Couple Kissing Emojis & Text

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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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