Rat Dot Art

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢄⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣉⣶⠴⠖⣤⠤⠽⠶⠦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢛⠻⢝⡆⠀⠀⢿⠇⠀⣴⣰⠗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠶⠖⠋⠚⠛⠿⠃⠀⠀⠀⢀⡴⣿⠙⣣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠘⠘⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⡀⠺⢬⡳⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠈⠳⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⠀⣠⡄⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⢤⣶⣒⣚⣋⣉⡉⠤⠤⠺⠟⣧⠀⠀⣀⣴⠾⢉⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣆⡻⢤⣀⣉⠓⠒⠒⠎⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢿⣿⣿⣶⣄⠀⠀⠀⣀⣠⣠⣠⣀⣤⣤⣤⣤⣤⣬⣤⣄⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⣿⠶⣦⣀⠀⠸⡆⠀⠙⠛⠏⣻⣷⣴⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠛⠛⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣴⣧⣞⣴⠉⢷⣦⣵⡀⠀⣠⣴⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⠀⠈⢡⣶⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢻⡿⣿⣵⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣾⡿⣿⣿⡿⣿⣷⡶⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⣀⠀⠙⢻⣿⢿⣿⣿⣿⣯⡸⡌⢧⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠸⢣⣤⣿⣾⣿⣿⣧⢿⣿⣜⣷⣿⡀⢻⡙⢳⣯⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣀⣹⡿⡿⣿⡟⣠⣽⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣯⣿⣿⣿⣿⣿⣿⣴⣿⣏⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣻⣭⣿⣭⣷⣿⣿⢯⠹⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣾⣩⣿⣏⢹⣿⣿⣿⡿⣿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢻⣤⣿⣿⣧⣸⣿⣿⣿⡿⣥⠾⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢿⣿⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣟⠡⠏⣶⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢻⣇⢿⣞⣿⢻⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⢿⣿⠿⣦⠿⣮⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣿⣸⣷⡷⢜⣻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⡴⠶⠖⣶⡶⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣻⡟⢿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣯⡁⠲⣤⠿⣏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠉⠁⠀⠈⠙⢶⣌⢷⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠛⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣦⣽⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡿⣷⣯⣻⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣨⠘⢛⢿⣿⣿⢦⣛⣚⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠿⠛⠀⠠⣤⣾⣿⣿⣿⣖⠿⣏⣥⣽⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⣤⣤⡴⠶⠶⠶⠶⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡇⠀⠀⡀⣾⣿⡛⢿⣿⣿⣯⡷⠿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⡆⠀⠀⠀⠀⠀⢻⣿⣿⣿⢻⣿⣿⣿⣏⣿⢠⣤⣶⣽⣾⣷⣽⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣏⣯⡟⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠻⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠉⠉⠉⠉⠉⠛⠿⠶⠾⠷⣦⣽⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⡋⠉⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⠠⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠉⠙⢋⡉⠉⠉⠹⣇⣀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⠀⠈⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠛⣻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⣀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠠⣤⣄⠀⠀⠀⠀⠙⢷⣶⣤⣄⢹⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠘⣷⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠿⢿⣇⠀⠀⠀⠀⠠⠿⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠁⢀⣠⣤⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡀⠘⠿⣿⣿⣿⣿⡿⠿⠟⠛⣉⣉⣉⣉⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⠿⢃⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣦⡴⢶⣶⣶⣆⠸⠿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣷⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⠿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⠛⠻⣿⣿⣿⣿⣦⡈⠉⠛⠻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⡈⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠈⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⡀⠸⣿⣿⣿⣿⣟⣀⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡿⠟⠛⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣧⣀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠶⠶⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⣀⡼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⡴⠿⡶⠤⢤⡤⠟⠗⢶⣦⣤⣀⣀⣨⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣏⣀⠤⠂⠀⠀⠀⠐⢿⣿⣿⣷⠈⠛⢿⡦⠤⠼⢷⣶⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⡿⢹⡈⠘⢩⣉⡙⠓⠲⠿⠉⠁⠀⠀⠀⣦⡤⠖⠉⠉⠉⠚⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠤⠊⢁⡼⣧⣁⡷⠬⠤⠞⠉⠢⣄⠀⠀⠀⠀⠀⠀⠘⣯⣭⣽⠅⢀⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⢠⠏⠀⠀⠙⣆⣄⣀⣀⡀⠀⠈⠳⣄⠀⠀⠀⠀⠈⣏⣉⣁⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠋⠀⠀⠀⠀⠈⠙⠦⡀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠂⠀⠀⠀⠀⠀⢴⡶⠾⠛⠁⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⣻⠇⠀⠀⠀⠀⠀⢰⡗⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣴⡞⠛⠉⠀⢠⡏⣀⣀⣤⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣷⡖⢫⣴⠶⢾⣇⠙⣾⣻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠻⡄⠈⠻⡼⠛⠛⠓⢦⣄⣀⣄⣠⣠⣿⠈⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣻⡄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠴⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢿⣿⡄⠀⠀⠀⠀⣤⡖⠉⠀⠀⠀⠀⠀⠀⠀⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⢹⣧⡀⠀⠀⢲⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⠈⠻⣄⢠⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣤⣶⡶⣶⢾⠋⠉⠙⠂⠈⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣽⠽⠃⣠⠾⠀⣠⡶⠶⠶⢾⢧⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡛⠯⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⠶⢿⣷⠶⠞⠋⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⣠⡀⣿⠛⢷⣤⣈⠙⠻⢿⣳⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⢤⣤⣼⣶⣿⡟⠋⠀⠀⠉⠛⠿⢶⣦⣌⣉⠓⠚⠿⠿⣿⣶⣦⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⢱⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⣦⣤⣄⣉⠙⠻⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⡋⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢄⡙⢿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡷⢾⠆⡀⢀⢀⡆⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣼⡇⣿⢈⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠛⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢏⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⢾⣿⣿⣿⠿⠿⠿⠿⠿⠶⣶⣿⣿⢿⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠶⠶⡶⢶⠿⠛⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⡦⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣋⣄⣀⡀⠀⠀⠀⠀⠀⠉⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⣀⡴⠓⠉⠉⠀⠉⠉⠻⢶⡀⠀⠀⠀⠀⠉⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠀⠀⢀⠤⣀⠀⠀⠀⠀⠀⠀⠉⠛⠢⠄⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠞⠁⠀⣀⣤⡀⠀⠀⠘⠊⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠋⣀⣀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠘⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⠓⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣸⣟⣄⠘⣯⠍⠍⣉⠒⠂⠤⡀⠀⢠⣾⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠙⣧⣀⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠐⢁⠎⠈⠉⠓⠒⠻⢦⡀⠉⠒⢄⡀⠀⠀⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⣣⠈⠙⠳⣄⠙⢦⡀⠀⠀⠀⠀ ⢀⠋⠀⠀⠀⠀⠀⠀⠀⠙⣄⣄⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣁⠀⠀⣀⣄⡲⢿⡀⠀⠀⠈⠳⣄⠹⣄⠀⠀⠀ ⡌⠀⠀⠀⠀⠀⣠⣶⣏⠉⠙⡌⢷⣼⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠋⠉⠉⠉⢉⡽⠉⠀⢸⡱⠀⠀⠀⠀⠈⡆⢹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣯⡵⢶⣴⢿⠛⠋⠉⣺⡶⣦⣤⣙⡿⠾⠋⠁⠀⠀⠀⠀⢼⡟⣻⣃⣴⢰⠇⠀⠀⠀⠀⠀⢻⠀⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢀⡴⣿⣿⢠⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠋⠳⠏⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣧⢧⡼⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢻⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⠛⠉⠉⠙⠛⠳⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣁⣤⣤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣠⡿⠖⠋⠉⠁⠉⠉⠛⠛⣗⠤⠀⠀⠀⠀⠀⠀⠈⠛⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡯⠟⠛⠉⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⣴⢛⣒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⡟⠁⠀⠀⢀⣤⣤⡄⠀⠀⠀⠈⠋⢉⣩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠻⠁⠀⠀⠀⠀⠙⠿⠿⠃⠀⠀⠀⠀⠀⠈⠻⡷⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠹⣿⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⢶⡛⠙⡿⡖⠶⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⣻⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠘⢿⡦⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡠⠖⡿⢧⣷⣌⠀⠻⣍⡉⠒⠤⣄⡀⠉⠙⠂⠀⠀⠻⣞⡛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⠃⠀⠀⠀⠀⠀⠸⡿⠶⣤⣄⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⡜⠁⠀⠀⠈⠉⠉⠛⢿⣦⠀⠀⠉⠳⢄⡀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠻⣦⡀⠙⢷⡀⠀⠀⠀⠀⠀ ⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡽⠋⠀⠀⠀⠀⡀⠢⣦⣿⡄⠀⠀⠀⠀⠙⣦⠀⠻⣄⠀⠀⠀⠀ ⣸⠁⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⢿⠙⢆⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣭⠿⠗⠒⠒⠒⠖⢿⡿⠟⠀⢸⡧⡄⠀⠀⠀⠀⠈⢳⡄⠹⣆⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⢀⣾⣻⡿⠦⠀⠀⢇⣈⣽⣾⣷⡀⣀⠀⠀⠀⢀⣠⣀⡀⣀⣶⡿⠛⠀⠀⠀⠀⠀⣠⡴⣏⣀⠀⠀⠸⣯⠀⠀⠀⠀⠀⠀⠀⣧⠀⢻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡶⠟⣿⣼⢿⡏⠉⠁⠀⢙⣿⠾⡷⣴⣤⣭⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⢸⣯⡎⣩⢋⣴⡗⢸⠿⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠸⠇⢀⣴⢾⡿⡏⢠⠀⣤⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⠟⠁⢷⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⡞⣸⠁⣸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢿⠋⢷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⢿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⢀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡉⠈⢿⡜⣺⣞⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠁⡀⠀⠙⠋⠁⠀⠉⠉⠉⠐⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣴⠁⠀⢠⠀⠀⠀⠀⡄⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣔⠏⢀⠂⡰⠏⡀⠀⠀⡞⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣙⣤⣮⠊⠀⠀⣀⢩⣇⡳⠄⠀⢀⣔⣏⠐⠠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠶⠦⠬⠝⠁⠀⠀⠉⠢⡈⢢⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡱⢈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠒⠂⠬⠍⢉⣁⣀⣉⠠⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⡤⠀⠠⠀⠄⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣛⣻⡷⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠹⣷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⣡⣶⠏⠉⠉⠉⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⣿⣿⢦⣀⣤⣤⡴⠶⠶⠶⠶⠶⠶⢺⠟⣺⣿⡃⠀⣠⣾⣶⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠐⢿⣶⣿⠟⠛⣰⡿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢀⣀⣼⡿⢧⢫⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⠇⠀⡟⢩⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠛⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠚⠓⠿⣏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡷⠖⠃⠀⠀⠀⢢⠀⠀⠀⢠⠃⠀⠀⠀⠀⢠⠀⣐⡆⠈⢧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⡿⠁⠀⢠⣶⣦⣦⠀⠀⠀⠀⠀⢀⣴⣿⣻⣅⠀⠀⠀⠟⠀⠀⢳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⢋⡾⠀⣿⣁⠠⡄⣿⣿⡿⠻⣇⠀⠀⠀⠀⠓⢿⣿⣿⡟⡀⠀⠶⣀⣀⡀⡈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠰⡃⣾⠇⠀⡙⣷⠀⠀⠂⠋⠁⠀⡀⠀⠀⠀⠀⢀⣀⡀⠀⣀⡤⠖⠀⠀⠀⠈⢁⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣸⡏⠀⠀⣇⠻⣄⣀⠒⠂⣶⢿⠀⠀⠀⠀⠀⠀⢛⢿⣯⣁⣠⣤⣴⣶⣦⡄⣼⣿⣿⠀ ⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⢰⣯⡇⠀⠀⠘⢆⣈⣿⡤⣾⣥⣼⠀⠀⠀⠀⣼⢯⣿⡾⢿⠒⢠⡤⠊⠉⢁⣴⣿⣧⣽⡄ ⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣸⠀⠒⠛⢻⣷⣞⣯⢿⡘⣿⣿⣿⣾⡗⠀⣀⢭⣿⠓⠶⢄⣀⣠⣿⣿⣿⣈⠿⡇ ⠀⠀⠀⢰⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⢀⠴⠃⠈⠛⢿⣿⣀⠙⠛⣿⣅⣀⣀⣼⣷⡜⣷⣾⣿⣿⣿⣿⣿⡏⢸⠀⢹ ⠀⠀⠀⣸⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣫⠀⠀⠀⢠⠏⡿⣮⣿⡿⡭⢍⣡⣞⣁⣿⣿⣯⡹⣿⣻⣿⠝⠁⠁⠈⠀⣸ ⠀⠀⠀⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⢿⠀⢀⡏⠸⠀⠈⠉⠁⠉⠛⠿⣿⣿⣿⣿⣿⢷⣼⠋⠉⠀⠀⠀⠀⢰⠇ ⠀⠀⠀⢸⣿⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠈⣧⣿⡶⠀⠇⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣛⡆⡉⠙⠲⡀⠀⠀⢠⠟⠀ ⠀⠀⠀⢸⣿⣼⠀⡆⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡹⣷⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠼⢶⣿⠏⣴⣿⣿⣴⣿⣿⡾⠃⠀⠀ ⠀⠀⠀⠈⡟⣿⠘⣗⢤⢧⣤⠀⠀⠀⠀⠀⢀⠀⠀⠘⣝⡦⣄⠀⠛⣦⠀⠀⠀⠀⢧⣄⡀⢠⣌⣹⡷⠿⣿⠿⠿⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡸⡄⡌⣾⡀⣏⠣⣤⡄⠀⠀⠘⣧⠆⠀⠘⢿⣮⣵⣦⣀⢀⠀⡀⠀⢀⣉⠉⢤⣽⡾⢓⠄⣿⣷⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡇⣷⢰⣇⣧⠈⠂⣜⠿⣆⠀⠀⠈⠀⠀⠀⠈⠻⣿⣟⡟⣿⣿⣭⣽⣿⣿⣽⣿⣿⡟⢾⣷⣽⠳⣽⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⢸⡏⣿⣿⣦⠀⠻⡄⣿⣄⡀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀ ⢀⣀⣠⣤⣾⣿⣿⠰⣿⡼⡝⣿⣦⣇⣿⣮⡁⠀⠀⠀⠀⠀⡀⢸⣿⣿⡟⣩⡯⡷⠚⠙⣛⡶⠦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠿⠿⠿⣿⠿⠿⡆⢈⣷⣧⣣⡃⢽⣽⡽⢷⣤⣠⣤⠘⣿⠿⠟⢻⣿⠿⣧⣙⣛⠛⠛⠓⠿⠖⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠸⢧⣼⣾⣶⣿⣦⣀⣎⣹⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⢰⠶⡖⠒⠢⡤⢄⣴⣉⣷⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣄⠀⠀⠘⢿⣷⠀⢹⣿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠯⡒⠀⠀⠀⠀⠻⡿⠟⠛⠓⠤⠖⠒⠒⠒⠒⠒⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⣇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣴⡒⠉⣹⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣧⡏⠀⠀⡝⠀⣠⡟⠓⠢⢄⣀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⢁⣀⣼⣥⠞⠁⠀⠀⠀⠀⠀⠉⣟⠒⢳⡄⠀⠀⠀⠀⢠⠶⡾⠉⠒⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠟⠛⠒⠁⠀⠀⠀⠀⠰⠾⠿⠿⠿⠿⢋⣈⣢⣀⣠⠞⠋⠉⠓⠢⢄⡀⠈⠑⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠿⠯⠭⠤⠼⠃⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⢣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠐⠒⠢⠤⢄⣀⡉⠉⠉⠀⠒⠒⠒⠀⠉⠀⣠⠞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠒⠒⠒⠒⠒⠊⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⠰⣶⠶⠀⠀⠶⠀⠀⠲⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠊⠁⠃⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⣰⠊⠉⠉⠉⠳⠄⠀⢠⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠐⠈⠁⠀⠀⠀⢀⠴⠂⠀⠀⠈⠙⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠤⢺⡃⠀⠀⡀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠘⠛⠂⣀⣈⣑⡀⠀ ⠀⠀⠀⡠⠎⡀⠤⠞⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠳⠀⠀⠂⠈⠄⣒⠊⡠⠻⠂⠀ ⠀⢀⠜⡠⠊⠀⠀⡧⣤⣀⠀⣘⣇⠀⠀⠀⠀⠀⠀⠀⢀⠁⣠⠊⠁⠀⠀⠀⠀⡀ ⠀⡘⠸⠀⠀⠀⢠⠃⢀⢣⣄⠀⠉⠳⢆⣀⣀⠀⠀⣀⠾⣎⡆⣉⢿⡄⠀⠀⠀⠀ ⠀⡇⡇⠀⠀⠀⠀⠳⠓⠖⠋⠀⠀⠀⠀⠀⠙⢯⠉⡳⡢⡀⠉⠁⠉⠁⠀⠀⠀⠀ ⠀⣇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠔⠖⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

…ᘛ⁐̤ᕐᐷ

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

ᘛ⁐̤ᕐᐷ 🐭

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠈⠻⣮⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠋⠀⠀⠀⠀⠙⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣤⣤⣀⡀⠀⠀⣀⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⠀⠀ ⢀⣤⣾⡿⠟⠛⠛⢿⣿⣶⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣀⣀⣤⣶⣿⡿⠿⢿⣿⡀⠀ ⣿⣿⠏⠀⢰⡆⠀⠀⠉⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡿⠟⠋⠁⠀⠀⢸⣿⠇⠀ ⣿⡟⠀⣀⠈⣀⡀⠒⠃⠀⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀ ⣿⡇⠀⠛⢠⡋⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀ ⣿⣧⠀⠀⠀⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⢸⣧⣤⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀ ⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⣷⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀ ⠈⠛⠻⠿⢿⣿⣷⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣷⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣷⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣷⣶⣶⣤⣤⣀⡀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣷⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣤⣄⣀⡀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣻⣷⣶⣾⣿⣿⡿⢯⣛⣛⡋⠁⠀⠀⠉⠙⠛⠛⠿⣿⣿⡷⣶⣿

⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠉⠉⠉⠙⠛⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠀⠀⠀⠀⣠⣴⠶⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣀⣤⡴⠟⠋⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠉⠙⢷⣄⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠹⣧⡀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠈⠛⣷⣤⣴⠶⠟⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠛⣻⡿⠀⠀⠀⠀⠀⢀⣤⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢀⣴⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⣠⣾⡿⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⢀⡾⢫⣿⠁⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⢀⣴⠟⢡⡟⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣰⠟⠁⢠⡿⠀⢿⡄⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⢠⣾⠋⠀⢀⡿⠁⠀⠈⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣴⢿⡟⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣾⠋⠘⣧⡀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀

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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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