⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡴⣶⡶⣶⢶⣶⢶⣤⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⣿⣽⣻⢾⣳⡿⣯⢿⣽⢿⣞⣿⣽⢾⣳⣟⡿⣟⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣻⢷⣻⡷⣯⣟⡿⣽⣻⣽⢿⣽⣻⣾⣻⢾⣟⣯⡿⣽⣟⡷⣯⡿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣶⣿⣻⢾⣽⣟⣯⣿⣽⢾⣟⡿⣽⢯⣿⣞⣯⡷⣟⣿⢾⡯⠛⠋⠚⠻⣽⣻⢷⣯⣟⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣻⢾⣽⣟⡷⣯⣷⣟⡾⣿⣽⣻⢯⣿⣳⣯⡿⣽⢿⣽⡛⠀⠀⠀⠀⠀⢸⣟⡿⣾⣽⢾⣻⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣟⣾⡽⣟⣷⣯⢿⣻⡾⣽⣻⢷⡏⠉⠉⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⣸⣯⢿⣳⣯⣿⣻⢾⡿⡄⠀⠀⠀ ⠀⠀⢠⣿⣳⢿⣞⡿⣯⣷⣻⣟⡷⣿⠟⠉⠹⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣦⣶⣾⣻⡽⣟⣯⣷⢯⣟⣯⡿⣿⣆⠀⠀ ⠀⢠⡿⣯⣟⣯⡿⣽⣷⣻⢷⣻⠟⠁⠀⠀⠀⠹⡿⣤⣶⢶⡿⣿⢶⡶⣤⣀⠀⠀⠀⠀⠈⠻⣽⢿⣽⢾⣟⣯⡿⣽⣷⣻⡄⠀ ⠀⣾⣟⣷⣻⣽⣻⣽⡾⣯⣿⠃⠀⠀⠀⠀⣠⣾⣻⣽⡾⣿⡽⣯⣟⣿⡽⣯⣷⣄⠀⠀⠀⠀⠙⣿⢾⣻⣽⣾⣻⢷⣯⡷⣷⠀ ⢰⣟⣾⡽⣯⣷⣟⡷⣿⣽⡆⠀⠀⠀⠀⣼⢯⣷⣟⡷⣿⣳⡿⣯⣟⣾⢿⣽⡾⣽⣧⠀⠀⠀⠀⢸⡿⣯⣷⢯⣟⡿⣾⣽⣟⡂ ⢸⣯⡷⣿⣻⠎⠁⠀⠀⠉⢿⣄⠀⠀⢸⣟⣯⣷⢿⣽⡷⣿⡽⣷⣻⣽⣟⣾⣽⡷⣯⡇⠀⠀⠀⠀⣿⢷⣯⡿⣯⢿⣳⡿⣾⠇ ⢸⡷⣟⣯⡗⠀⠀⠀⠀⠀⢈⡷⠀⠀⣿⢯⣷⣻⣟⣾⣽⢷⣟⣯⡿⣾⣽⢾⣳⡿⣯⢿⠞⡷⠿⠶⣿⣻⣾⡽⣟⣿⣽⣻⣽⡇ ⢸⣟⣯⡿⣽⣆⡀⠀⠀⣠⣾⠋⠀⠀⢸⣟⣷⣯⢿⡾⣽⢿⣞⣯⣿⣳⣯⡿⣯⢿⣽⡇⠀⠀⠀⠀⣿⢷⣯⣟⡿⣞⣷⣟⡷⡇ ⠸⣯⣷⢿⣯⣟⣿⣻⣟⣯⣇⠀⠀⠀⠀⢻⡾⣽⣯⢿⣻⣯⣟⣷⢯⣷⢿⣽⣻⣯⡗⠀⠀⠀⠀⣸⣟⡿⣾⣽⣻⢯⣷⣟⡿⠅ ⠀⢿⣞⡿⣾⣽⢾⣷⣻⣽⣾⣄⠀⠀⠀⠀⠙⢟⣾⢿⣽⡾⣽⡾⣿⣽⣻⡾⡷⠋⠀⠀⠀⠀⣰⣯⢿⣽⡷⣯⣟⣿⣳⣯⡿⠀ ⠀⠘⣯⢿⣳⣯⣿⣞⣯⡷⣟⣾⢦⡀⠀⠀⠀⣰⣯⠛⠾⠻⢽⡟⠷⠯⠓⠉⠀⠀⠀⠀⢀⣴⣟⣾⣟⡷⣟⣯⡿⣾⣽⣳⠁⠀ ⠀⠀⠘⣿⢯⣷⣟⣾⢯⣟⡿⣽⣻⢿⣦⣀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠿⢻⣟⣾⣽⢾⣻⣟⡷⣿⣽⢾⠃⠀⠀ ⠀⠀⠀⠘⢿⣳⢿⣾⣻⢯⣿⣻⣽⢿⡾⣽⡾⣧⣄⣀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⢹⡷⣯⣿⣻⢾⡿⣽⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣟⣾⢯⣿⣳⣯⣟⣯⡿⣯⣟⣷⣻⢯⣿⣟⡿⣟⡿⣟⣿⢦⠀⠀⠀⠀⠀⣸⢿⣽⣞⡿⣯⢿⠳⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠯⣿⣳⣟⡷⣯⡿⣽⣷⣻⣽⢯⣿⣳⣯⢿⣻⣽⢿⣽⣻⢷⣤⣤⣤⣴⣟⡿⣾⣽⣻⡽⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢞⣿⣽⣻⢷⣯⣟⣾⣟⡷⣿⣽⣻⢯⣟⡿⣞⣿⣻⡾⣽⣳⡿⣞⣿⣳⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⣻⣾⣽⣳⣯⢿⡷⣯⣟⡿⣽⣻⣯⡷⣿⡽⣿⣽⡻⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠙⠯⠿⠽⠾⠟⠿⠳⠯⠟⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀