⡗⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣽⣿⣿⢾⣿⣿⡿⣟⣯⡿⣵⡞⣼⢫⣜⡱⣋⠞⠤⡉⠎⠙⣂⠘⢢⠉⠊⠙⠀⠀⠀⠳⠠⠀⠀⠀⠀⠈⢧⠁⠀⠀⠐⠢⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣍⡉⠙⢓⣲⠆⠀⠀⠀⢀⣠⡤⠴⠒⠛⠋⠉⠉⢹⠉⠉⠙⣓⡒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢯⠉⠉⢧⣀⣠⣴⠚⠉⠀⠀⠀⠀⢠⣤⣤⡀⢸⢀⡖⢻⣉⣉⣷⡀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣧⡴⠞⠉⠉⠉⠉⠉⠉⠑⠲⢦⣼⣿⣿⠃⢸⣸⡄⠘⢦⡀⠈⡇⠀⡤⠶⠶⣿⣷⡦⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⢦⠀⠀⠀⠀⠀⠀⠀⢲⡶⠤⣬⣙⡲⠤⠬⣧⣷⣄⣀⣈⣹⣃⣠⣧⠴⠚⠙⠛⠛⠓⠒⠦⠬⣝⡲⢤⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡽⠏⢀⣀⡤⠤⠤⣄⡀⠀⢳⡶⠤⢿⡍⠙⠒⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠒⠶⣄⠀⠉⠓⠮⣙⠦⣀⠀⠀⠀ ⠀⠀⢸⣄⡼⠋⢀⣠⣤⣀⠀⠙⣆⠀⢳⠒⠒⢿⡀⠀⠀⠀⠀⠉⠙⠓⠲⠤⣄⣠⡏⠀⣠⡴⣶⣤⡀⠈⢧⠀⠀⠀⠈⠓⠾⢷⡄⠀ ⠀⠀⠀⢿⠁⢠⣿⣿⣿⣟⣧⠀⢸⠀⠸⢤⣀⣀⣉⣙⣒⠲⠦⠤⢄⣀⣀⠀⠀⢸⠀⠰⡯⣿⣿⡯⣷⠀⢸⠆⠀⠀⠀⠀⠀⣾⣿⡄ ⠀⠀⠀⢸⡄⠀⢯⡏⣗⣺⠏⠀⣸⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣉⣉⣙⡛⣛⡛⢿⣆⠀⠻⢧⣯⡽⠃⢀⣼⣀⡀⠀⠀⢀⣀⣨⡿⠁ ⠀⠀⠀⠀⠹⣄⠀⠉⠉⠁⢀⡴⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠧⣄⡀⠀⢀⣠⠞⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡶⢽⣿⣮⣿⣍⣭⣕⣎⣿⣲⡂⢆⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢶⣿⣮⣫⣵⡟⣿⠝⠣⠟⢹⠈⣿⡘⠣⠎⠭⣷⠳⡿⢯⣥⣂⡖⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣪⣖⣯⣾⡿⠗⠋⠉⠀⠀⠀⠀⠀⢸⠀⣿⡅⠀⠀⠀⠀⠁⠉⠛⠫⢿⢧⣗⠎⡕⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⣣⢪⣷⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠠⣟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠿⢮⡹⡍⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⢁⣜⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣯⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⢿⣂⡙⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢾⣳⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡀⣯⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠽⣿⣌⢶⠀⠀⠀⠀ ⠀⠀⢠⠣⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣧⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⡣⣫⠄⠀⠀ ⠀⢀⢣⣽⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⣧⢛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣩⢯⡀⠀ ⠀⡎⢘⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣧⢫⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⢊⡷⠀ ⢰⠀⣻⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⡬⢳⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣼⡆ ⡇⢘⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡽⢱⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢣⣧ ⢁⣧⢗⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠓⠄⡀⠀⢱⣻⠿⠫⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡜⣧ ⣿⣿⣚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⣀⣈⠀⠀⠀⠀⠙⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢍⡇⣿ ⣿⡟⢼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⢠⣴⣴⣿⣿⣿⣿⣦⣄⡄⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⢹⣟ ⢹⣧⡾⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡀⣤⣴⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣷⣦⣄⢀⠀⠋⠢⡀⠀⠠⠀⠀⠀⠀⠀⠀⡸⣷⣼⡟ ⠸⣿⣫⣿⠀⠀⠀⠀⠀⠀⡠⠊⠀⣀⣤⣾⣿⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣶⣤⣀⠀⠑⢔⡄⠀⠀⠀⠀⢀⠇⣣⣿⠇ ⠀⠻⣧⢽⣇⠄⠀⡀⠔⢁⣠⣴⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣿⣿⣦⣀⡏⠢⢀⠀⠀⡜⣬⣽⡿⠀ ⠀⠈⠽⣟⣿⡗⢊⣤⣾⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣷⣄⡑⠚⣔⣻⡿⠁⠀ ⠀⠀⠐⠽⣯⠿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢉⠿⢹⣷⡿⠃⠀⠀ ⠀⠀⠀⠈⠘⢧⡻⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣺⢯⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠡⡙⢾⣟⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣏⣶⣿⡿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠫⠿⢻⣻⣗⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣎⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢍⡳⣿⣖⡯⣢⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣐⢬⢚⣽⣾⡿⠫⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠹⢛⡗⣿⣽⣯⣟⣦⣶⡶⣖⢆⠆⡰⡒⡖⣔⣯⣵⣂⣧⣿⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠓⡿⣽⣿⣿⣿⣭⡿⣿⣿⡾⢿⠻⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠀⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠀⠁⠈⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠑⠲⢤⡀⠀⠀⠀ ⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀ ⠀⣠⠏⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⠀⣀⠀⡀⣀⠀⣀⠀⡀⢀⠀⡀⢀⠀⡀⢀⠀⡀⢀⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⢦ ⢰⠃⠀⠀⠀⠀⢀⣴⣾⡟⣯⢻⣝⣻⢻⣿⣟⣿⣏⡿⣹⢏⡿⣹⢧⡻⢵⣫⡝⣯⡝⣮⢻⡵⣫⡝⣯⢻⡹⣏⡻⣝⣏⠿⣹⢏⡳⣝⢧⢯⡽⣹⠯⣝⢯⡻⣽⢻⣦⡀⠀⠀⠀⠀⠈ ⡏⠀⠀⠀⠀⠀⣾⡟⣧⢻⣜⣷⠾⠛⠉⠉⠈⠉⠉⠙⠻⢾⣵⢫⡞⣽⢣⢷⡹⢶⡹⣎⢷⡹⡵⣻⡜⣧⢻⣜⡳⣭⢞⡽⣣⢯⣝⢮⣛⠾⣜⢧⣛⢮⡳⣝⢮⢯⡝⣿⡄⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⢸⣿⡽⣎⣷⠛⠀⠀⠀⣠⣤⣤⣤⣤⡀⠀⠀⠙⣿⣜⢧⣛⢮⡝⣧⢻⡜⣧⢻⡵⣣⢟⡼⣳⢎⣷⡹⣎⢷⡹⣞⡼⣣⢏⡿⣜⢧⣛⢮⡳⣝⢮⡳⣝⢾⡇⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⢸⡿⣼⣽⠃⠀⠀⣴⣿⣛⢧⣛⡾⠋⠀⠀⡀⠀⠈⢿⣮⡝⣮⡝⣮⢳⡝⣮⢳⣭⢳⣏⢾⡱⣏⢶⡹⣎⢷⡹⣎⠷⣭⢻⡼⣹⢮⡝⣮⢳⡝⣮⢳⡝⣾⡇⠀⠀⠀⠀ ⡃⠀⠀⠀⠀⢸⣿⢾⡇⠀⠀⣼⡿⢶⣹⡾⠋⠀⠀⢠⣼⣷⠀⠀⢸⣷⡝⣮⡝⣮⢳⡝⣮⢳⣎⠷⣎⢷⡹⣎⠷⣝⢮⡳⣝⢮⡻⣜⢧⡻⡵⣫⢞⡵⣫⢞⡵⣫⢞⡵⡇⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⢸⣿⣻⡇⠀⠀⣿⣿⡽⠋⠀⠀⢀⣴⡿⣹⣿⠀⠀⢠⣿⡞⣵⢻⡜⣧⢻⣜⡳⣎⠿⣜⢧⡻⣜⡻⣜⢧⡻⣜⢧⡻⣜⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⡽⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣹⣧⠀⠀⠸⠏⠀⠀⣀⣴⡿⣫⢞⣵⠏⠀⠀⣸⣿⡝⣮⢳⡝⣮⢳⣎⠷⣭⢻⡜⣧⢻⣜⡳⣝⣮⢳⡝⣮⢳⡝⣮⢳⣭⢳⡽⣎⢷⡹⣎⢷⣹⢳⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣱⢻⣧⡀⠀⠀⠀⠾⣿⣧⣿⡵⠟⠁⠀⠀⣰⣟⢧⡻⣜⢧⡻⣜⡳⣎⠿⣜⢧⡻⣜⡳⣎⢷⡹⣎⣷⣹⣮⣷⣽⣮⣷⣮⣷⣳⡝⣮⢳⡝⣮⢳⣏⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⣜⢧⣛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢻⡝⣮⢳⡝⣮⢳⣭⢳⣭⢻⣜⣧⣿⡼⠷⠟⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢷⣽⢎⡷⣎⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⣜⢧⣛⢾⣜⡻⢿⡶⣶⢶⡶⣶⢿⡻⣝⢮⡳⣝⢮⡳⣝⢮⡳⣮⣷⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣞⣵⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⣜⢧⡻⣞⡼⣹⢧⡻⣜⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⣟⣼⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣟⡼⣫⢷⡹⣞⡵⣫⢵⣫⢞⡵⣫⢞⡵⣫⢞⣽⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣏⢾⡱⣏⠷⣎⢷⡹⣎⡗⡯⣞⡵⣫⢞⣵⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⡟⣮⣝⢮⡻⣜⢧⡻⣼⡹⣵⢫⣞⣵⠛⠁⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⣟⢶⡹⣎⢷⡹⣎⢷⣣⢟⡼⣷⠛⠀⠀⠀⠀⠀⣀⣴⡾⣟⡻⣭⢳⡝⣮⢳⡝⣮⢻⡽⣻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⣯⢞⡵⣫⢞⡵⣫⢞⡵⣫⠟⠁⠀⠀⠀⢀⣴⡾⣟⢧⡻⣜⡳⣭⢳⣝⣮⣷⣹⣎⢷⡹⣵⢫⢾⡹⢿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⡷⣫⢞⡵⣫⢾⡱⣯⡾⠁⠀⠀⠀⠀⣴⣿⢫⢷⡹⣎⢷⣭⠷⠛⠛⠉⠉⠉⠉⠙⠛⠷⣯⡟⣮⡝⣧⢻⡽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⣟⡵⣫⣞⡳⣏⣽⠏⠀⠀⠀⠀⢀⣾⠿⣜⢯⡞⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡟⣶⡹⣎⢷⡹⣝⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⡧⢯⡵⣎⢷⡿⠃⠀⠀⠀⠀⢀⣿⣏⠿⣜⣳⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢏⡷⣹⢶⣹⣾⣧⢻⡜⡾⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣏⠷⣳⣹⡾⠁⠀⠀⠀⠀⠀⣼⡿⣜⡻⡼⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⣧⢻⡜⣧⡿⠏⠉⢻⣧⢻⡹⢯⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡯⣝⢧⡿⠁⠀⠀⠀⠀⠀⢰⣿⡝⣮⢳⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⣧⢻⡜⣧⡿⠛⠀⠀⠀⠸⣯⡳⣝⢧⢿⡇⠀⠀⠀⠀⠀⠀⠀⢨⣾⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣷⡹⣾⠁⠀⠀⠀⠀⠀⠀⣿⡿⣜⢧⣛⣿⠁⠀⠀⠀⠀⠀⠀⣠⣾⡟⣧⢻⡜⣧⡿⠋⠀⠀⠀⠀⠀⠀⣿⡟⣼⢫⢾⣿⠀⠀⠀⠀⠀⠀⡀⣰⣿⢻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣷⣽⠇⠀⠀⠀⠀⠀⠀⠀⢹⣿⢎⡷⣭⢿⡆⠀⠀⠀⠀⣠⣾⡟⣧⢻⡜⣧⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣿⡝⣮⣛⢾⡏⠀⠀⠀⠀⠀⠀⢰⣿⢣⢿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣏⠾⣜⡻⣧⠀⠀⣠⣾⢟⡵⡻⣜⢧⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⡝⣶⡹⣾⠃⠀⠀⠀⠀⠀⢠⣿⢳⣏⢾⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣟⡼⣳⢻⣦⡾⣟⡵⣫⢞⣵⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢣⡟⣶⣹⡏⠀⠀⠀⠀⠀⣰⡿⣏⠷⣎⣟⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⢞⡵⣫⢞⡵⣫⢞⣵⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⢿⡱⣏⢾⣱⡟⠀⠀⠀⠀⠀⣴⣿⡹⣎⠿⣜⢮⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡞⣵⢫⡞⣵⢻⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⣟⡽⢎⡷⣹⣾⠟⠀⠀⠀⠀⢀⣾⡟⡶⣝⡞⣯⡝⣞⡇⠀⠀⠀⠀ ⠆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣫⢞⡵⣫⢞⡽⣻⢟⡷⣶⢶⡶⣿⢻⣏⢷⡹⣞⡼⣫⣾⠟⠁⠀⠀⠀⠀⣴⡿⢧⡻⣵⢫⡞⣵⠻⣜⡇⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣼⣧⢻⡜⣧⢻⡜⣧⢻⡜⣧⢻⡜⣧⢻⣼⡷⠛⠁⠀⠀⠀⠀⣠⣾⢯⡝⣧⢻⡜⣧⢻⣜⡻⣜⡃⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠾⢷⣽⣮⣷⣽⣾⠷⠟⠛⠋⠁⠀⠀⠀⠀⠀⣠⣾⢿⡱⣏⢾⡱⣏⢾⡱⣏⢾⡱⢯⡁⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢮⡝⣧⠃⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⢿⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢻⣜⡃⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣟⡻⣜⢧⡻⣜⢧⣛⠷⣎⢷⡹⢮⣳⡝⣧⢻⣜⡳⢮⡅⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⢸⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⢾⡻⣝⠾⣜⡳⣝⢮⡳⣝⢮⣝⣯⣞⣧⣛⣧⢳⡝⣮⢗⡮⣝⡳⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣟⢶⣛⡷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⢾⢿⣫⢟⡼⣣⢟⡼⣻⣜⡳⣝⢮⣷⠟⠛⠉⠀⠀⠈⠉⠙⠻⢾⣵⢫⢾⡱⣏⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡟⣮⢳⡝⣧⢻⠷⣶⢦⣤⣤⣤⣤⢶⡴⡶⡶⢶⡞⣿⢻⡝⣯⢳⡝⣮⢳⡭⣞⡵⣫⢞⡵⣳⢎⡷⣽⠏⠁⠀⠀⣠⣤⣴⣤⣤⡀⠀⠀⠙⢿⣎⢷⣹⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣟⡼⣣⢟⡵⣫⢟⡼⣫⢞⡵⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⣎⢷⡹⣎⢷⡹⣎⠷⣝⢮⣿⠁⠀⠀⣴⣿⢻⡝⣮⡿⠋⠀⠀⡄⠀⠈⢿⣎⢷⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣯⢞⡵⣫⢞⡵⣫⢞⡵⣫⢞⡵⣫⢎⡷⣹⠧⣏⢷⡹⣎⢷⡹⢮⣳⡝⣮⢳⡝⣮⢳⣭⣛⢮⢿⡇⠀⠀⣼⣟⢮⣳⡿⠉⠀⠀⣠⣾⣷⠀⠀⠸⣿⣞⡇⠀⠀⠀⠀ ⡅⠀⠀⠀⠀⢸⣟⢮⡳⣝⢮⡳⣝⢮⡳⣝⢮⡳⣝⢾⣙⢧⡻⣜⢧⡻⣜⢧⣛⢷⣣⢟⡼⣣⢟⡼⣳⠮⣝⢮⢿⡇⠀⠀⣿⣯⡾⠃⠀⠀⣠⣼⡟⣮⣿⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⢸⣟⢮⣝⢮⡳⣝⢮⡳⣝⢮⡳⣝⢮⡳⣝⢮⡳⣝⢮⡳⣝⢮⡝⡾⣜⣫⢞⣵⢫⡞⣵⢻⡜⣯⢾⣧⠀⠀⠙⠋⠀⠀⣠⣶⡟⣧⣛⣶⠏⠀⠀⣸⣟⢾⡇⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⢸⣟⠾⣜⢧⡻⣜⢧⡻⣜⢧⡻⣜⢧⡻⣜⡳⣝⢮⡳⣝⢮⡳⣝⡳⣭⢳⣏⡞⣧⢻⡜⣧⢻⡜⣮⢻⣧⡀⠀⠀⠠⠾⣿⣶⣽⡶⠛⠁⠀⠀⣼⣟⢮⣻⡇⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠘⣯⣟⡼⣣⢟⡼⣣⢟⡼⣣⢟⣼⣣⢟⣼⢳⣝⣮⢳⣝⣮⣳⢭⣳⡭⣗⣮⡝⣮⢳⡝⣮⢳⡝⣮⡳⣝⣻⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢻⣜⡳⣿⡇⠀⠀⠀⠀ ⢻⠀⠀⠀⠀⠀⠹⣷⣝⢧⣛⢾⡱⣏⢾⣱⣛⢮⡳⣏⡞⣧⢏⡞⣧⣛⠶⣭⢳⡝⣾⡱⢮⡝⣞⢧⡻⣜⡳⣝⢶⡹⣎⢷⡺⣝⠿⣶⡶⣶⢶⡶⢿⡻⣏⣞⡳⣎⣿⠟⠀⠀⠀⠀⠀ ⠈⢷⠀⠀⠀⠀⠀⠈⠙⠻⠾⠷⠿⠾⠷⠷⠿⠾⠷⠯⠾⠵⠯⠾⠵⠯⠿⠼⠧⠿⠶⠿⠷⠿⠾⠷⠿⠾⠷⠿⠾⠷⠿⠾⠷⠿⠿⠶⠿⠿⠷⠿⠷⠿⠾⠾⠟⠋⠁⠀⠀⠀⠀⠀⡰ ⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁ ⠀⠀⠀⠈⠓⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠔⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣻⡄⠀⠀⠀⠀⠀⠀⢿⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠀⠀⢀⣠⠞⠉⢻⡄⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⢀⣀⣉⣁⣀⣀⣀⣉⡀⠀⠀⠀⠀⠀⠘⣿⣶⣶⣶⣶⣶⣶⠀⣴ ⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣧⠐⠶⠶⡶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄⡉ ⠀⡄⠸⠟⠉⠁⠀⠀⠈⠙⠻⣶⣶⣶⣶⣶⣾⣿⠟⠉⠀⠀⠀⠈⠙⠃ ⠀⠁⠀⠀⣠⣾⠿⢿⣷⡄⠀⢈⣭⣭⣭⣭⣭⠁⠀⣶⣿⠿⣿⣷⡀⠀ ⠀⠀⠀⠀⢿⣿⣄⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⣼⣿⡇⠀ ⠀⠀⠀⠀⠈⠛⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⡿⠛⠉⠙⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⠿⠿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠟⠋⠁⠀⠀⠀⠙⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢄⠉⢸⠀⢸⠁⠉⡅⠀⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡼⠀⠸⣀⡼⠀⠀⠑⠾⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣤⣄⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣿⣿⣷⠀ ⠘⠻⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣶⣶⣶⣶⣶ ⣤⣴⣶⣾⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁ ⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢙⣿⣿⣷⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣟⣿⣿⣿⣿⣭⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣼⣿⡿⠟⠛⠛⠛⠓⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⢤⡈⠒⢄⠤⠐⡄⠀⠀⠀⠀⠀⢮⠱⡀⠀⣹⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⡆⠉⠁⠀⠀⠀⠀⠀⠈⢦⠙⡄⣹⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⡇⢼⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⣹⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⣴⠃⠀⠀⠀⠀⠀⠀⢠⡔⠃⣼⠁⣾⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⣀⣀⣀⡠⡤⠖⢉⡀⣂⣀⠒⠒⠂⠐⠠⠊⠉⢥⠤⠚⠁⠀⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣀⣤⣯⣤⠤⠤⠤⠾⠶⠿⠿⠿⠿⠿⠿⠿⠷⠷⣷⣶⣆⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⣠⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⡠⣤⣼⡶⠿⠖⠛⠛⠓⠺⠾⣤⣀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢾⣷⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⢀⢀⣀⣂⣐⣀⣀⠀⠀⠀⠀⠀⠀⠈⢧⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⠿⡿⢿⣿⣶⣄⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣠⣴⣿⣿⠿⢿⣿⡿⠂⠠⣿⣿⣟⣻⣿⣷⣄⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⣀⠀⠀⠀⠙⠉⠉⠉⢹⣿⣿⣆⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠀⢰⣟⡃⢲⣤⣤⣿⣄⠀⠀⢸⣿⣿⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣿⣿⣿⣿⡀⠀⠉⠳⠌⣛⠿⠿⠛⠀⣤⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣽⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣧⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⠿⢷⣦⣤⣄⣀⣀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⢻⣿⠟⠉⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠛⠉⠀⠀⣿⣿⠿⠛⠉⠛⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⠁⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠗⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢰⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⣿⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡿⠁⢇⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⡴⠛⠁⠀⠈⠹⡄⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠑⣄⠀⠀⠀⠀⢠⡏⠀⡠⠊⠁⠀⠀⠀⣀⣤⣴⣿⣆⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠞⠀⠀⢠⢻⣇⠀⠀⠀⠈⠓⠦⣄⣸⣿⠔⠁⠀⠀⠀⣠⣴⢿⣹⣓⡞⣶⡹⣷⣄⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸⣻⣿⣷⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣴⡾⣟⣯⢷⣳⡽⣞⣳⡽⣏⡿⣷⣶⣦⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⢸⣿⡽⣿⣶⣄⣀⣠⣤⣼⣿⣤⣴⣿⠿⣽⣻⣞⣯⢷⣻⣽⣳⣿⣟⡿⣛⣿⣿⣿⡟⠉⢻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡜⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⣯⣿⣷⣿⣾⣿⣿⣿⡿⣟⣯⢿⡽⣽⣾⣿⡇⠃⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⢩⣿⡟⣻⣿⢿⣿⣇⠀⠀⠀⣸⣿⣿⢿⣛⣿⣛⡿⣛⣯⣟⡽⣞⣯⡟⣷⣿⣿⠃⠀⠀⠀⠀⠀⠹⣶⡄⠀⠀⠀ ⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡿⣾⢿⣷⣶⣾⣿⡿⣾⣏⡿⣶⣏⣿⣹⡾⣾⣹⢿⣾⡿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀ ⠀⢠⠎⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠸⣿⣿⡽⣾⣽⣯⣽⣧⣿⣷⣾⣽⣳⣟⣾⣳⣿⣷⣿⠿⠷⠛⠋⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⢻⣿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙ ⡞⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢸⣇⠀⢀⣀⠀⠀⢀⡀⠀⠀⠀⣀⣀⣠⣄⣄⣤⣤⣤⣶⣶⣶⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⢠⣿⣾⣷⣿⢺⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⠇⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣽⣯⣛⣿⣷⣜⣻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⡏⠀⠀⠀⠀⠀⠀⣰⣿⢿⡽⣿⢷⡿⣿⣯⣽⢧⣿⡻⣾⡷⣿⡿⣽⡿⣿⣞⣿⡿⡼⣿⣿⣶⢻⣿⣻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠟⠀⠀⠀⠀⠀⠀⢰⣿⡿⣯⣻⡽⣯⢷⢯⡷⣿⣳⢯⢷⣻⣿⣿⣟⣳⣟⣿⡿⣾⣿⣟⣽⣿⣻⣟⣾⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⡷⣯⢿⡽⣯⣟⢾⣿⢧⣻⣏⣿⣷⣻⣯⢷⡾⣽⣿⣳⣿⣿⣺⣿⡽⣿⣞⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢯⡿⣽⣏⡿⢾⣹⣿⣟⢮⡷⢯⣿⣞⣽⣿⣛⡾⣿⢷⣫⣿⣿⡳⣿⣿⣽⡾⣿⢾⣇⠀⠀⠀⠀⠀ ⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢯⣿⢿⣽⣳⣿⣽⣻⢷⣿⣞⡧⣟⣯⣷⣻⣾⣯⢿⡽⣿⣯⢷⣻⢾⣿⣹⣿⡞⣿⣽⣞⣿⡄⠀⠀⠀⠀ ⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣯⢿⣻⣾⣳⣿⡷⢯⣿⠷⡾⣝⡾⣽⣟⣳⣿⣯⢿⡽⣟⡾⣏⡿⣯⣷⢯⣿⡿⣽⣿⡞⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣻⢞⣿⢷⣿⣟⣿⣻⢯⣿⢻⡽⣏⣷⣻⡽⣳⣿⢯⡿⣽⢯⡽⣯⣟⣷⣻⣟⡾⣿⡷⣿⣟⡷⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣟⣻⢾⣻⢾⣿⣿⡽⣿⢫⣿⡿⣝⣶⣻⡗⣿⣿⢯⡿⣽⣏⣿⣳⣻⢮⣟⣿⡽⣿⣿⣽⣯⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣫⣟⣯⢯⣟⣿⡯⣟⡱⣿⡿⣽⡳⣞⣿⡽⣻⢯⡿⣽⣳⡞⣷⢯⢷⣻⣾⣹⣷⣯⣿⠿⠛⠁⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣞⡷⢯⣞⡿⣞⣿⣿⣼⡿⠿⠿⢷⣽⣾⣼⣿⣽⣯⣿⣵⣯⠾⠿⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠛⠛⠛⠛⠛⠛⠛⠛⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠀⠀⠀⠀⠀⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣯⣤⣤⣤⣀⣀⣀⡀⠀⠀⣀⣀⣤⣤⣶⠶⣖⣶⣿⣛⣿⡿⢿⡿⣟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠘⢻⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡽⢯⣙⠳⣭⡽⢾⣹⢶⣛⣯⠷⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣵⢟⣿⣟⣷⣿⣿⣿⣿⣿⣿⠻⠴⣋⣭⠓⣥⠖⢫⡽⢺⡝⢾⣻⣟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡿⣳⢟⡿⢿⣿⣿⣿⣿⡧⠄⠺⢉⠴⢋⠴⢉⡣⢞⣫⣝⣯⣷⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡾⣱⢾⣵⢿⣽⣿⣿⣿⣿⠊⠐⢋⡔⢩⡔⣩⡕⣉⡷⣛⡿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣳⢟⣵⣿⣽⣿⣿⣿⣿⣇⠀⠊⠼⣠⢞⣡⢞⣭⢞⡵⢚⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⣫⡶⣻⡿⣿⣿⣿⣿⣿⠀⠀⠒⠁⢊⠵⣫⡶⣫⠶⣻⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡵⢞⡽⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣡⠞⣣⢞⣷⢚⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣐⣿⣾⣿⣾⡿⢾⡷⣿⡿⠡⢂⣼⣿⡞⣷⢻⡕⠉⣽⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⣿⡯⢜⠫⣿⢶⣿⣷⣿⡷⢣⡾⣵⢋⡖⡴⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢏⢺⣿⣹⠆⣻⣽⣷⣿⣞⢛⡡⢫⡾⡷⢋⠈⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⣿⠲⣧⠜⡏⡻⠏⣿⣟⠵⣯⠛⠁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡎⠳⢑⢈⣳⡑⠌⡇⢸⡏⠐⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⡆⢈⠢⡑⢎⣯⡇⡇⠸⣏⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢬⣣⢐⡏⣺⠟⡄⡇⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠴⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠯⠻⠿⠿⠿⢿⠿⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠡⡠⠐⠠⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⢠⡀⢀⠀⢒⠓⢢⡀⣀⡀⠈⠐⢀⣀⡀⡀⠀⠀⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢲⣬⣀⡁⠠⡀⣅⢀⡐⠐⡉⢉⣩⠀⠀⠀⠀⠉⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠦⠶⠶⠶⠖⠒⠒⠂⠸⣿⣿⡟⡟⢞⠞⣿⣓⣞⣻⣯⣭⣵⣶⣿⣿⣽⡿⣿⠷⠶⠶⠖⠛⣛⣛⡛⠂ ⠀⠀⠀⠀⠠⠀⠀⠀⡀⡠⡀⢔⣤⣶⣽⣴⣀⣂⣶⡤⠤⢴⠶⠶⠻⣻⣟⣯⢫⣭⡹⣭⢏⣌⡹⢂⡕⣠⢒⠷⣊⡓⠐⠈⠈⠁⠉⠀⠀⠀⠀ ⠐⠂⡂⣤⣶⣮⢷⠣⠏⠛⡛⣉⠩⠙⠕⠚⠀⣊⣀⣡⣥⣥⡴⢶⠾⠿⠳⠎⠓⠚⠙⠉⠉⠀⠉⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠊⣙⠞⠛⠉⠁⡀⠀⠀⠒⠂⠁⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠂⠀⠈⠀⡀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠀⠁⡀⠁⢀⠀⠂⠈⠀⠀⡀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢈⠀⠂⢀⠐⠀⠀⠄⠐⠈⠀⣀⣀⣠⣤⣤⣤⣦⣴⣤⣶⣴⣶⣤⣦⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠉⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠂⠁⡀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠉⠙⠲⢤⣀⡀⠀⠀⠀ ⠀⡀⢁⣠⣴⣾⣿⣿⣿⣿⡿⠟⣋⣭⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀⣈⠙⠛⠿⣿⣿⣿⣯⣿⣻⢿⡶⣤⡀⠀⠀⠉⠙⠲⢦⡀ ⣰⣶⣿⣿⣿⣿⣿⢟⣋⣥⣶⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣍⡻⢿⣿⣿⣿⣷⣯⣟⣟⡦⣤⠐⠈⠈⠃ ⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⢻⣿⣿⣿⣾⣯⣟⡷⣯⣓⠦⠀ ⣿⣿⣿⠏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢻⣿⣿⣿⣿⣿⣿⣽⣻⠀ ⣿⡿⢣⣾⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⣀⣤⠀⠀⣷⡖⠲⠶⠶⠶⠶⢤⣤⣀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡹⢿⣿⣿⣿⣿⣿⠀ ⠏⣼⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⢐⣩⣽⣿⠀⠀⢻⣿⣿⣿⣿⣶⣶⣤⣄⠉⠓⢦⣄⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡹⣿⣿⡿⠿⠀ ⢸⣿⣿⣿⣿⣿⡿⠋⠀⣠⣆⣠⣶⣿⣿⣿⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠘⢷⠄⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⣿⣿⣶⠀ ⣿⣿⣿⣿⣿⠟⠀⢀⠜⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⠋⠀⢰⢦⡄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣧⡀⢀⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣿⣿⡿⢿⣿⣿⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠺⠿⠿⠿⠿⠿⠿⠋⠀⠀⠙⠿⠿⠿⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀ ⠶⠶⠶⢶⣄⠀⠀⢀⣴⣄⠀⠀⢀⣴⠶⠶⠶⠶⠆⠀⣶⠀⠀⠀⢠⣶⣄⠀⠀ ⣶⣶⣶⣾⡟⠀⣴⡟⠁⠙⣷⡄⠈⢻⣷⣶⣶⣶⡆⠀⣿⠀⠀⣼⡟⠉⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣶⣶⣶⠶⠶⣿⣿⡷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠿⠛⠛⢻⣿⡿⠉⠀⠀⠀⣿⣿⣿⣦⣨⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠉⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⢠⣿⣿⡿⠟⢿⣿⡇⠛⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣼⠿⠋⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠐⠁⠀⠀⠀⠀⣰⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡋⠉⠛⠛⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋⣼⣿⣿⡤⠀⠀⠀⠀⠀⣠⠞⠻⠿⠿⠆⠀⠀⠀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣻⣿⣿⠃⠀⠀⠀⠀⠀⠀⣰⣟⣴⣾⣿⣿⠟⠀⠀⠀⠀⣠⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢷⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠋⠀⣠⠀⠀⢀⣾⡏⠀⠀⠈⠒⠳⠦⠤⣼⡶⠶⠾⠟⣽⡿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⠀⠀⢀⡾⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣿⡇⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⢹⣿⣦⣀⠀⣀⠀⠀⠀⣀⠀⠀⠀⢹⣿⣿⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣴⠶⠦⠤⠤⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠤⠤⣀⣀⡀⠀⠀⢈⣻⣦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡖⠋⠀⠀⠙⢷⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⡠⠞⠛⣇ ⠀⠀⠀⠀⠀⠀⢶⣶⠒⠦⣄⣠⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⠔⠉⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠉⢛⣷⠞⠛⢿⣦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠘⠒⠒⡞⠋⢙⣷⣶⠞⢟⢻ ⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⣠⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠂⠈⠉⣩⠀⠀⠀⠀⠀⠈⠉⠉⠉⡟⢰⣼⠚ ⠀⠀⠀⢀⣴⠟⠉⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣾⣿⠀ ⠀⢀⣴⠟⠁⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⢀⡴⠃⠀⢠⣴⠟⢻⠂⠄⠀⠀⠀⡎⠀⢹⠏⠀ ⢀⣿⣧⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⢠⡾⠁⠀⢠⡟⠁⠀⡈⡇⠀⠀⢀⡼⠥⠔⠋⠀⠀ ⢸⡀⠈⠻⢦⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⢀⣤⢿⡅⠀⠀⣾⠁⠀⣸⡏⣣⡀⣠⠞⠀⠀⠀⠀⠀⠀ ⢸⠳⢦⣀⠀⣿⠷⠦⠤⠤⠤⠤⣀⣀⣀⣀⣀⣤⣾⡿⠗⠒⠒⠒⠊⠹⠁⡼⠁⠀⢰⡇⠀⠀⣿⡇⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⣈⠣⣀⠀⠉⠁⠀⠘⢦⠉⢉⡽⠗⠊⠉⠙⠻⢿⣏⡀⠀⠀⣀⣀⣀⠴⠚⠁⠀⣰⣿⠁⠀⠀⠻⣵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣄⠀⠉⠑⠢⠤⣤⣀⣛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡿⠀⠀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠻⢦⣤⣀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⣼⡿⠁⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠛⠻⠶⠶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠓⠂⠂⠓⠲⠂⠂⠒⠒⠀⠐⠓⠚⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠋⠀⣀⣀⠙⢦⠛⠉⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡞⠀⠠⠚⠉⠀⣀⣉⣳⣷⡂⠐⠒⣂⣀⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠼⠀⠀⢀⡤⠚⠉⠀⠀⣤⣀⠈⡏⠉⠀⠀⣀⡉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠔⠁⠀⠀⠀⠘⠓⣦⣄⡀⠀⠛⣋⣤⣧⣀⣀⣀⣓⣡⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢛⣿⠟⠉⠠⣄⣀⣀⣠⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣈⣇⣀⣀⣿⣆⣀⡀⠀⢀⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⣴⠚⠭⢍⣓⣒⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⠀⠀⠈⠦⠤ ⡆⠀⠀⠀⠲⣝⠛⠛⠒⣢⣾⣿⣿⣿⠿⣛⣛⣛⣉⠽⠋⢹⠛⢿⠁⠀⠀⡰⠀⠀ ⠻⢷⣤⣤⠤⣀⣀⠀⣴⣿⣿⡿⠋⢀⣀⣤⠞⠋⠁⠀⠀⢸⠀⠪⡀⢀⠜⠁⠀⡠ ⠀⠀⠀⠉⠉⠛⠛⣿⣿⣿⡿⠶⠛⢉⣿⣧⣤⣤⣤⣤⣤⣬⣽⣶⣌⡧⢀⠔⠋⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠁⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠘⣾⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣠⣶⣾⣿⡿⢿⠿⠟⠛⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠖⠲⢤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣾⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣺⣿⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢴⣶⣶⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠷⢾⣷⣶⣾⣿⣿⣿⣿⣿⠿⠿⠷⠙⣦⣤⠀⣀⣀⣀⡀⠀⠀ ⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⣀⣀⣀⠲⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⠛⠀⣄⠀⠀⠀⠀⠀⠀⠈⣀⠀⢉⣑⠄ ⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠁⢘⣤⣤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣿⣶⠤⠤⠤⠚⢛⣿⣿⢧⠞⠁⠀ ⠀⠘⢄⡂⠀⣇⠀⠀⠀⠈⠿⣄⠋⣿⣿⣥⡜⢋⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⣋⡀⠀⣤⣲⠚⣿⣿⣿⣿⣦⠀⠀ ⠀⠀⠀⠙⢧⣀⢀⢀⠀⠀⠀⠀⠀⠀⠄⢠⡀⠀⠠⠒⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⢓⣚⣉⣉⠉⠩⠭⠭⠭⡉⢇⠀⠀ ⠀⠀⠀⠀⠀⢳⠌⠰⢆⣂⣤⣤⣤⣀⠀⠀⠀⠈⠉⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⠓⠀⢀⣠⣤⣤⣤⣤⣀⣠⣄⣠⣼⡆⠀ ⠀⠀⠀⠀⠀⠀⢳⣴⣿⣿⣿⡿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣿⣿⣿⠿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣭⣽⣿⣿⣿⣿⣯⣿⣿⣇⣀⣠⣤⣤⣤⣴⣶⣶⣤⣄⣀⣁⣉⣉⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣸⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣮⡻⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣣⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⠾⠿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⢏⣽⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⠤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠛⠉⠀⣰⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⣈⣉⡻⣿⣿⣦⣀⠀⣹⡅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⡿⠛⠁⠀⠀⠀⣴⣿⣿⡿⣜⣿⣿⣿⣿⣿⣿⣿⡿⣻⡿⢛⢛⣛⣛⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠿⠓⠉⢳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠺⠿⠟⠻⠿⠷⠿⠾⠷⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⠉⠋⡏⠉⠐⣿⣿⡿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀ ⠀⠀⠀⠀⢀⡤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣠⠴⠀⠀⠀⠀⠀⠀⣆⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⢿⡇⠀⠀ ⠀⠀⠀⣰⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⡿⠏⠁⠀⠀⢀⣠⣤⣦⡄⢿⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡘⢻⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠁⠀⠀⣤⣶⣾⣿⣿⣿⣧⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⣾⠆⠀ ⠀⣿⣦⣄⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢛⣉⣭⣤⣤⣴⣶⣦⡄⠈⠀⠀⣨⣿⣿⣿⣿⣿⣿⣧⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡁⠀ ⠀⣿⣿⣿⣿⣷⣮⣥⣉⣌⣉⣈⣉⣁⣉⣀⣠⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⠄⠀⢢⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡃⢤⢄⡒⠒⠌⠃⠌⠐⠀⢀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⣴ ⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⢿⣿⣿⣿⣿⣿⣿⣿⠏⠹⣃⣬⣼⣿⣿⣿⣿⣿⣿⣿⡿⠀⠊⠉⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⠟⠁⠘ ⠐⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣟⣉⣉⣉⣉⣻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣋⣉⣉⣉⣉⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠛⠛⠓⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠋⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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