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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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