⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⡿⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠿⠿⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⢉⣤⣶⣿⣿⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⣾⣿⠋⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⢠⣿⣿⣉⠙⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⣄⡀⣹⣿⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⣿⣿⠿⣿⣷⣄⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣄⠈⠻⠿⠿⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠆⠀⢀⣼⣿⠏⠀⠈⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣼⣿⢿⣿⣦⣄⡀ ⠀⠀⣀⣾⣿⠿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⣤⣤⣤⣿⣿⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⣾⣿⣿⣶⣶⣿⡿⠏⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣤⣿⣿⠿⠇ ⣰⣾⣿⣿⣏⣠⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣋⠉⠉⠉⠁⠀⣠⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀ ⠹⠟⠛⠻⢿⣿⣿⠃⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠿⢿⣿⣷⣾⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣴⣦⣤⣤⣤⣀⡀⠛⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠲⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠙⠿⠟⠸⣷⣼⣿⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣦⡀⠙⠻⣿⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠿⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⠉⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣆⢀⣾⣿⣿⣿⣿⠿⢿⣿⣷⣶⣶⣴⣶⣶⣿⣿⣿⡿⠋⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⣿⡿⠛⠁⠀⠀⠀⠻⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⣿⣿⠃⣿⣿⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⢸⣿⠃⠀⢀⣿⣿⣿⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣿⣿⣿⣿⣍⡀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⠗⠀⠀⠀⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡏⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⣸⣿⣿⣇⣴⣾⣿⣿⣿⠿⠟⠛⠛⠛⠻⠿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⡉⠀⠀⠙⢿⣿⣷⣶⣶⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠁⠉⠛⢿⣿⣦⡀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣿⣿⣷⣶⣶⣶⣶⣶⣤⣤⣴⣶⣿⣿⣶⣶⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠻⢿⣿⣦⣠⣾⣿⡿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⣤⣸⣿⡿⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⢿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⢿⡿⠋⠁⠀⠀⠺⠿⠋⠉⠁⢀⠀⡀⠀⠀⠀⠈⠉⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⠓⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⣾⣷⣽⣦⣠⣌⣷⠀⢀⣻⣼⣭⣍⣙⣿⣿⣿⣿⣯⡄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡄⠀⠀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠼⠷⠂⠀⣀⠀⠀⣀⣤⣽⣿⣿⣿⣿⣴⣶⣿⣿⣿⣿⠉⠡⠁⢀⣼⡀⢸⣿⣿⣿⠈⣿⣿⠟⠛⢿⣿⡿⠁⠀⠀⠀⠉ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡀⢀⡀⠀⡀⢀⣼⠋⣰⣿⣿⣿⣿⣿⣭⣿⣯⠍⠰⠿⣿⣏⣵⠶⠒⢰⡿⣷⣷⡼⢿⣿⣷⣿⡟⠁⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⡇⣿⣧⣼⡿⠟⠃⠀⠀⠀⠉⠉⠉⠙⠀⠀⠀⠀⣠⣿⡟⣿⣧⣾⣿⣿⣿⣿⣝⣿⣠⣿⣿⣷⠀⣴⡄⠀⠀⠀⠈⢀⡄⠀⠀⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⣿⣿⣧⣿⣿⡟⠁⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠠⢤⣀⠈⠋⠘⠻⠿⣻⣿⢛⣿⣿⣧⣿⣿⣿⣿⠟⠰⠟⠘⣧⡀⣠⣶⣏⣷⣦⣦⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠙⢿⣿⡇⠀⠀⠀⠀⠈⠉⠛⠓⠛⠃⠀⠀⠀⠀⠀⠀⠀⣿⣤⣿⣿⡄⢹⣿⣿⣧⣿⣿⠛⠛⢛⠃⣴⣿⣿⣿⣷⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠏⢸⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⢀⣴⣾⣿⠃⠀⢠⠀⣠⣶⣶⣴⡶⣦⣀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣽⣿⡅⣀⡛⠿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⡇⠈⢿⣿⣿⣿⣿⣿⣶⣮⣧⣠⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠿⣿⠁⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠀⠘⡷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠈⠻⣿⣿⡿⠛⠀⠀⠙⠻⠿⢿⡿⢿⡿⠛⠋⠀⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡦⠀⠀⠀⢠⣶⣶⣦ ⣿⣿⣿⣿⣿⠃⣦⢓⣿⣮⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡶⠖⠀⠛⠷⠶⠶⠞⠛⠳⢶⣤⣤⣤⣤⣤⣤⣄⠀⠈⠻⣽⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⡏⠀⡀⠀⣼⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠘⢧⡙⠾⠇⠻⣄⣀⠀⠀⠀⠀⣠⠤⠞⢿⣿⠃⣷⣶⣾⣿⣶⣶⣶⣶⣤⣼⣷⣿⡄⣤⠀⠀⠀⠀⠀⢠⢵⣜⣧⡀⠈⠙⠛⠿⣷⣿⣿⣿⣿⣧⡇⣀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡄⠀⠙⠀⠀⠀⠀⢿⣌⣷⠴⠚⠉⠀⠠⠒⢻⣿⢠⠿⣿⡛⠛⠛⠛⠛⠛⠛⣿⣿⠿⣧⢿⠀⠀⠀⠀⠀⠋⣰⣿⢷⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣧⣴⣧⣠⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣶⣦⣼⣆⣠⠶⠛⠉⠀⠀⠀⠀⠀⣀⡴⠻⣧⣿⠀⠙⣿⠶⠶⠶⠶⠶⠾⠿⠋⠀⠻⠸⡇⠀⠀⠀⠀⣸⠃⣿⢸⠓⠦⡀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣌⡷⣮⣿⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⠀⢀⣴⠏⢸⠇⡼⡆⠑⢲⠤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣶⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⣾⡿⠁⠀⡞⡄⣇⠀⠀⠈⠀⠀⠉⠓⢤⣀⠀⠀⠀⠀⠀⠀⠙⢿⣿ ⠿⠿⠿⠶⠿⣵⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡿⠋⠀⠀⣼⠁⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣇⠀⠀⠈⠀⢀⣼⣿⡿⠋⠀⠀⠀⢀⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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