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

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

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠀⠀⠀⣠⡖⠐⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⡸⠁⢠⠃⠀⢀⣴⠟⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠃⠀⣏⣀⡤⠚⠁⠤⠤⠾⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣧⢸⠀⠼⠋⠁⢀⣀⣀⣀⠀⠀⠀⠀⠀⢉⡓⠶⣤⣄⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠋⠁⣠⠁⠀⠛⠋⠁⠀⠀⠀⠀⠀⠤⠤⣉⡒⠖⠤⢄⣈⠛⠛⠳⠤⢤⣤⣤⠄⠀⠀ ⠀⠀⠀⠀⡜⠁⢀⡤⠊⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⠄⠀⠀⠉⠑⠒⠶⣈⡉⠁⠀⠀⠀ ⣀⣀⣀⠤⠖⠊⠁⠀⠀⢸⠁⠀⢀⠀⠀⠀⠀⡄⠀⠀⢶⠀⠘⣆⠀⠳⡀⠀⡄⠀⠰⢤⣤⠬⡭⣶⡶⠶ ⠀⠀⠀⠀⠀⣠⠏⠀⠀⠈⠀⠀⢸⡄⢠⠀⠀⣧⣷⠀⢸⡀⢠⠘⣆⠀⠱⡀⢻⠾⣆⢢⡹⣆⠀⠀⠀⠀ ⠀⠀⢀⣤⡾⡟⠀⡄⠀⡆⠀⠀⠀⢧⠸⡄⠀⢻⢹⡇⢼⢷⠈⡆⢹⢣⡀⠱⣼⡳⡙⢆⠱⠙⡆⠀⠀⠀ ⠰⠶⠟⠋⢰⠃⠀⡇⠀⢹⠀⢹⡘⡜⡆⢳⡀⠸⠈⣷⢸⣾⡆⠸⠸⡄⠑⡄⢻⡇⠱⡘⣷⣧⢹⡀⠀⠀ ⠀⠀⠀⠀⡎⡸⠀⢱⠀⠈⢧⠀⢇⢷⣽⡌⢧⠀⡷⢾⡀⡇⠱⡀⠃⡷⠒⠛⣺⣷⢄⠙⣽⣏⢧⣧⠀⠀ ⠀⠀⠀⢰⣿⡷⣧⠀⢣⡀⠈⡆⠸⢸⠙⣿⣄⣱⣷⣴⣧⣇⠀⠹⣿⣇⣴⣶⣿⣿⣈⢦⠘⣞⠘⠉⠀⠀ ⠀⠀⣤⠟⣱⣷⡟⣶⡤⢷⣄⣰⣀⣿⣄⣘⣬⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⡀⠳⣌⡇⠀⠀⠀ ⠀⠀⠀⠘⠋⣸⡷⡿⣇⡿⣶⡽⠏⠛⠉⠉⠙⢿⣿⣿⣿⣿⠏⠀⠀⠻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⠁⢳⣿⡦⠋⣧⡀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⠀⠑⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡆⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠺⣍⢉⡟⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣇⡀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⠀⠈⠉⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠹⢿⣶⣤⣄⣀⣀⣀⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠉⠻⣿⣷⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣾⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⡿⠛⠻⢿⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠞⠛⠁⠀⠀⠈⠉⠉⠀⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠤⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠐⢈⡡⠄⠀⠀⠀⠀⠀⠂⠠⢄⡁⠒⠄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⢉⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡈⠢⡀⠀⠀⠀ ⠀⠀⡠⢃⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠈⢂⠀⠀ ⠀⡐⣀⣊⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣑⣀⢣⠀ ⢰⠀⢿⡟⠉⠉⠀⠀⠈⠉⠉⠙⢶⣶⣶⡶⠚⠉⠉⠉⠉⠉⠉⠉⢹⡿⠀⡆ ⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠏⠹⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⠁⠀⢸ ⡇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸ ⢃⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⢸ ⠘⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⠇ ⠀⠱⠀⠀⠀⠀⠀⠀⠙⠳⢒⡤⠤⠀⠀⠤⠤⣐⠾⠋⠀⠀⠀⠀⠀⠀⡞⠀ ⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀ ⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠒⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢼⣿⣿⣷⣦⣄⣀⡄⠀⣀⣤⣶⣿⣿⣿⠄⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢻⣿⡇⠀⠿⠟⠋⠉⠙⣿⣇⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⢠⣤⣿⣦⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣜⠁⠀⠈⠑⣦⣄⣀⡎⢹⠀⠀⣀⣠⣼⡏⠁⢀⣿⡆⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⠙⠛⣋⣽⣿⣿⣉⡙⠛⢋⣤⣶⣿⣽⡇⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠻⣟⣶⣶⣒⣫⡽⠞⠋⠉⠛⠯⣽⣿⣾⣿⡾⣟⠀⣦⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⢉⣥⣶⣿⣿⡧⠹⣷⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⡿⠁⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠘⣆⠀⠠⠈⠉⠀⠀⠀⠀⠉⠉⠑⠺⠿⣿⣉⣉⡇⣠⣷⣾⠿⢛⣡⣤⣴⡿⠀⠀⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⣦⡀⠀⠘⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣭⠽⠟⠛⠋⢉⣷⡿⠁⠀⢀⣾⠟⠳⣄⠀⠀ ⠀⠀⠀⠀⠘⣿⡟⠀⠀⠈⠻⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠏⠀⠀⠀⠀⠹⠀⠀⠈⠳⣄ ⠀⢀⡀⠀⠀⠸⣇⠀⠀⠀⠀⠈⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾⠋⠀⠀⠀⠀⠀⠀⢰⠀⣠⣶⡾⢿ ⠰⣼⣿⣲⣤⡀⣹⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⡷⠶⠶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣿⡤⠧⠏ ⠀⠙⠛⠛⣱⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀ ⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠛⢻⣷⠿⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢸⡋⠋⠽⠽⢷⣤⣀⠀⠀⠀⢠⡏⡀⠘⢤⡸⠿⠛⠋⠙⣶⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⠀⠀⠉⠀⠀⠀⠀⠀⢽⣷⡀⠀⠸⣝⠳⣄⠀⠀⠀⣀⣀⣠⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⡓⠦⠤⠤⠤⠒⠒⠚⣻⣿⣷⠀⠀⠈⠙⢎⡉⣉⣁⣀⣀⡤⠶⠿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡾⠟⠛⠛⠛⢃⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀ ⠀⠀⠀⠀⢠⠋⠟⠀⠀⣠⣤⠀⠀⠛⠋⣽⣍⠙⠛⠀⠀⠀⠀⠀⠀⠀⠘⠀ ⠀⢀⣀⣀⣀⣲⠀⠀⠸⣿⣿⠇⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠓⠀⠒⡆⠀⠘⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⢀⣠⣾⡿⠀⠀⠀⠀⡇ ⠀⠀⠀⠹⠀⠀⠆⠀⠀⠀⠐⢹⠀⠀⢠⣤⣤⣶⣾⣿⠟⠋⠀⠀⠀⠀⢠⠀ ⠀⠀⠀⠀⠁⠀⠈⢂⠀⠀⠰⡀⠑⠄⡈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⠂⠀ ⠀⠀⠀⠀⠀⠎⠉⠈⢭⠉⠉⠁⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠤⠐⠁⠀⠒⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⠛⠛⠛⠛⠛⠛⠳⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀ ⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀ ⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀ ⣿⠀⠀⠀⠴⢶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⣶⣶⣶⡶⠶⠀⡀⠀⣿⡀ ⣿⠀⠀⠀⠀⠘⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠇⠀⢀⠁⠀⢸⡇ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠆⠀⠀⣿⠁ ⢹⣇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⠊⠀⠀⢰⡟⠀ ⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢠⡿⠁⠀ ⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢀⣴⠟⠀⠀⠀ ⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣤⣀⣀⣤⣤⣴⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠉⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠟⠛⠛⠛⠛⠛⠃⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦⡘⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⡿⢿⠿⢿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡾⠀⠀⠀⠀⣠⣶⣶⣦⠀⠀⠀⠉⠉⠀⣴⣾⣷⣄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡇⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣠⡤⠤⠠⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⢸ ⠛⠓⠐⠒⠒⣲⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⡌ ⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠸⡄⠀⠀⠀⠀⠀⢸⠁⠀⡆⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁ ⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠛⣄⠀⠀⠀⠀⠘⣆⠀⠙⢤⣀⠀⠈⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣦⣀⣀⣀⣀⣈⡶⠀⠀⠈⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⣀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢀⣠⠔⠛⠒⠒⠢⠤⠖⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⣰⣦⣴⣶⣶⣶⣤⣤⠀⠀⠀⠀⠀⢀⡉⢳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠙⣆⠀⠀⠀ ⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⣻⣿⣿⣿⡛⠛⠲⣿⣀⠴⠶⠶⣶⣤⣤⣤⣿⡆⠀⢹⡆⠀⠀ ⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣅⠀⠀⠀⣶⣿⣿⣿⣿⣿⠀⢠⣿⣧⠀⠀⣴⣿⣿⣿⡇⣿⣧⠀⠀⢿⠀⠀ ⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⠬⠿⠿⠿⠿⠏⠐⣛⡥⠉⠓⠾⢿⣿⣿⣿⣧⣿⡿⠀⠀⢸⡆⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣨⠷⠛⣿⠇⠀⠀⢼⡇⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠋⠀⠀⠀⣸⡇⠀ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣄⣠⡀⣀⣠⣄⠀⠀⠀⢻⠇⠀ ⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠉⠉⢀⡴⠛⢯⣿⠛⠙⡿⠦⣭⣠⡀⠀⣼⠀⠀ ⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡞⠀⠀⣼⠁⠀⢰⣀⡄⠈⠻⣷⢼⡇⠀⠀ ⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠃⠀⢸⠇⠀⠀⣸⠏⠀⢀⣾⠁⠀⠹⡄⠀ ⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⣿⠀⠀⣴⡏⠀⠀⣾⣿⠷⣶⠾⣧⠀ ⠀⠀⠀⠀⠈⢿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠆⠀⠟⠀⠀⠿⠓⢠⡄⣿⠙⢷⣴⣶⡿⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠆⠀⠀⣼⡃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠘⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣷⣶⣶⣶⣶⣶⣦⣤⣼⣧⠀⠀⠀⠀⠀⠀⢀⣿⠀⣇⠀⠀⠀⢸⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠘⡄⠀⠀⠀⣀⣤⡿⠛⢧⣹⣦⣀⣴⣾⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⣀⣈⣉⣿⠆⠀⠀⠿⣍⣉⡩⠴⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠤⠤⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠐⢈⡠⠄⠀⠀⠀⠀⠀⠂⠀⠀⡁⠒⠄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⢉⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣌⡑⠠⡈⠢⡀⠀⠀⠀ ⠀⠀⡠⠃⡴⠃⣤⠶⠶⣤⣄⣀⠀⠀⡠⠛⠉⠉⠉⠉⠓⢄⠈⠢⠈⢂⠀⠀ ⠀⡰⠀⡎⠀⠀⠁⢀⡴⠦⡀⠀⠀⡜⠀⠀⢀⣀⠀⠀⠀⠀⢳⣀⠁⡀⢣⠀ ⢠⠁⠀⠀⠀⠀⠀⠸⣔⣴⠃⠀⠀⠁⠀⢰⠁⠀⡆⠀⠀⠀⠈⡿⣄⠐⠀⡆ ⡄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⢷⡄⠈⠢⠘⠀⠀⠀⠀⡼⠟⠙⣆⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢄⡀⠀⠀⢀⡠⠞⠁⠀⠀⢹⠀⢸ ⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣸⠀⡸ ⠘⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠇ ⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡜⠀ ⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀ ⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠊⠁⠀⠀⢹⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠒⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠀⠈⠉⠀⠐⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⠀⢠⣶⣤⣀⢀⠀⢀⣤⣾⡟⠦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠉⠉⠹⣿⡀⠛⠉⠙⢧⡀⠱⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠀⠀⠀⠐⠀⠒⣤⣀⣝⡀⣀⣠⡞⢉⣧⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠨⣦⣀⡈⣥⡺⠿⣬⣭⣾⣿⡟⡄⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⣛⢭⣿⣷⠸⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⠐⠒⠒⠒⠂⠤⢤⡒⡚⣻⣹⢿⣃⣠⠇⠀⢀⠀⠀ ⠀⠀⠀⣵⡄⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⢉⣽⠏⠀⠰⠋⠢⡀ ⠀⢠⠀⠘⡆⠀⠀⠑⠦⣄⣀⣀⣀⠀⠀⠀⣀⡠⠚⠁⠀⠀⠀⠀⡤⢼ ⠈⠻⠽⣢⠇⠀⠀⠀⠀⠀⠉⠉⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠻⠇⠉ ⠀⠀⠀⠁⠀⠀⠀⠀⣤⣤⣤⣄⠀⠀⠀⠀⢰⣿⣷⣶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⠀⠀⠀⠀⡘⢻⠽⢿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠁⠫⠑⠚⠓⣤⡀⠰⣧⡈⠒⠋⠉⢹⣶⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠩⢗⠀⠀⠒⣒⣿⠷⠀⠉⠫⠀⠨⠭⠽⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡐⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄⠀⠀⠀⠀ ⠸⠀⠀⠘⡀⠀⠀⠀⢀⠔⠁⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀ ⠀⢃⠀⠀⠡⠀⠀⠠⠁⠀⠀⠈⠙⣿⣶⣶⣦⠀⢠⣤⣤⣤⣤⣄⡀⠀⠣⠀ ⠀⠈⠆⠀⠀⠡⢀⠃⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠈⠁⣿⣿⡇⠉⠁⠀⠀⢃ ⠀⠀⠈⠄⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠸ ⠀⠀⠀⠈⢆⠀⠀⠐⡄⣀⡀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢂⠀⡠⠜⠁⣰⣤⠀⠀⠀⠛⠋⠛⠻⢷⡄⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠫⣀⣴⣾⣿⠛⠀⠈⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁ ⠀⠀⠀⠀⠀⠠⣾⣿⡿⠛⠉⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀ ⠀⠀⠀⠀⠀⠀⠸⠁⢤⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⢀⡠⠃⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠂⠉⠁⠒⠂⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠊⠁⠀⠐⣿⣿⡿⠿⠆⠀⠀⢠⣬⣷⣤⡄⠀⠀⠀⠀ ⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢄⠀⠀⠀ ⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢳⡈⢆⠀⠀ ⠀⠆⠀⠀⠀⠀⠀⢠⠔⠂⢩⣿⣿⣯⠉⣿⠚⢉⣽⣶⣺⡇⠘⡆⠀ ⢠⠀⠀⠀⠀⠀⠀⠀⠉⠒⠈⠻⠿⠟⠰⠗⠑⠺⠿⢿⣿⡇⠀⣷⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠹⠃⠀⣹⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠚⠋⢉⠝⢿⠟⠺⠽⣠⠀⡆⠀ ⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡇⢠⠇⠀⡷⠀⣸⠛⢅⠀ ⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⠀⣼⠁⢰⣿⠲⣺⠀ ⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⢹⠄⠉⣝⠀ ⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⡜⡇⠀⠘⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠘⡀⠀⣠⡼⠓⣽⣤⡴⢇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠃⠀⠈⢀⠈⠁

⠀⠀⢀⣼⠆⠀⠀⠀⠀⠀⠙⠒⠉⠀⠀⠀⠀⠀⠔⠊⠀⠈⠉⠒⠮⣵⣦⡀⠀⠁⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠂⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⢾⠏⣐⣻⡂⠘⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡚⢿⣾⣿⣆⠠⠤⠤⣈⠙⠂⢄⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⢦⣄⠙⠫⣷⡖⠛⠉⠑⠀⠀⠙⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⡤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠂ ⣿⣾⢿⣿⣦⡈⠙⢦⡀⠈⠂⠀⠀⠀⠈⢳⣄⣀⢀⣠⠤⠲⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠖⠒⠚⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠛⢷⠙⢯⣿⣷⣄⠙⢦⡀⠀⠀⠈⠉⢝⠀⠉⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⢉⣀⣀⣀⣀⡠⠤⠤⣤⣤⣤⣤⣴⣶⠒⠒⠒⠒⠒⠒⠒⠛⠲⣶⣴⠀ ⠸⡇⢀⣴⠿⠿⠝⢟⣦⡀⠙⢆⠀⠀⠀⠈⢳⡤⠔⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣯⡽⠏⠟⠋⢉⣠⠸⣆⣬⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀ ⡟⠛⠉⠴⣿⡿⠾⠚⠻⣿⡄⠈⢧⡀⠀⠀⠀⠳⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠋⠀⠀⠀⠀⢸⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸ ⣿⣦⡀⠘⢿⣀⡀⢶⠂⠈⣿⡆⠀⢳⣤⠀⠀⠀⠙⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⣿ ⣍⣻⣿⣶⡎⣹⣧⠈⠃⠀⠻⣿⡀⠀⣿⠢⣤⣄⠀⢀⣴⣦⣤⠀⠀⠀⠀⢠⣾⣿⣿⠋⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿ ⡿⣻⣏⣿⣿⠁⢀⣀⣦⡀⠐⠚⣧⠀⠘⡆⠈⠉⠉⠁⣉⣤⠤⠤⣀⠀⣰⣿⣿⡟⠁⠀⠀⠀⠀⠀⣀⣤⡤⣄⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣾⣿ ⡞⠉⣿⣿⣿⠀⠀⣹⠀⠀⠀⠈⢻⡀⠀⢷⡄⠀⠀⣾⠃⠀⠀⠀⣈⣿⣿⡿⠋⠀⣀⡤⠖⠛⡋⠉⠙⠻⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣸⠿⢿ ⡇⡰⠟⣿⢻⠀⠀⢩⣧⣠⠀⠀⣩⡇⠀⢸⡷⠀⡄⠈⠳⣤⢠⣾⣿⣿⣿⡥⣴⣯⣥⣤⣤⣴⣯⣤⣤⣤⣤⣿⣿⠿⣿⣿⠿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀ ⣷⣾⣿⡏⢸⠀⠀⡁⠟⠳⠀⢰⣿⡇⠀⢸⡇⠰⠻⢀⡤⢾⡾⠿⠭⠿⠗⠒⣿⡖⠛⠛⠛⠛⠉⠉⠉⠹⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⣽⠛⠀⢸⡷⢠⠇⠀⠀⠀⣸⣹⡥⠤⠚⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⣼⣇⣚⡤⠶⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣾⣷⡶⠶⢶⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡛⠉⠉⠁⠀⠀⠈⢻⣷⠉⢣⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣷⣤⡀⠀⠀⠀⢀⡀⠀⠀ ⠻⢿⣿⣝⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⣿⣄⡴⠃⠀⠀⠀⠀⣠⠤⢠⣾⣿⠁⣫⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸ ⠀⠘⢿⣿⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣖⣀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⣠⠔⠋⠁⢠⣿⢻⠋⣀⣿⣿⢿⣿⣿⣿⣷⡀⠀⠀⠀⢀⣾ ⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠧⠼⠖⠋⠉⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⡾⡧⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢺⠀⠀ ⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⡇⡇⢸⠀⣿⡿⣧⠁⣿⣿⣿⣿⣿⠀⠀⢸⢀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⢤⡄⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡇⣇⢸⠀⢿⣿⣿⡀⣿⣿⣿⣿⣿⠀⠀⠈⠉⢉ ⡇⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠒⠋⠉⠀⠀⠀⣀⣠⠗⠀⠀⠀⠐⢫⡭⠿⠞⠉⣿⣷⣿⣮⣴⡞⣿⣿⡇⢿⣿⣿⣿⣿⠀⠀⠀⠀⢸ ⣧⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠒⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⣯⣾⡇⣽⡛⠻⢿⣿⠀⢀⣠⣤⣾ ⡏⠀⠀⣀⣀⣀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣶⣶⣶⣶⣄⡀⠀⠀⠀⣄⣀⣀⣀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⣾⠃⠐⠚⠟⠛⣹⠿⣿⣿ ⣧⠀⢰⠛⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡍⢀⡿⠀⠀⠀⠀⠁⠀⠠⠊⡘ ⡟⠀⠘⠢⢌⣛⣛⣛⡟⠛⠛⠛⠋⠁⠀⠀⠤⢿⣿⣟⢛⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠛⢃⣘⣊⣁⣠⡄⠀⠀⠀⠀⠀⠈⡀⠀⣹⣿⣿⣿⣿⣿⣿⣟⣫⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⡶⠶⢺⣦⣤⣭⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡦⣶⣦⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⣀⣀⣨⣥⣶⣿⣿⣿⣿⣿⣿⡿⠟⠛⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀ ⠠⢤⣤⣴⣷⣿⣾⣿⣿⣧⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣶⣿⣿⣿⣦⣤⣤⣤⣶⣶⣴⣴⣴⣤⣦⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡰⢛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠤⠤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠛⠉⠉⠛⠓⠦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣛⣛⣿⡿⠂⠀⠀⠀⠈⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣓⣒⣒⣒⣒⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠶⠶⠶⢶⣒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣐⣒⣒⣛⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳ ⠀⠀⠀⠀⠀⠀⠀⢠⡯⣤⣥⣰⣶⣖⣞⣓⣛⣛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⠿⠿⠿⠿⠟⠳⠤⠿⠒⠶⠶⠀⠀⠠⢤⡤⠤⠄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⣤⣤⡄⡄⢀⣤⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⢸⡯⣭⠭⠭⠭⠉⠁⢠⡒⠛⠉⡍⢳⡆⠀⣠⡖⠻⡏⠙⣦⢼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡟⠁⢀⣿⣧⣞⡁⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⢠⣟⣻⣻⣿⣫⣭⣭⠽⠌⠛⠢⠤⠔⠋⠀⠀⡇⠓⠦⠥⠞⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠳⠶⠛⠁⠇⠀⠙⠂⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⣸⠛⠛⣷⠛⠲⠦⠤⠭⠿⠦⠄⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⢿⡭⢽⢿⡄⠀⠀⢉⣉⡉⠉⠉⠀⠀⠀⠀⢠⣼⡆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠈⢿⣙⣾⣓⣀⣐⣒⣒⣒⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⡶⡏⠉⣉⣑⣒⣒⣒⡂⠀⠀⠐⢶⠶⠆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠠⠴⠖⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣭⡉⠉⠵⠆⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠼⠿⠿⣿⣯⡥⠤⠴⠖⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⢿⠛⠛⠛⠉⠉⠀⠀⠀⢿⡈⠙⣍⠹⡦⣄⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣭⣿⣯⣿⣭⠥⠄⠀⠀⠀⠀⠀⠀⠾⢷⡀⠘⣦⣽⣬⣧⠀⡻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣶⣿⣾⣛⣻⣿⣿⣿⣿⡟⠻⣥⣀⡀⠀⠀⢀⣀⡴⠋⠹⣄⠸⣿⣿⣿⣷⠃⢈⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠾⣿⣭⠿⠿⣿⣿⣿⣿⣣⣿⠄⠀⠈⠉⣽⣽⣻⢷⡀⠀⢀⡾⠳⢬⣽⣯⡧⠴⠋⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡧⠄⠉⡉⡿⠿⣿⡿⠿⠿⠯⠭⠿⣦⣄⣀⣻⡌⠁⠸⣥⡞⠋⠀⠀⠀⠀⠀⠀⢀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⣹⠀⡂⠐⠶⠀⠤⢼⣏⣵⣈⣉⠉⠉⠀⠀⢹⣯⣀⢛⣠⡟⡇⠀⠀⠀⠀⠀⠀⠀⣼⣃⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣭⣯⣈⣉⣉⣉⠀⠀⠈⣿⣓⡂⠀⠀⠀⠀⠀⠀⡇⠉⡯⣗⠀⡇⠀⠀⠀⠀⠀⠀⢠⣷⠋⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣯⢭⡯⠭⠭⠭⣥⠤⠀⢰⣿⣟⠒⠒⠒⠀⠀⠀⠀⡇⠀⡯⡗⠀⡇⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿ ⣿⣿⣿⡿⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⣇⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⣸⣿⣿⣿ ⣿⣿⣿⣿⣴⣶⣶⡿⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠂⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⢀⡀⠀⠈⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣷⣦⡀⠈⠓⢄⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠋⠀⣴⠟⠁⢀⣤⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠟⠋⠉⠉⠉⠉⠛⠿⣦⡀⠀⠙⢤⠀⠈⢦⠀⠀⠀⠀⠀ ⠀⠀⢀⡼⠁⢠⠾⠁⠀⠸⡿⠋⠁⠈⠙⠛⠿⠿⠶⠗⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠻⣦⠀⠀⠱⡄⠀⢳⡀⠀⠀⠀ ⠀⢀⡾⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⣴⡶⣶⡄⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢧⠀⠀⠘⠀⠀⠱⡀⠀⠀ ⠀⡜⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⢸⠋⡀⣀⣿⠀⠀⠀⠀⡿⠀⠀⠀⠀⡴⠋⠈⢳⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠘⡄⠀⢳⠀⠀ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣥⣾⠏⠀⠀⠀⠀⣇⠀⠀⠀⢸⡁⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢸⣿⢻⣧⡀⠀⠀⠀⣇⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠘⢿⣦⡀⠀⠈⢷⣀⣰⠟⠀⠀⠀⠀⠀⠀⠀⣸⣿⠎⠙⣷⠀⠀⠀⢹⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠁⠀⠀⢹⣇⠀⠀⠈⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠁ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣼⠀ ⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠉⠉⠉⠙⠛⠛⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡇⠀ ⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⡾⠀⠀ ⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡼⠁⠀⠀ ⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣠⠖⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⠃⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠉⠉⠀⠀⠀⠀⠀⠈⠉⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢱⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀ ⠀⠈⣇⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠰⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀ ⠀⠀⠹⡄⠀⠀⠀⠀⢇⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣶⣤⣤⣤⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠱⡀⠀⠀ ⠀⠀⠀⢳⠀⠀⠀⠀⠈⣆⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠛⠛⠀⠀⠘⣿⠿⣿⣿⣿⣿⠿⣿⣿⡆⠀⠀⠀⠹⡀⠀ ⠀⠀⠀⠈⢇⠀⠀⠀⠀⠘⣆⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠘⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⡄ ⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠳⣄⠖⢲⡀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⢀⡴⠋⠀⠀⣱⣄⡀⠀⠀⠀⠀⠈⠛⠋⠉⠛⠻⠿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡴⠚⠁⠀⢀⣴⣿⣿⣿⣿⠒⠢⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣠⣶⣿⣿⣿⣿⡋⠁⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⣀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠒⠒⠒⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢳⠀⠀⣀⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠒⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠐⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⣄⣀⠀⠈⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⣀⡴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⢤⣀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠋⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠈⢦⠀⠀⠀⠀⠀ ⠀⠀⢀⡼⠁⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⢳⡀⠀⠀⠀ ⠀⢀⡞⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠱⡄⠀⠀ ⠀⡜⠁⣾⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠲⠶⢶⣦⣄⡀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠞⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣷⠀⢳⠀⠀ ⢸⠁⠘⠻⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⣇⠀ ⡏⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⠛⠛⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡟⠀⠀⠀⢻⠀ ⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠀ ⡃⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⢠⠁ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠭⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀ ⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀ ⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣗⡒⠤⠤⢄⣀⣀⣀⣀⣠⡤⠤⠖⣺⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀ ⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠤⠤⠤⠤⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀ ⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⣄⣀⣀⣀⡀⠀⣀⣀⣀⣠⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⠿⠟⠛⠛⠋⠉⠉⠉⠛⠛⠻⠿⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀ ⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀ ⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀ ⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢹⣿⡆ ⢸⣿⠃⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⡈⠀⠀⣿⣧ ⣾⣿⠀⠀⠀⠀⠀⠉⠛⢻⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⡇⠀⠀⢸⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠇⠀⠀⠀⡸⠀⠀⠀⢸⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢠⠃⠀⠀⠀⢸⣿ ⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣾⡿ ⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢰⣿⠇ ⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⢠⣿⡟⠀ ⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀ ⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣴⣶⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣤⣤⣤⣄⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠿⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢡⣿⣶⣽⣧⡀⠀⠀⠀⠀⣴⡾⣿⣿⣿⣷⣦⣉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣿⣿⣿⣿⡏⣧⠀⠀⠀⢰⡿⢰⣿⣿⣿⣿⣿⣿⣦⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢻⣿⣿⣿⡗⣿⠀⠀⠀⠸⣷⡸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢷⣌⠻⠿⣿⣷⠇⠀⠀⠀⠀⠙⢷⣿⣿⣿⣿⣿⣿⠟⠁⣠⡾⠃⠈⠑⢤⡀⠀⠀⠀⠀⢠⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠙⠛⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠽⠷⠶⠟⠋⡀⢀⠀⠀⠀⠹⡄⠀⠀⢠⣿⠇⠀ ⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢧⠱⡈⢧⠀⠀⠀⠇⠀⣠⣿⠋⠀⠀ ⠀⠀⢀⣿⠀⣼⡿⠿⠶⣦⣄⠘⢿⡶⠷⢦⣌⠛⠛⠛⠷⠶⠶⠶⠄⠀⠙⢄⠀⠀⠀⠀⠈⢧⠙⠆⠀⢀⣀⣴⡾⠟⠁⠀⠀⠀ ⢠⡞⢛⣿⣷⣿⣇⠀⠀⠀⠹⢷⣿⠁⠀⢨⡿⠛⠻⣶⡀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⢀⣀⣤⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀ ⢸⣄⣿⠋⠈⠙⠻⢦⣄⠀⠀⠀⠙⢷⣦⣟⡅⠀⠀⢹⡿⠶⠶⠶⢶⡶⠶⠶⠶⠶⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠛⢿⣧⡀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠉⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣼⡁⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣟⣻⣤⡀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠻⣿⠛⠒⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⣀⡴⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡾⠋⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡞⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠁⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡇⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠘⣇⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀ ⠀⠀⢹⡄⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣦⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀ ⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠈⢷⠀⠀ ⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠛⠋⢹⣿⣿⣿⣿⣿⡉⠛⠿⢿⠃⠀⠀⠀⠀⠈⣇⠀ ⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢻⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀ ⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢳⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇ ⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿ ⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠈⢷⣀⡾⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣶⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠛⠛⠿⠿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⢀⣠⠖⠋⠀⠀⠀⣰⣴⣿⣿⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠁⠀⠀⢀⣠⣾⣿⣿⣿⣿⡿⠏⠀⠉⠉⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣾⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣯⡼⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⣀⠴⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠯⠤⠤⠤⠤⠤⠴⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣠⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣔⢤⣀⠀⠀⠀⠀⠀⠘⣗⣦⠀⠈⠂⠡⡀⠰⡌⣆⠀⠢⡀⠀⠀⣼⡞⡴⢀⡞⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠑⠢⣤⡀⠀⠀⠈⢳⡳⢄⡀⠀⠘⠂⠙⡄⠀⠀⠀⠀⢠⡿⡜⣠⠋⠀⡤⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠶⠤⣨⣤⣀⣀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡰⠃⠠⠈⢀⣀⣸⣇⠀⠀⠀⢰⠐⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠓⠢⢦⣄⣀⠀⠀⠀⢀⡏⠀⣡⣤⠼⠻⠛⠉⠀⡹⡄⠀⠀⠘⡆⢳⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠷⢤⣸⡧⠞⠛⠁⠀⠀⠀⠀⠀⠡⣻⡀⠀⠀⣧⠈⣇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⣿⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢂⣠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⢁⡿⠤⠤⠴⠶⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣠⣧⠀⠸⡆⠀⢳⠀⠀⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣴⠖⢋⣠⠟⠁⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢀⡴⣋⣀⣸⡀⢸⢹⡀⢸⡇⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣟⣥⡶⣫⡇⠀⠀⢀⡞⠁⠀⠀⠀⢀⣠⠤⠖⠒⠒⠒⠚⠛⠲⣤⣀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⣼⠇⠀⠀⣠⡴⠋⠀⠉⠁⠈⣇⢘⠈⣧⠀⡇⠀⡆⠀⠀⠀⠀⠀⠀ ⠀⢰⣟⢹⡿⠛⢹⠁⠀⠀⡟⠀⠀⠀⣠⣘⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣵⣤⣄⠀⠀⠻⣇⠀⠀⠀⢸⡟⢀⣤⣾⠋⠀⠀⢀⣀⣤⣤⣿⢸⣿⡟⡄⠁⠀⡇⠀⣠⡴⠂⠀⠀ ⠀⢸⢹⠘⠀⢁⡏⢀⠀⠀⡇⠀⠀⠀⠈⢻⣿⠛⠛⢛⠛⠛⠿⠿⠿⣿⣶⣶⣶⣶⣮⠉⡛⠲⢦⣈⣧⠀⠀⣾⠶⢶⣿⣶⠶⠿⣿⣿⠛⢛⡟⠙⣰⡟⠁⢧⠀⠀⣧⠞⠋⠀⠀⠀⠀ ⠀⢸⢸⡀⢀⠟⣇⣿⡇⠁⣷⠀⠀⠀⠀⠀⠹⣷⡀⠈⢻⣆⠀⠐⠾⣿⠃⠀⣸⠏⣿⠀⠘⠒⠛⠉⠀⠀⠀⠙⠟⢹⠧⣅⡀⠰⡟⠋⣠⡞⠀⢠⣿⠁⠀⣾⢀⢀⣿⠁⠀⠀⠀⠀⠀ ⠀⠸⣆⠙⠘⣇⣿⢿⣧⢠⠏⢇⠀⠀⠀⠀⠀⠈⠻⢤⣀⠙⠷⣤⣀⣀⣤⠾⠃⠀⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠙⠻⠦⣤⡾⢋⣀⠴⠋⠿⠀⢠⣿⡆⢸⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢦⡀⢠⣥⣌⠻⣾⡀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠭⠭⠤⠔⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠂⠐⠂⠉⠀⠀⠀⠀⠀⣸⠙⡇⣼⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠲⣄⠈⠓⢷⡇⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢰⠇⠉⠓⠦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠁⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠿⣿⣿⠓⢦⠤⡀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⢸⡀⠹⣄⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠸⡇⠀⢘⢦⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠓⢸⡆⠀⠀⠀⠀⠈⣿⣷⠀⢳⠀⠸⡄⠑⣄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣷⠀⠀⠀⠀⠀⢹⣿⡀⠸⡄⠀⢻⡀⠀⠱⣄⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⢻⡆⠀⠀⠀⠀⠀⢹⣷⡀⠹⡄⠀⢧⠀⠀⠀⠙⠦⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣆⠀⢿⡀⠀⠀⠀⠀⠀⢻⣷⡀⠙⣦⠘⢧⠀⠀⠀⠀⠈⠓⢯⣢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠹⣆⠈⣧⠀⠀⠀⠀⠀⠀⢻⣷⡄⠈⢳⣌⠆⠀⠀⠀⠀⠀⠀⠉⠓⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠞⠁⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣌⠳⠼⣄⠘⣆⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⢀⡞⠸⡇⠀⠀⡿⢾⠶⠶⠾⣿⢿⠂⠀⠀⠀⠀⠀⠀⠀ ⠙⢷⡀⠹⡄⠙⣆⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣦⣀⡀⠀⢀⣰⣿⡇⠀⠀⠀⡼⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⡀⠙⣦⢻⣶⠸⣦⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⢹⣿⣿⣿⣿⡇⠀⢀⡾⠁⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣦⠈⠫⣿⣇⠹⣧⡀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠀⠀⠑⢤⠀⠀⠀⠀⠀⠀⠀⢸⢡⠇⠀⣾⣿⣿⣿⣿⣷⠀⠜⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢷⡄⠘⣿⡆⢻⣷⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆⠀⠀⠀⠑⢤⠀⠀⠀⠀⠀⠀⣾⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣄⠈⢿⡈⢧⣷⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣄⠀⠀⠀⠑⢆⠀⠀⠀⢰⠃⠀⢀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⢧⡀⢳⡘⡏⢳⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠙⢦⣠⠇⠀⠀⣼⣿⣿⣿⣿⡟⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠇⠱⡄⠹⡽⣆⣷⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣤⣀⡀⢀⡏⠀⠀⢠⣿⣿⣿⣿⠏⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠐⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⠀⡀⠀⠀⠒⠽⣧⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢁⡏⠁⠀⠀⠀⠀⠈⠙⡄⠀⢀⡴⠚⠉⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣄⠀⣠⣤⠀⠀⡜⠁⢘⣦⣤⣿⣀⣀⣀⣀⡀⠀⠀⠀⠘⣶⠋⢀⣀⠄⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣷⡶⣹⠳⡇⠀⣸⠁⢀⣿⣩⡿⠄⠀⢸⣯⡙⢿⡉⠉⠐⡾⢧⣔⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣾⣿⡇⠐⠧⣤⡇⠀⠸⣿⣿⢷⡀⢀⡞⠉⠹⡌⠁⠀⠀⢻⣏⡁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠛⡟⠀⠀⠘⡇⠀⢠⣿⣧⣤⡅⣼⣧⡄⠀⣹⡤⠀⠀⠀⠀⠈⠹⡖⠤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣧⣴⠁⣸⡿⠿⠷⠽⣿⣿⠾⠃⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⢰⣿⠉⣿⡟⠁⠀⠀⠀⠀⠀⠈⠁⢺⠟⠃⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⠔⢻⣀⠰⠛⠷⣿⣿⣎⠙⢦⡀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢈⠀⠄⠀⠐⠀ ⠀⠀⠀⠀⡟⢳⡀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⢹⣿⣍⣻⠦⠽⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠑⣶⠀⠤⠖⠋⠀⠀⠀⣀⠄ ⠀⠀⠀⡰⣇⠈⠻⡄⠀⠀⠀⠀⠀⠈⣦⣴⣊⣉⠈⠛⢿⣦⢄⠀⠀⠓⠂⠐⠂⠀⣀⡠⠖⠉⠀⠀⠀⡰⠃⠀⠀⠀⢀⣠⠄⠀⠼⠶ ⠀⠀⡼⠁⢸⠀⠀⢹⡀⠀⠀⢠⣔⣋⣁⣀⡀⠀⠀⠀⠀⠈⠙⠒⠦⠶⠤⠖⠒⠋⠁⠀⠀⠀⠀⠀⢰⠁⠀⠀⣀⣤⠟⠁⠀⠀⠀⠀ ⠀⢀⡇⠀⡇⠀⠀⠀⡇⠀⡴⠋⠀⠀⠀⠉⠛⠻⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡠⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠘⣇⠸⠀⠀⠀⢰⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⣶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠟⠀⠀⠀⣠⣇⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡏⠀⠀⠀⢀⡝⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⣀⣀⣀⡤⢚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⣄⣀⣤⡾⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠉⠉⠲⢄⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣶⣤⣤⣀⣀⣀⣀⣠⡤⠔⠊⠉⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠟⠉⣿⣄⣄⣀⣠⠴⠛⠓⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠚⠋⠉⠃⠀⠀⠀⠀⠀⠈⠓⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠤⠤⠤⠤⠤⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣤⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢾⡇⠉⠛⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⡶⠦⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢧⡀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢀⣠⣤⠶⠞⠋⠉⠛⠊⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣄⠀⠀⣻⡀⠀⠀⠀⡾⢋⡭⠤⠀⢀⣠⣴⣶⣶⣶⡶⣶⣶⣤⣤⣄⣀⢤⣀⠀⠀⠘⠻⣗⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣆⢣⣬⣧⠀⠀⠘⣿⠁⠀⠂⢠⣾⣿⡇⣿⣏⣿⣱⣿⣿⣿⣿⣿⣿⣷⣦⣙⢦⡀⠀⠀⠙⣮⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡿⣿⣿⣇⠀⠀⠙⣆⠀⠀⣿⣿⣸⣧⣸⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⢿⣿⣷⣝⣆⠀⠀⠸⣧⡈⢢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡽⡿⢻⣆⠀⠀⠈⠻⢿⣿⣾⣿⣿⠟⠋⢀⣠⢾⣿⣿⣻⠷⢼⣧⣿⣿⢿⣿⣟⠇⠀⠀⠙⣷⢰⡷⡄⠀⠀⠀ ⣤⣀⣀⠀⠀⠀⠈⣧⢳⡽⣛⣆⠀⠀⠀⠀⠀⢀⣤⣠⣖⣶⢯⣀⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣆⠀⠀⣾⣿⡇⣿⣿⡄⠀⠀ ⣊⡟⢻⣽⣿⣻⣶⣾⣎⣮⠟⣪⡣⡀⠀⢀⡤⢿⣿⣿⣿⣿⣴⣾⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣶⣄⡇⢻⣇⢸⣿⣿⡄⠀ ⠻⢷⣞⣻⣴⣯⣞⣩⢿⣿⣾⢋⢽⣿⢶⣯⣖⣺⣿⣛⣅⠻⣿⣷⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣷⠀⢻⢸⣿⣿⣇⠀ ⠀⠀⠀⠉⠉⠛⠛⠿⣿⣿⣾⣧⠃⡼⣳⣎⣙⡿⠉⣻⣯⣾⣻⣍⣿⣟⣾⣝⢿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣮⡣⢀⣿⣿⣿⡿⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣉⣀⣾⣁⣀⣹⠿⣷⣿⣿⣿⢯⡉⢿⡇⢿⣿⡏⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀ ⡳⣄⠀⠀⠀⠀⠀⠀⢀⣼⣛⣯⡿⠿⠿⢿⣿⡻⢿⡿⣶⠏⣉⢼⣯⣽⣾⣿⣿⣾⣿⢽⣿⠟⠈⠙⠲⢿⣿⣟⣻⣿⣿⣿⠟⠀⠀ ⣳⣾⣷⣄⠀⠀⠀⣀⣼⣿⡟⣡⣾⣿⣿⣧⣌⡿⢃⡖⢁⣼⣵⣾⣿⣿⣿⣿⣿⣿⢿⡿⠁⠀⠀⠀⠀⠀⠈⠻⣿⡿⣿⠏⠀⠀⠀ ⣿⣿⢛⡿⣳⣄⣸⣿⣚⣿⡿⢿⣿⣶⣽⠟⢫⣤⠏⣴⣿⣿⣿⣿⣿⣿⣵⣿⣿⣛⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀ ⢷⣿⡏⡴⢉⠏⣿⣿⢻⣿⡛⢯⣿⠋⠁⢀⠟⠁⣼⣿⣿⣿⣿⡿⣿⣿⣟⣻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣻⣷⣾⢴⣷⠇⣼⣸⣧⣠⣾⠷⡚⠁⠀⠀⣰⢉⣿⣿⠿⠽⠿⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⣿⣿⣿⡟⠿⣿⡻⢿⣿⢿⣄⠀⠀⢀⠀⠀⠉⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠻⢿⡏⣿⡶⣀⣻⣿⡿⠿⠿⠝⢦⡘⢱⡀⠀⢻⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢴⡋⣠⣤⡈⠋⣁⣠⣴⠶⠶⠶⣄⣱⣏⡝⢦⠈⢦⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢨⡗⢿⡿⠀⠾⠋⣀⣤⡤⣤⣤⣬⣍⠹⣄⠀⣳⡈⢦⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣇⠀⣴⣶⡀⠸⠟⠹⠿⠛⠉⠉⠥⠀⠈⠢⣬⣧⡈⢆⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⠙⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡀⠐⣌⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠀⠈⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣌⠢⠙⠲⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠈⠙⠢⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢶⣦⣀⠈⠉⣉⠉⠋⠉⠛⣛⡿⣿⣶⣦⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠻⠿⣍⡛⠛⠉⠁⠀⠈⠙⠻⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⣶⢿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀ text here ⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀

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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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