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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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