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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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