⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⢶⣿⣻⣟⣿⣻⣟⣿⣶⣶⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢾⣻⣟⣯⣷⢯⣿⣞⣷⣻⣞⣷⣻⣞⡷⣯⡿⣽⢯⣟⡿⣷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣻⡽⣯⣷⢯⣷⢯⣿⢾⣽⣞⣯⣟⣾⣽⢾⣻⢷⣟⣯⡿⣽⣻⣽⢯⡿⣽⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⡷⣯⡷⣟⡿⣞⡿⣽⣻⢾⣻⡾⣽⡾⣽⡾⣽⣻⡽⣟⣾⣽⣻⡽⣷⢯⣟⡿⣽⣻⣟⡷⣄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⡾⣟⡷⣯⣟⡷⣟⡿⣽⣻⣽⢿⣽⣻⢷⣟⣯⡿⠓⠛⢯⣿⣽⣻⢷⣯⢷⣟⣯⡿⣯⣟⣯⣷⢯⣟⣯⣷⡄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣴⡿⣽⣻⣽⢷⣻⣽⢿⣽⣻⢷⣯⣿⣞⣯⡿⣾⣳⠇⠀⠀⣸⢷⡋⠀⠈⢹⣟⣾⣽⣻⢷⣯⢷⣯⣟⣯⡷⣯⣟⣧⠀⠀⠀⠀

⠀⠀⢀⣾⢿⣽⣻⢷⣯⣟⡿⣞⡿⣾⣽⣻⢾⠀⠀⠈⠉⠓⠻⠀⠀⢀⣿⣻⠁⠀⠀⣾⣻⣞⣷⣻⣟⣾⢯⣷⢯⣷⢿⣽⢾⣯⣷⡀⠀⠀

⠀⠀⣾⣽⣻⢾⣽⣻⢾⣽⣻⡽⣟⣷⢯⣟⣧⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠷⣯⣟⡾⣷⣻⢾⣻⣽⣻⢾⣟⡾⣟⣾⣳⣷⠀⠀

⠀⣸⣟⣾⡽⣯⡷⣟⣯⡷⣿⡽⣟⣾⢿⡽⣞⣷⢯⡷⠀⠀⠀⠀⠠⣤⣀⣀⠀⠀⠀⠀⠀⠉⠻⣷⣻⢿⣽⣞⣯⡿⣞⡿⣯⡷⣟⣾⣇⠀

⢀⣿⣽⣞⣿⣳⢿⣯⢷⣿⣳⢿⣯⣟⣯⢿⣻⢾⣻⠃⠀⠀⠀⠀⣸⡿⣽⢯⣷⣦⡀⠀⠀⠀⠀⠘⣯⢿⡾⣽⣞⡿⣽⣻⢷⣻⣯⢷⣻⡄

⢸⣟⣾⡽⣞⣯⡿⣞⣿⢾⣽⣻⢾⣽⢾⣻⢯⣟⡟⠀⠀⠀⠀⢀⣿⡽⣯⢿⣞⡷⡇⠀⠀⠀⠀⠀⣟⣯⡿⣽⣾⣻⣽⢯⣿⣳⣯⢿⣯⡇

⣿⣻⢾⣽⣟⡷⣟⣯⣟⡿⣞⣯⡿⣾⣻⢯⣟⣯⠃⠀⠀⠀⠀⠈⠑⠛⠛⠛⠚⠋⠀⠀⠀⠀⠀⣰⣟⡷⣟⡿⣞⣷⢯⣿⣞⣷⣻⣟⣾⣽

⣿⣽⣻⢾⣽⣻⡽⣷⢯⣟⣯⡷⣿⣳⢿⣯⢿⡝⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⣽⣾⣻⡽⣿⡽⣾⣻⢷⣻⣞⡷⣟⣾⣽

⣿⢾⡽⣟⣾⣽⣻⣽⢯⣟⡷⣟⣷⣟⡿⣞⣯⠇⠀⠀⠀⠀⣸⣟⣿⣻⣶⢦⣄⠀⠀⠀⠀⠈⠻⡷⣯⡷⣿⣳⡿⣽⢯⣿⡽⣾⣻⢯⣷⢿

⢸⣟⡿⣽⣳⣯⢷⣻⣯⢿⡽⣟⣾⡽⠻⣽⡻⠀⠀⠀⠀⢀⣿⣞⡷⣟⣾⢿⡽⣧⠀⠀⠀⠀⠀⢹⡷⣟⣷⢿⡽⣯⡿⣾⡽⣷⣻⣟⣾⡇

⠈⣿⣽⣻⢷⣯⢿⣻⣞⡿⣽⣻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⢯⣟⣯⣟⣯⡿⠃⠀⠀⠀⠀⠀⣸⢿⣽⢾⣯⢿⣳⣿⣳⡿⣽⣳⢿⣞⠃

⠀⢹⣷⣻⣟⡾⣟⣷⢯⣟⣯⣷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⢠⣿⣻⢾⣟⡾⣿⡽⣞⣷⣟⣯⣟⡿⡞⠀

⠀⠀⢿⣳⣯⣟⡿⣞⣿⣽⣳⣟⣾⣳⣯⢿⣽⠇⠀⠀⣰⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣟⣷⣻⣟⡾⣟⡷⣟⣯⡷⣯⣷⣻⡽⠀⠀

⠀⠀⠈⢿⢾⣽⣻⣽⢾⣳⡿⣞⣷⣟⡾⣟⡾⠀⠀⢀⣿⣳⠃⠀⠀⣾⣟⣿⣻⣟⣿⣻⢯⣷⣻⢾⣳⣯⣟⡿⣽⣻⢷⣻⣽⡾⡽⠁⠀⠀

⠀⠀⠀⠈⢻⡾⣽⣾⣻⣽⣻⣽⡾⣽⣻⡽⣷⢦⣤⣼⢷⡛⠀⠀⢨⣷⣟⣾⣳⣟⣾⣽⣻⢷⣻⢿⣽⢾⣽⣻⣽⢯⣟⣯⡷⡟⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠙⢷⢯⣷⢯⣷⢯⣿⣽⣳⡿⣯⢿⡾⣽⣻⣟⣿⣳⣟⣷⣻⢾⣽⢾⣻⢾⣽⣻⢯⣿⣞⣯⡷⣿⡽⣯⣟⡾⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠙⢯⡿⣞⣿⣳⣯⢷⡿⣽⣯⢿⣽⣳⢿⣞⣷⣻⡾⣽⣟⡾⣿⣽⣻⣞⣯⡿⣾⣽⣳⢿⣳⡿⡽⠊⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⣷⣟⡾⣿⡽⣷⢯⣿⣞⣯⡿⣾⣽⣳⢿⣻⣞⣿⣳⣯⢷⣻⢷⣻⢷⣯⣟⣯⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣻⣽⣟⣾⡽⣞⣿⣳⣯⣟⣯⡷⣿⣞⡷⣯⡿⣯⣟⣯⡿⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠓⠿⠯⢷⣟⣾⡽⣞⣿⣳⠯⠿⠳⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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