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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠈⣿⣿⣿⣝⣻⣿⣿⣇⢠⣤⣤⡶⠿⣿⣩⡿⠻⠷⠶⠾⠟⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣻⣿⣿⣿⣿⡀⠈⢻⣿⣿⣿⣗⣻⣿⡿⠁⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠉⠁⠘⣷⠀⠀⢻⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠴⠿⠿⠛⠛⠿⢶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣀⣀⣀⣤⣿⠇⠀⠀⢻⣷⠿⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣯⣭⣽⣯⣭⣭⣿⠿⠿⣾⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣽⡟⢠⡄⣴⡿⢛⠷⣦⣄⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠛⠋⢹⡟⠉⠀⣽⠿⠋⠀⢠⣾⡿⣿⣿⣟⠿⢶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣇⣻⣿⠟⠀⠈⠻⣷⡀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠰⠿⠿⠷⠿⠷⠶⠶⢾⣷⣤⣼⣿⠇⠀⠀⢸⣿⣷⠿⣻⣿⠀⠀⠀⠙⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀⣿⣷⣌⣿⣿⠀⠀⠀⠀⠀⠙⣷⡄⢻⣧⡀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣦⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⣀⣶⠈⠻⣿⣟⣛⣿⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⠘⢿⣿⣉⢉⣉⣹⣇⣤⣶⣦⣤⡀⠈⣿⡄⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠶⠶⠶⠾⢻⡿⠀⠀⠀⠈⢉⣥⣴⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣆⣼⢟⣿⡟⠉⠉⠉⠙⠛⠛⠋⠉⠀⢸⣧⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣤⣿⠁⠀⠀⠀⠀⠀⠀ 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⢹⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢯⡳⢧⣛⢮⡳⢯⣾⡟⣧⢻⡵⣻⣜⡳⣽⢳⢧⡻⣼⢣⡟⣵⣫⡝⣧⢻⡼⣳⢮⡽⣳⡾⠃⢰⠟⠀⠀⠀⠀⠀⠈⠻⣤⡀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⢻⡄⠀⠻⣿⣮⡽⣚⡧⣟⡼⢧⣻⡜⣧⣛⢧⡻⣜⡳⣭⢳⣎⠷⣝⢮⣳⢻⣿⣮⢳⡝⣞⣳⡝⣞⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠘⣿⣯⢿⣿⣦⣤⣀⣀⣀⣀⣤⣴⣶⡿⣟⢧⢯⡝⣧⢏⡷⣹⣿⢯⣝⢮⢷⣹⢳⢮⣝⢮⣛⡮⢷⣭⢳⣛⢶⣣⢟⡞⣧⢻⡵⣫⣾⠟⠁⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⡀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠙⠻⣷⣏⡷⣹⢞⡽⣲⢽⡲⣝⢮⡳⣭⢳⣭⢳⣞⡻⣎⡷⣭⢳⡻⣿⣏⣾⡹⢶⣹⢞⡼⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿ ⠀⢹⣿⣎⢷⣫⢟⡿⣻⢟⡿⣻⡝⣧⢻⡜⣯⢞⡽⣎⠿⣜⣿⡿⣹⢎⡟⣮⢳⣏⡞⣮⢳⡝⣞⡳⣎⠿⣜⣧⣛⢮⡽⣚⣧⡿⠛⠁⠀⢠⡟⠀⢀⣠⣴⠶⢶⣄⣤⣤⣄⠀⠉⠿⣤⡾⠋⠀⣀⣠⣄⣀⣤⣤⣄⡀⠀⠀⢿⡀⠀⠀⠙⠻⣿⣵⢫⣞⡵⣫⢷⡹⣎⠷⣭⢗⣞⡳⣎⢷⡹⣞⡵⣫⢗⡿⣿⣖⡻⢧⣛⣮⢳⣭⢻⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿ ⠀⠀⢻⣿⣎⢷⣫⢞⡵⣫⢞⡵⣻⡜⣧⢻⡜⣯⢞⣭⢻⣼⣿⡝⣧⣛⢾⡱⣏⢾⡹⣎⠿⡼⣭⢳⣝⡻⣼⢲⣭⡳⣝⣿⠏⢀⣠⣤⣴⣾⣤⠾⠋⠁⠀⠀⠀⠿⣇⠀⠘⣿⣤⣾⣿⣷⣀⣾⠋⠁⣸⡟⠁⠀⠈⠛⠳⣦⣈⣷⣀⠀⠀⠀⠉⢿⣿⣜⡳⣝⢮⣳⢭⣻⡜⣯⢞⡵⣫⢞⡵⣫⢞⡵⣫⢞⣿⣯⡽⣫⢞⡼⣳⢎⡷⢮⣝⡻⣟⡿⣿⣶⣶⣿⡿⣿⢟⡻⣼⣿ ⠀⠀⠀⠻⣿⣧⣛⢮⣳⢭⡻⣜⢧⡻⣜⢧⡻⣜⢯⣚⠷⣾⣟⡾⣱⢏⡾⣹⣎⡷⣝⢾⣹⢳⡭⣗⢾⡱⣏⠷⣎⠷⣿⠃⢠⡿⠋⠀⠈⢹⣦⠀⣀⣀⣆⠐⠀⠈⢿⡇⠀⠘⣿⣿⣻⢿⣿⠁⠀⢰⡟⠀⠀⠀⣀⠀⠀⠀⣩⡿⠛⠛⠻⣦⡀⠀⠙⣿⡽⣎⡷⣹⢎⡷⣹⢎⡿⣜⢧⣛⢾⡱⢯⡞⣭⡻⡼⣿⣳⢭⡻⣜⢧⡻⣼⢳⣎⢷⡹⣞⡵⣫⢞⡵⣻⡜⣯⣳⣿⠏ ⠀⠀⠀⠀⠈⠻⣿⣧⣟⣎⣷⡹⣎⢷⡹⣎⢷⡹⢮⣝⣫⣿⣯⢗⡯⣞⡵⣻⣿⡼⣹⢎⡷⣫⢞⡽⣎⠷⣭⣛⢾⣹⣿⣤⣼⣧⡀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠀⠀⠈⣿⡀⠀⢻⣿⣟⣿⡇⠀⢠⣿⠀⠁⠀⢰⣿⣿⣶⣾⡟⠀⠀⠀⠀⣹⡇⠀⠀⠈⢿⣷⡹⢧⣻⣜⡳⣏⢾⡹⢮⡽⣺⣽⢧⡻⣵⢫⡗⣿⣯⢷⡹⣎⢯⡳⣭⢳⣎⢷⡹⣎⢷⣙⢮⠳⣥⢛⣶⣿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢛⣿⣿⡿⢟⡻⡱⢭⠞⣭⡓⢮⡱⢿⣷⣫⢞⡵⣫⣽⣿⣳⡝⣮⢳⡝⣮⢳⣭⢻⡼⣹⡿⠋⠙⣿⣄⣽⣷⣀⠀⠀⠀⢹⣿⣟⣿⣧⠀⠀⠀⢻⡇⠀⢸⣿⣿⣿⠀⠀⣸⡇⠀⠀⢀⣾⣿⡿⣿⡟⠀⠀⠈⢀⣴⡿⠛⣿⠶⣤⣘⣿⡝⣧⢗⡾⣹⢞⣭⣛⢧⡻⣵⣿⢧⣻⡜⣧⣛⣿⣟⢮⡳⣝⢮⡳⣭⢳⢎⡷⡹⡜⣎⢎⢧⣛⣴⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⡿⢋⠕⡨⢃⠱⡙⠬⡙⠴⣉⠧⡙⢞⣿⡵⣫⢞⡵⣻⣿⣷⡽⣎⢷⡹⣞⡳⢮⡳⡽⣿⡃⠀⠀⠘⣿⣿⣿⣿⣆⠀⠀⠀⣿⣿⡿⣿⡆⠀⠀⢸⡇⠀⢸⣿⣿⣿⠀⠀⣿⠀⠀⢀⣸⣿⣿⣿⡟⠀⠀⠀⢠⣾⣿⣷⣾⠟⠀⠈⢹⣿⣟⣮⢻⣜⡧⢿⡼⣹⡞⣵⣿⣿⣛⡶⣝⣧⣛⣾⣯⢳⡝⣎⡳⣝⢲⣋⠾⣶⣽⣾⣾⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⠟⠁⡐⠀⠂⠄⠁⠂⠁⠂⠑⡐⠠⢂⠉⠆⡹⣿⣧⢻⡼⣽⣿⣻⣿⣾⣭⢳⣭⣛⢧⣟⣿⣿⣧⠀⠀⠀⢸⣿⣷⢿⣿⣷⡀⠀⠈⣿⣿⡿⣿⣧⡠⢘⣧⣀⣾⣿⣿⣿⣆⣠⣿⠀⢠⣼⣿⣿⣷⡿⠀⠀⢀⣼⣿⣿⣟⣿⠏⠀⠀⢸⢹⣿⣟⢿⣻⣯⣿⣻⣝⡻⣽⣻⣿⣿⡻⣟⢿⣛⣿⣿⢛⡻⣜⢣⡛⣜⢣⢋⡛⡜⣙⢻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠈⠀⠄⠙⢿⣷⣝⡶⣻⣿⠋⠙⠿⣷⣮⡝⣾⣿⣿⣻⣿⣷⡀⠀⠀⢻⣿⣯⡿⣿⣿⣤⣀⣸⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣷⡿⣿⣿⣿⣿⣿⣿⢿⣳⣿⠁⠀⣠⣾⣿⣿⣻⣾⡟⠀⠀⠀⣸⣿⣿⣿⣯⢷⣻⢷⣫⢷⣿⣿⣿⣽⣯⢷⣽⢾⣧⣿⠧⣯⠖⣼⠧⢞⡾⣩⡯⢉⡽⠃⢌⣷⠉⠻⣷⣤⡀⠀⠀⠀⠀ ⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡿⠉⠀⠀⠀⠈⠙⢻⣿⣿⣳⡿⣽⣿⣿⣄⡀⢸⣿⣿⣽⢿⣽⣿⣿⣿⢿⣯⣷⢿⣾⢯⣷⣿⣳⡿⣯⣿⣟⣾⣽⣯⡿⣽⡿⣿⣿⣿⣿⣿⣿⣟⣷⡿⣿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣽⣿⠿⠟⡏⠙⣿⣿⡝⣾⣯⣿⢿⢹⢂⡿⢈⣼⡇⢺⢉⡟⢀⡼⣁⡄⢨⣿⠀⠀⠈⠻⣷⣆⠀⠀⠀ ⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⢀⣾⣿⢯⣿⣽⡿⣞⣿⣿⣷⣾⣿⣟⣾⣿⣻⡾⣷⣻⣯⣿⢾⣟⣯⣿⣻⣾⢿⣽⣟⣷⣿⣻⣾⢷⣿⣻⣽⣷⢿⣽⣯⢿⣞⣯⣿⣽⣿⡀⣤⣿⣿⣿⣿⣯⣿⣿⣿⡉⠔⢀⠼⠇⠀⠉⢿⣿⠿⠋⡥⠬⠿⡤⠿⠯⠼⠥⢼⣞⣀⣾⣖⢱⠁⢀⢿⠀⠀⠀⠀⠈⠿⣷⡄⠀ ⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣼⠟⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⣿⣽⡾⣟⣿⣳⣯⣿⣻⣽⣾⣟⣾⢿⣽⡿⣽⡷⣿⢯⣿⢯⣷⡿⣽⣟⣿⢾⣻⣾⢯⣿⢯⣷⣿⣻⣾⣟⣿⢾⣿⣻⣽⡷⣿⢿⣿⣿⣿⢯⣿⣿⣿⢾⣟⣿⣷⠈⠑⠂⠀⠀⠀⠈⢿⣖⢲⠒⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠊⠓⠒⣒⡸⠀⠀⠀⠀⠀⠀⠙⣿⣦
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠁⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠙⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢻⣷⣤⡀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣽⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⢀⣠⣶⡿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠈⠛⢿⣷⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⠟⠛⠉⠉⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠉⠉⠛⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣾⡿⠛⠉⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠙⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣄⣀⣀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⣿⡿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠿⠿⢿⣿⣿⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡄⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠛⢿⣿⣦⣠⣾⡿⠉⠀⠀⠀⢀⣠⣴⣾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⣄⡀⠀⠀⠀⠀⠀⠙⢿⣦⡀⣠⣿⣿⠛⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⣼⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⢀⣼⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣷⣦⣄⣄⠀⠀⢀⣀⣤⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⣿⣷⡀⢰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣡⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⡿⣿⣿⣋⣴⣿⠿⣿⡇⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⣿⣿⣿⣾⠻⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠿⠟⠛⢋⣽⣿⠟⠉⠉⠉⠉⠉⠁⠀⠀⠻⠿⠿⠛⠁⠀⣿⡇⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⣿⡇⠛⢿⣷⣿⣿⡟⠻⠿⠿⢿⣿⣶⣶⣶⣶⣶⣶⣦⣬⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠋⠁⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⣿⡇⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣿⡇⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣍⠉⠛⠛⠿⢿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣅⠀⣀⣰⣿⡇⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠁⠀⠀⣿⡇⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⠀⠀⠀⠈⠛⢿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠘⢿⣦⣄⡀⠀⠀⠀⣀⣤⣾⡿⠋⠀⠙⠛⢻⣿⣿⣿⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠟⠋⣸⣿⠈⠙⠻⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⣿⣿⣦⣤⣤⣾⡿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠛⠛⠛⠛⠛⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠉⠀⠀⠉⠉⠀⠉⠙⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢠⣖⣶⣦⡀⢠⣤⣤⣘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣻⣷⡄⠀⣶⣿⣛⠳⡄⢨⡛⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡍⠀⠉⠉⢩⠀⡏⠹⠙⠉⣣⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠈⠉⠀⡆⠀⠀⠙⠋⠁⠀⢸⠷⠋⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⡄⠀⠀⣦⣄⣴⠀⠀⣰⢃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢨⡄⠤⠅⠀⠀⠀⠀⣩⠖⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣦⣶⠾⣟⣿⣦⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⣀⠤⠤⢀⡀⠀⠀⠀⣹⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⣿⣷⠐⠶⢃⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⠈⠒⠓⠀⠀⡀⢀⣴⣟⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⡇⠈⢿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣠⣤⣶⡾⠟⠁⠈⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣪⢕⡻⣧⡁⠀⠀⠹⠿⠿⣿⢿⣿⡿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠛⠛⠉⠀⠀⠀⠀⠘⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠭⣒⠭⠚⠁⠹⠳⣄⠀⠀⠀⢀⠟⣼⢯⠑⠛⢷⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⢢⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⠕⠊⠁⠀⠀⣐⠠⠀⠀⠀⠑⡦⢤⠥⠞⠁⠀⠀⠶⠂⠀⠁⠂⠀⠀⠀⠀⠀⠀⣀⣠⣬⣿⡆⠀⠀⠀⢀⣀⡴⡾⣽⢯⣻⡽⣷⣄⠀⠀⠀⢀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⢾⢡⠃⠀⠀⠀⠘⡇⠉⠀⠄⠀⠀⠀⠀⢡⠱⡐⠄⠀⠀⢣⡐⠐⢑⠀⠘⡀⠀⠀⣠⣾⣟⣯⢷⣻⡼⣏⣷⢻⣽⢾⣹⢷⣏⣯⡷⣻⣳⣟⣷⡄⠀⠀⠀⠀⠠⠀ ⠀⠀⠀⠀⠀⠀⡾⢃⠏⠀⠀⠀⠀⠀⡋⠀⠀⢸⠀⠀⠀⠐⡀⡀⡥⠀⠀⠀⠥⠿⡀⢠⠉⡐⠀⢀⣾⡿⣽⣾⣽⣿⣿⣻⣽⣾⢟⡼⣯⢷⣿⡽⣾⡝⣷⡽⣾⡽⣿⣆⠀⠈⠀⠄⠀ ⠀⠀⠀⠀⠀⠈⡇⠀⡀⠠⠠⠀⠀⠀⠘⠀⢰⡋⣤⡀⠀⠀⢁⢐⠀⢰⠀⠀⣞⣿⡷⣺⡠⠂⢢⣿⣿⣽⣿⣿⣿⣯⣷⣿⡿⣞⣿⣿⣳⣿⣿⡹⣧⣟⣳⣟⣷⣻⣿⣿⡇⠀⠐⠀⡀ ⠀⠀⠀⠀⠀⢨⣿⣴⡆⠀⠀⠀⠀⠀⠀⠪⠣⠿⠇⠛⠂⠀⢠⡘⡀⢀⡆⠀⠘⢏⣷⣿⠔⣜⣿⣿⡷⡿⣿⣿⣟⣾⣿⣿⣟⣻⣿⣻⣽⣷⠇⠈⢁⠙⠷⣫⣷⢯⣷⣿⡇⠀⠌⠀⠀ ⠀⠀⠀⠠⢀⣾⣿⡷⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠘⠀⠀⢀⣼⡃⢷⣟⠛⣷⠀⢠⣿⣷⡾⣿⣿⣳⣴⣿⣿⣟⣾⣿⣿⢧⣹⣿⣽⣿⣿⠍⠂⣄⠘⠋⢀⣴⣟⣿⣟⣿⡇⢀⠠⠈⠀ ⠀⠀⠐⠀⠸⠳⢻⡓⠀⠀⠀⠀⢀⠀⢰⠀⠀⠀⠀⠁⠀⠀⠹⣇⢸⣏⠀⢸⢀⡜⠉⠙⠳⢳⢾⣽⢿⣿⡿⣾⣿⣟⡟⣾⣟⣿⣻⣿⣍⠆⠀⠍⠛⢀⣼⢻⣾⡿⣽⣿⣧⠀⡀⠂⠁ ⠀⡀⠀⢨⣁⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⡆⠀⠀⠀⡅⠀⠀⢸⡧⢸⣿⢠⡸⠊⠀⠀⠀⠀⠀⡻⠿⣾⣿⢿⣽⣿⣻⡿⣯⣿⣾⢟⡶⣏⣾⣞⣮⣠⣴⣽⣿⣿⣿⣿⣿⡟⠀⠐⢀⠁ ⠀⢀⠀⠚⠿⢿⣷⣶⣦⣤⣤⣀⣇⠀⠀⡀⢀⠈⠀⠄⠀⠀⠞⢿⠷⣻⠋⡀⠀⠉⠁⠁⠒⠒⠀⠀⠁⠀⠉⠙⠛⠋⠛⠀⠁⠈⠉⠛⠽⣮⡽⢯⣟⣿⣻⣿⣿⣟⣿⣿⡗⢈⠀⠂⠄ ⠠⢀⠀⠀⡀⢺⠟⠛⢻⣿⠿⡿⡇⠀⠀⢀⠀⠄⠈⠀⠀⠀⠀⠈⢴⡟⠐⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠻⣟⣾⣿⣿⣿⣳⣯⣿⣿⡭⠀⠄⡈⠄
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