⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⢶⣿⣻⣟⣿⣻⣟⣿⣶⣶⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢾⣻⣟⣯⣷⢯⣿⣞⣷⣻⣞⣷⣻⣞⡷⣯⡿⣽⢯⣟⡿⣷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣻⡽⣯⣷⢯⣷⢯⣿⢾⣽⣞⣯⣟⣾⣽⢾⣻⢷⣟⣯⡿⣽⣻⣽⢯⡿⣽⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⡷⣯⡷⣟⡿⣞⡿⣽⣻⢾⣻⡾⣽⡾⣽⡾⣽⣻⡽⣟⣾⣽⣻⡽⣷⢯⣟⡿⣽⣻⣟⡷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⡾⣟⡷⣯⣟⡷⣟⡿⣽⣻⣽⢿⣽⣻⢷⣟⣯⡿⠓⠛⢯⣿⣽⣻⢷⣯⢷⣟⣯⡿⣯⣟⣯⣷⢯⣟⣯⣷⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣴⡿⣽⣻⣽⢷⣻⣽⢿⣽⣻⢷⣯⣿⣞⣯⡿⣾⣳⠇⠀⠀⣸⢷⡋⠀⠈⢹⣟⣾⣽⣻⢷⣯⢷⣯⣟⣯⡷⣯⣟⣧⠀⠀⠀⠀
⠀⠀⢀⣾⢿⣽⣻⢷⣯⣟⡿⣞⡿⣾⣽⣻⢾⠀⠀⠈⠉⠓⠻⠀⠀⢀⣿⣻⠁⠀⠀⣾⣻⣞⣷⣻⣟⣾⢯⣷⢯⣷⢿⣽⢾⣯⣷⡀⠀⠀
⠀⠀⣾⣽⣻⢾⣽⣻⢾⣽⣻⡽⣟⣷⢯⣟⣧⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠷⣯⣟⡾⣷⣻⢾⣻⣽⣻⢾⣟⡾⣟⣾⣳⣷⠀⠀
⠀⣸⣟⣾⡽⣯⡷⣟⣯⡷⣿⡽⣟⣾⢿⡽⣞⣷⢯⡷⠀⠀⠀⠀⠠⣤⣀⣀⠀⠀⠀⠀⠀⠉⠻⣷⣻⢿⣽⣞⣯⡿⣞⡿⣯⡷⣟⣾⣇⠀
⢀⣿⣽⣞⣿⣳⢿⣯⢷⣿⣳⢿⣯⣟⣯⢿⣻⢾⣻⠃⠀⠀⠀⠀⣸⡿⣽⢯⣷⣦⡀⠀⠀⠀⠀⠘⣯⢿⡾⣽⣞⡿⣽⣻⢷⣻⣯⢷⣻⡄
⢸⣟⣾⡽⣞⣯⡿⣞⣿⢾⣽⣻⢾⣽⢾⣻⢯⣟⡟⠀⠀⠀⠀⢀⣿⡽⣯⢿⣞⡷⡇⠀⠀⠀⠀⠀⣟⣯⡿⣽⣾⣻⣽⢯⣿⣳⣯⢿⣯⡇
⣿⣻⢾⣽⣟⡷⣟⣯⣟⡿⣞⣯⡿⣾⣻⢯⣟⣯⠃⠀⠀⠀⠀⠈⠑⠛⠛⠛⠚⠋⠀⠀⠀⠀⠀⣰⣟⡷⣟⡿⣞⣷⢯⣿⣞⣷⣻⣟⣾⣽
⣿⣽⣻⢾⣽⣻⡽⣷⢯⣟⣯⡷⣿⣳⢿⣯⢿⡝⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⣽⣾⣻⡽⣿⡽⣾⣻⢷⣻⣞⡷⣟⣾⣽
⣿⢾⡽⣟⣾⣽⣻⣽⢯⣟⡷⣟⣷⣟⡿⣞⣯⠇⠀⠀⠀⠀⣸⣟⣿⣻⣶⢦⣄⠀⠀⠀⠀⠈⠻⡷⣯⡷⣿⣳⡿⣽⢯⣿⡽⣾⣻⢯⣷⢿
⢸⣟⡿⣽⣳⣯⢷⣻⣯⢿⡽⣟⣾⡽⠻⣽⡻⠀⠀⠀⠀⢀⣿⣞⡷⣟⣾⢿⡽⣧⠀⠀⠀⠀⠀⢹⡷⣟⣷⢿⡽⣯⡿⣾⡽⣷⣻⣟⣾⡇
⠈⣿⣽⣻⢷⣯⢿⣻⣞⡿⣽⣻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⢯⣟⣯⣟⣯⡿⠃⠀⠀⠀⠀⠀⣸⢿⣽⢾⣯⢿⣳⣿⣳⡿⣽⣳⢿⣞⠃
⠀⢹⣷⣻⣟⡾⣟⣷⢯⣟⣯⣷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⢠⣿⣻⢾⣟⡾⣿⡽⣞⣷⣟⣯⣟⡿⡞⠀
⠀⠀⢿⣳⣯⣟⡿⣞⣿⣽⣳⣟⣾⣳⣯⢿⣽⠇⠀⠀⣰⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣟⣷⣻⣟⡾⣟⡷⣟⣯⡷⣯⣷⣻⡽⠀⠀
⠀⠀⠈⢿⢾⣽⣻⣽⢾⣳⡿⣞⣷⣟⡾⣟⡾⠀⠀⢀⣿⣳⠃⠀⠀⣾⣟⣿⣻⣟⣿⣻⢯⣷⣻⢾⣳⣯⣟⡿⣽⣻⢷⣻⣽⡾⡽⠁⠀⠀
⠀⠀⠀⠈⢻⡾⣽⣾⣻⣽⣻⣽⡾⣽⣻⡽⣷⢦⣤⣼⢷⡛⠀⠀⢨⣷⣟⣾⣳⣟⣾⣽⣻⢷⣻⢿⣽⢾⣽⣻⣽⢯⣟⣯⡷⡟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠙⢷⢯⣷⢯⣷⢯⣿⣽⣳⡿⣯⢿⡾⣽⣻⣟⣿⣳⣟⣷⣻⢾⣽⢾⣻⢾⣽⣻⢯⣿⣞⣯⡷⣿⡽⣯⣟⡾⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢯⡿⣞⣿⣳⣯⢷⡿⣽⣯⢿⣽⣳⢿⣞⣷⣻⡾⣽⣟⡾⣿⣽⣻⣞⣯⡿⣾⣽⣳⢿⣳⡿⡽⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⣷⣟⡾⣿⡽⣷⢯⣿⣞⣯⡿⣾⣽⣳⢿⣻⣞⣿⣳⣯⢷⣻⢷⣻⢷⣯⣟⣯⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣻⣽⣟⣾⡽⣞⣿⣳⣯⣟⣯⡷⣿⣞⡷⣯⡿⣯⣟⣯⡿⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠓⠿⠯⢷⣟⣾⡽⣞⣿⣳⠯⠿⠳⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀