Eye of Horus ASCII Art

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𓂀

⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⢉⣕⡞⣼⣿⣿⣿⣿⣿⡟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣳⡀⢻⣤⣴⣴⣶⣶⣶⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣼⢧⣿⣦⠬⡜⣼⡝⣿⢹⣿⣿⡟⣁⡀⣴⣿⡟⣹⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣗⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢰⣿⢀⣿⢀⠨⢳⣷⢴⣧⣸⣟⡟⠉⢁⡾⠋⣀⡴⢃⡠⣠⣿⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠋⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣾⣧⢸⣻⠀⢩⡏⠀⣸⣯⣿⡿⠒⣲⠟⠘⣩⠿⣠⠏⣴⣿⢯⣟⣹⣄⡿⣿⣿⣿⠏⣿⣿⣿⣧⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠘⢸⡇⣰⣿⠏⣿⣀⡼⠧⢶⣶⣳⡞⢳⠞⣿⣣⠏⠀⢠⣞⣀⣸⣿⣿⠀⢻⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡦⣿⣷⣿⢹⠀⣯⣞⣧⣔⣯⣿⣯⡾⢃⣾⠟⠁⢀⣴⡟⢀⣼⡟⣾⡿⣐⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣸⣿⣧⢹⣾⣴⣿⠋⡇⢸⣸⣿⣿⣿⣿⣿⣿⣯⣶⠟⠋⢀⣴⣫⢏⣴⠟⣽⣿⡟⠀⠈⢹⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢳⠇⣿⣿⣿⣿⢹⡀⠃⢸⡜⣿⢹⣿⣷⣿⣿⡿⣷⠶⠚⠛⢛⡿⠋⣠⣾⣿⣿⣤⣦⣀⢸⡟⣠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⡞⣸⢻⣿⣿⣿⣾⣗⠄⠘⡇⣿⠚⠻⠿⠯⠿⠅⠀⠠⢄⠍⢨⡙⠊⠑⣿⣿⣯⣿⡿⠻⣿⢡⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣾⢣⡟⢸⠀⣿⣿⣷⣿⣦⠀⣷⣹⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠛⠿⠿⡿⣁⣼⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢠⣇⣼⣿⣾⠀⣿⣿⣮⡛⢿⣧⣽⡿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠶⠆⣰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡼⣼⣿⡏⡟⣼⣿⣿⣿⡻⣿⠃⣸⡟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢰⢳⢻⡿⣠⡷⣿⣿⣿⣿⡏⢻⣴⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣼⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡞⡞⣼⣷⢻⡇⣸⣿⣿⣿⡿⡟⠅⣴⣿⡟⢤⣀⠀⠀⠀⠀⠈⢿⡟⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢠⢻⢁⡿⠇⣸⠇⣿⣿⣿⣿⣇⣿⠞⣡⣿⣧⣤⣽⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡞⣸⠃⢀⣿⢀⣿⣿⣿⣿⣿⢥⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠒⠺⠷⣏⡀⣼⡿⢸⣿⣿⣿⣏⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⠀⠀⠀⠀⣀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠻⣿⣿ ⠀⠀⠀⠀⠈⠙⠳⢿⣿⣿⡟⢉⣰⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣿⣿⣷⣤⠖⠛⠉⠉⠀⠀⢸⡏⠁⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠤⢄⣀⠀⣨⡿⠟⢋⣿⡿⢯⣶⣝⣛⣛⣿⠿⢿⣿⢥⣠⠼⠻⣿⣟⣿⣿⣿⢿⣿⣿⡋⢤⡀⠀⠻⣌⣉⣻⣦⣀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⢀⣼⡟⠛⣛⣿⡿⠀⠉⢛⣻⣿⠿⠋⠀⢸⢹⠀⠀⠀⠀⠘⣾⣦⠉⠛⠷⢿⣿⣻⣦⡌⠢⡀⠘⣧⣙⡛⣿⣗⡚⠉⠉⠉⡇⠀⠀⢀⣀⣀⣠⣴⣿⣿ ⠀⠀⠀⢀⡤⡶⣿⠋⣽⠛⣿⡿⢁⣤⢶⡋⠉⠁⠀⠀⠀⢸⠾⠆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠛⣿⣦⡙⣏⠁⠈⣯⣙⠛⢿⣆⠀⣼⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢠⡟⢸⣷⣿⠉⡇⢀⣯⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⢿⣟⢧⡤⠶⠛⠋⠉⠻⣿⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⣶⣿⣧⣿⢃⠏⠀⡇⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣀⠀⠀⠀⢻⡝⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣟⢿⣯⣎⠤⠔⡇⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢴⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⡄⢿⠦⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡉⢿⣻⡄⢻⣿⣿⣿⣿⣿⣿⣿ ⠀⢸⣿⣿⣾⣇⠀⠋⡏⠀⠀⠀⠀⣀⡤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣻⣎⠀⠹⣵⡟⠙⠛⢿⣿⣿⣿⣿ ⣴⣿⣿⣿⣻⣿⣆⢰⠁⠀⠀⠀⠘⠁⣶⠿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⢻⣠⣴⠀⣼⡟⠛⠛⠛ ⣿⣟⠙⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⠁⠀⠀⠀ ⡏⠁⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀ ⣄⠀⢀⡀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣤⣀⠀⠀⠀ ⣿⣷⣌⢿⣷⣍⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠈⠊⣙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⣎⣻⣼⣷⡆⠀ ⣿⣿⣿⣷⣽⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠉⠛⠷⢶⣤⣄⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣷⣿⣿⡿⠿⠃⠀ ⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡦⢶⣄⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠙⣄⠀⠀ ⣸⣷⣿⣿⣿⢿⣿⣿⣿⣿⣿⡄⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀ ⠿⠿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳ ⠀⠀⠀⠁⠚⠉⠛⠙⠛⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢹⡟⣿⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⢹⣏⠀⠉⠓⠤⣄⣀⡠⠖⠋⢳⣀⣀⣀⣀⣀⣀⣾⣐⣈⣦⣀⣀⡤⠤⠖⠒⠒⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⠇⠸⣿⡄⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠷⠶⠾⡊⠦⣄⣀⡤⠖⠉⠀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⢧⠟⠀⠀⠙⢧⡵⠀⢀⣀⠠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣤⡴⠛⠉⠙⡆⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠒⠚⠛⠛⠛⠛⠒⠒⠒⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠋⠀⢀⣴⡾⠃⢀⠇⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⣜⠁⢀⣼⠛⠛⠤⣰⣫⠖⠀⡄⢸⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠘⢄⢸⢑⡷⢿⡿⢶⣄⠀⢈⠳⡄⣴⡧⢸⡏⠉⠳⡖⠲⠤⠤⢤⣄⣀⣠⡤⠴⠚⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠖⣚⣿⠀⠀⢄⡀⠙⠲⣍⣠⠋⠐⣠⣾⣿⢧⣴⣣⠏⣰⡿⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠈⢷⡀⠐⠭⣗⡀⡴⢁⢀⣼⣿⠂⠉⠢⣴⣁⡾⠋⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⠦⢄⣀⠀⠀⠀⠀⠀⢀⣠⡤⢒⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⢄⡀⠙⠧⣴⡋⣠⠟⠒⣤⣠⢀⠝⣄⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠉⠉⢉⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣜⡽⠡⣤⣼⡯⣍⡉⢲⠊⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡰⠟⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⡇⡀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣤⢞⡞⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

𓋹 𓂀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣄⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣀⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⣿⣦⠀⢀⣶⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⠇⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣈⠻⣿⣿⣷⣿⣿⣿⣿⣿⡿⠁⠹⣿⣿⣿⣿⣿⣿⠟⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡏⢠⣾⣿⣿⣷⣜⢿⣿⣿⣦⠀⠀⠀⠀⢀⣀⣈⡙⠛⠛⠋⠁⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣧⣝⣛⣡⣶⣶⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⢀⣿⣿⣿⣤⣤⣄⣀⣀⣀⡀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠈⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⡥⠀⠀⠀⠀⣠⠴⢀⣠⠤⢦⡀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡞⢸⠁⠀⠀⣠⢚⡥⠚⠉⠀⠀⠘⣗⡄⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⠇⡎⠀⠀⣰⡳⠋⠀⠀⣠⣤⠶⠢⡿⣸⣆⠀⠈⣧⣄⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡄⢳⣠⣾⡟⠓⠆⠀⠘⠙⢀⣤⣶⢿⣤⣹⡅⠀⣿⠈⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠸⡇⣾⡛⣶⡦⠀⠀⠀⠛⢱⢼⣷⠸⠋⢣⠀⡇⣹⠛⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢱⠀⠹⣏⠉⢟⣻⣀⠀⠀⠀⠐⠛⠛⠐⠀⠘⣴⡽⣇⠀⢸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢇⠀⠘⡄⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⢹⡀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢦⠀⢻⢦⡀⠈⠰⠶⠒⠂⠀⠀⢀⡤⠀⡇⢘⡆⢇⠀⠸⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⡼⡀⣟⡶⢄⡀⠀⢀⡠⠖⠁⠀⢀⡇⢸⢻⠸⡀⠀⣿⢇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⢳⠟⢀⠷⠈⣹⡇⠀⠀⠀⠀⣼⢣⡞⢸⠀⡇⢰⣼⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⣠⠋⢀⡼⠟⠊⠟⠀⠀⠀⠀⠀⣿⠀⠑⢯⣀⣇⣎⢏⡞⠀⠀⠀ ⠀⠀⠀⢀⡠⠾⠔⠓⢞⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣀⡈⠛⠿⠯⣀⠀⠀⠀ ⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠉⠉⠉⠉⠉⣧⡀⠀⠀⠀⠀⠀⠀⠑⡄⠀ ⠀⠀⢻⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⢸⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⡼⠃ ⠀⠀⠘⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⢠⠇⠀ ⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡎⠀⠀ ⢠⠇⣠⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⡄⠀⠀⡸⠀⠀⠀ ⢸⡀⠛⠄⢀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⠵⠀⠀⡇⠀⢀⠇⠀⠀⠀ ⠀⢷⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣰⠁⠀⣾⠀⠀⠀⠀ ⠀⠀⠑⢤⣀⠀⠀⢀⣠⠴⠋⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣀⡴⠁⠀⢠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⢻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠉⡽⠀⠀⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣾⠀⠐⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡄⠀⠀⢠⡀⠀⠀⠀⠀⠙⣄⠀⠀⠀⢰⠁⠀⠀⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡜⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣻⠁⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⠀⠸⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀

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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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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⡄⣸⣿⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠿⠿⠿⣿⢿⣿⡿⠿⠿⣷⣦⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿ ⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣠⣤⣤⣤⣤⡿⠛⠛⡟⣿⣿⡿⢻⡆⠀⠀⠀⠘⣷⣶⣅⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢹⣿⣿⣿⣿ ⣿⡀⢿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⢉⣹⠿⣿⣿⣛⣛⣛⣿⣿⣯⣭⣁⣀⣬⣿⣿⡏⠀⠀⠉⠀⠀⠀⢀⡿⠙⣿⣦⣄⡀⠀⠀⠀⠈⠉⠉⠉⠍⠛⠛⢿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿ ⣿⡇⢸⣿⣿⠿⠛⠉⠀⠀⣀⠴⢚⠉⠀⠀⠀⠈⠙⠛⠛⢻⣿⣟⠛⢿⡍⠀⣿⣟⡃⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠉⠛⣿⡶⣶⣿⣷⣤⣤⡤⠴⠾⠛⠙⠦⣍⠁⠀⠘⠿⢿⣿⣿ ⣿⠇⠀⠉⠀⠀⠀⠀⣠⣞⣵⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠙⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⣼⠏⢀⣴⠞⠋⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣦⡀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⢠⣾⣟⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣆⡀⢸⣿⣿⡷⣤⠀⠀⠀⠀⣼⣿⣿⣿⣞⠋⠁⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡿⠁⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠈⠳⣼⣿⣿⠀⠀⠀⠀⠐⢻⢿⣿⣟⣻⣽⣧⠀⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣧⡀⠀ ⠀⠀⠀⢀⣼⣯⢠⡤⠤⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣆⠀⠘⣿⣿⣦⣤⣀⡀⠀⢸⣿⣟⣻⣋⣩⣿⠞⠋⣠⣿⡿⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⢷⡀ ⠀⠀⢀⡞⠁⢻⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣿⣿⣷⠺⣿⡟⣿⡀⠉⠙⠓⡿⣿⣿⣿⡿⠻⢇⣀⡀⢿⣿⠇⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⡄⠈⢧ ⠀⠀⡼⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣹⣿⣿⡄⠹⣧⣿⣿⣦⡄⠀⣿⠿⣾⣿⠇⠀⠈⠉⠁⣿⡟⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠿ ⠀⣸⣁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠀⣏⠻⣿⣷⠀⠀⣿⣿⡇⠀⣸⠃⠀⢸⣿⠀⠀⠀⠀⣾⡿⣱⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠇⣿⣄⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⠀⠀⢹⡄⠈⢿⣧⠀⢸⣿⣧⠀⡏⠀⣶⣸⡿⠾⣦⣠⣾⠟⣰⠏⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡼⠀⣿⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢳⡀⠐⢿⣷⡘⣿⣿⠆⠻⡀⣿⢹⡅⠀⣾⠟⢁⣰⠇⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣸⠋⣼⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠳⣤⣀⣙⢷⣿⣿⡆⠀⢹⣿⣸⠇⣼⡿⠞⣹⠃⠀⠀⠀⢠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠙⢦⡸⠿⣿⣿⣦⣀⣸⣿⣿⣿⣿⣴⠞⠁⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⡀⠀⠀⠈⢳⣤⡀⠻⡟⠿⠛⢻⠟⢡⡾⠉⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⢦⡀⠀⠀⢳⡙⣦⠹⡓⣲⠋⡰⣿⠁⠀⠀⠀⢀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡆⠀⠙⢦⠀⠘⣇⠈⠣⡟⣡⠞⣹⠇⠀⠀⢀⡼⠋⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢀⣯⡷⠖⠚⠳⠶⣽⡄⠀⠴⠋⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⢀⡞⠉⠀⠀⢀⠄⠀⠀⠻⡆⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⡀⠸⣇⠀⢀⠀⠀⠐⠀⢀⢠⡇⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠙⢷⣄⡢⢄⣶⣾⡿⠋⠀⣠⠞⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠉⣳⣦⣤⠽⠿⠿⠿⣭⣤⣶⠚⠁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣖⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⣿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢢⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣤⡀⢸⣿⣬⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣶⣷⡞⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⡿⣏⡠⢄⡀⢉⣿⠯⢀⠘⣿⡇⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⢸⢸⣶⣎⢶⣷⣾⠉⣸⡜⠀⢹⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⡀⠀⠰⡀⠀⠀⣠⠀⡠⠒⠛⢉⠝⢿⣿⣿⣿⣶⡏⠀⠀⣸⣿⣿⣧⠃ ⠴⠦⣤⣶⣿⡟⡟⢻⣭⣯⠿⠍⢙⣷⣾⡿⢵⣟⠀⠈⢲⣾⠦⠌⠛⠻⣿⣿⣿⣆⠀⣿⣿⣿⣿⠀ ⠀⠀⣰⣿⣟⠻⠿⠏⣋⣤⡔⠺⠽⠟⢫⠑⠋⠁⠀⠀⠀⠈⠒⠶⢖⣉⣉⣻⣿⣿⣾⣿⣿⣿⠏⠀ ⠀⠀⣿⡿⣿⢀⣤⣤⣾⣤⣾⣶⡶⠀⢼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠒⣻⣿⣿⣿⣿⡏⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠋⢀⣾⣿⣿⣿⣿⣿⠁⠀⠀ ⠀⠀⠈⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣄⣀⣤⣄⣒⣊⣭⣿⠛⡟⠀⠀⣠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠉⠺⣿⣿⣿⣿⣿⢦⡠⠀⠀⠀⠈⠻⡏⠉⠀⠩⠟⠁⢠⠃⠀⣠⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣦⡙⢶⣤⣀⠀⠀⠈⠙⠢⠤⠤⠔⠋⣠⣾⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣎⣹⣏⠙⢶⢤⡀⣸⠀⠀⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠷⣦⢰⣿⣷⣦⣤⢞⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣶⣈⡱⢿⠉⢫⣁⠚⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡤⠤⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀ ⡤⠴⠖⠚⠋⠉⢩⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⣐⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⠀⠠⢤⣤⣼⣿⣿⣿⣿⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣦⣄⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠠⠴⣶⣾⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣷⣒⠺⡝⢿⣷⣄⠓⢬⡙⠶⢤⣀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠉⠻⢿⣿⣿⣧⡈⠹⢿⣿⣿⣿⣿⣿⣿⡿⣧⡄⠙⣿⣿⣄⡇⠀⢻⠿⡄⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡄⠀⠙⢿⣿⣿⢏⠞⠀⠀⣇⣿⣟⣹⡿⣦⠀⢸⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄⠀⠈⢻⣃⠎⢠⣤⠀⠈⠻⡛⠛⣃⣷⣷⡼⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⢟⠀⠈⠋⠀⠀⠀⠲⢞⡻⠟⠋⠁⠀⠀⠀⠀⠀⢀⡤⠴⡖⠒⡆⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣓⡤⣄⣣⠀⢧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⡞⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⣯⠻⣾⠃⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⢰⠃⢠⣿⣯⡉⠢⢄⠀⠀⠀⠀⠠⠄⠀⣻⡿⣿⣿⡁⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⠃⢠⡏⠋⠙⠻⣷⣄⠑⣄⠀⠠⠔⠒⠋⢁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⡏⢷⡒⣄⠀⠸⣿⣷⣈⣄⠀⠀⠀⠀⠐⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⠴⢤⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠙⢌⠻⠟⣳⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⡠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⣿⣿⡆⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⣿⣿⢻⣿⣿⣿⣿⠏⣿⡿⢓⡶⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠃⢠⣿⣿⢻⠹⣄⣀⣀⣀⣀⣀⣀⣠⠤⠤⠤⠔⠒⠉⠀⠀⢸⣿⣟⣾⣿⣿⣿⡏⣸⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠁⠀⣾⣟⢿⡘⡄⠈⠁⠀⠹⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⢿⣍⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠘⠈⢧⡃⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡏⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣏⣿⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠀⠀⣾⡿⠁⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠘⠀⠀⡰⠀⠀⠀⠸⣄⠈⠀⢄⠒⠒⠒⠂⠈⣀⣠⣞⣽⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡜⠁⠀⠀⠀⠀⠸⡄⢷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⣤⠖⣿⢷⣤⡀⠀⠀⠀⢈⣉⣉⣠⠼⠛⠛⠾⣤⣀⠈⣭⠀⠀⢀⣠⡾⠟⠛⠒⢦⣤⣀⠀⠀⢱⠀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣠⣴⣟⣹⣷⣿⣦⣿⣿⣿⡷⡖⠚⡍⠉⠀⠀⠀⠀⢀⠀⠈⠉⢻⢻⠏⠁⠙⣿⣆⠀⠀⢠⣻⡄⠉⠑⢺⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⡈⣿⡟⣟⣿⣿⣿⢟⠁⠀⠉⢹⠀⣧⠀⢰⣷⠀⠀⢸⣆⠀⢰⠃⢸⠃⠀⠒⢻⣿⡆⠀⠀⠙⣿⣖⡶⠃⠀⢇⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⡇⠘⣤⣾⣿⠿⠃⠈⢠⣄⡀⢸⡀⢹⣄⣿⡼⡇⠀⣸⣿⣷⣸⡠⣼⣲⠉⠉⢹⡇⢣⠀⠀⠀⣻⠟⠀⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠫⡉⣧⣠⣿⡟⢧⡤⠔⠒⠛⠛⠛⢺⡷⢼⣿⣿⡁⣷⠀⣿⣿⣹⣿⠿⡟⠹⣤⣀⡼⠀⢸⠄⢀⡔⠁⠀⡴⠁⠀⠀⠀⢀ ⠀⠀⠀⠀⢰⠁⠳⣌⢣⡀⣸⠏⠀⣀⡤⠔⠒⠀⢀⣼⡇⢸⣿⣿⣿⣧⣾⠿⣿⣿⠇⣸⣇⣀⠘⣀⠉⠑⠺⡴⠋⠀⢠⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠟⢦⠀⠀⠀⡘⢧⡀⠈⠁⠀⠀⠀⣶⣿⣿⡇⢈⣿⣿⣿⣿⠃⢠⣟⣿⠀⣿⣿⣿⣷⡏⠀⣠⠎⡠⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⠀⠀⠱⣄⠀⠀⠢⡈⠦⡀⠀⢀⣸⠟⠋⠁⡇⢈⣿⡟⢹⣮⢷⣿⣿⢛⣴⣿⡀⡈⠙⠒⡖⠁⠈⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠓⢌⠻⡁⠠⡖⢺⠋⡇⣼⡟⠀⢸⣿⢿⣿⣶⣾⡧⡟⢳⠙⢦⠞⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠑⢜⢶⠁⢸⠀⢿⣆⣧⠀⣼⡏⠀⢹⣿⣿⠀⡇⠈⡆⡞⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠁⢧⢸⣆⠘⣾⣼⣶⣿⣷⣴⣫⣟⣿⠞⢉⣾⠇⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠈⡇⠻⣦⠈⢻⣿⣵⣿⣿⣿⣿⠃⣠⡿⠏⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢳⠀⠙⠷⣾⣟⣿⢿⣿⠛⣧⣴⡿⠁⢀⣾⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⣄⡀⢻⠻⣿⡍⢸⣶⠻⠋⢀⣴⣿⠗⢲⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣼⣻⢿⡆⠑⢻⣹⡞⠈⣦⡶⠋⣿⡟⠀⠀⣿⠛⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠈⠳⢄⡙⠆⢸⣿⡧⠞⣻⡷⢀⠟⠁⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⠀⠀⠹⡆⣾⣽⡃⠀⡏⡇⣸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⣄⣀⣠⠤⠀⠀⢳⢳⡶⠂⣻⠘⠛⠁⠰⢹⠃⢿⣧⠉⠲⠤⣄⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀