⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣯⣟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣻⣽⣾⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡷⣯⣷⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⡷⣯⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣟⣷⢯⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡾⣯⡿⣯⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣯⣟⣷⢿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣳⡿⣽⣻⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣳⣿⣻⢷⠃⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣟⣧⣿⣻⣧⣼⣿⢿⣟⡿⣿⢧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⢯⣷⢯⣷⣟⡷⣯⣿⢾⣻⠽⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡿⣯⣟⣯⣷⢿⣽⣟⡾⠋⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣳⡿⣽⡾⣯⡷⠋⠀⠀⢀⣠⣶⢿⣻⣯⢿⣽⢯⣟⣷⡶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣳⡿⣽⣯⣟⡗⠀⠀⠀⣰⡿⣯⣟⣿⣳⢿⣻⡾⣟⡿⣾⣽⣟⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣽⣻⢷⣻⣾⠀⠀⠀⢰⣿⡽⣷⣻⠞⠉⠁⠀⠀⠉⠙⢷⣟⡾⣟⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣯⣟⡿⣽⡇⠀⠀⠀⣿⢯⣿⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⡿⣽⣟⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣞⣿⣻⣶⠀⠀⠀⢿⣯⣷⣻⣆⡀⠀⠀⢀⣴⡇⠀⠀⠀⣿⢿⣽⣾⣻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣞⣷⢿⡄⠀⠀⠘⢷⣯⡷⣿⣻⣟⡿⣿⢯⠇⠀⠀⠀⣿⣯⣷⢯⡗⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣾⣻⢿⣄⠀⠀⠀⠙⠹⡷⣟⣾⠿⠽⠋⠀⠀⢀⣼⡿⣾⣽⣻⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢳⣿⣻⢾⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⡽⣷⢯⢃⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⢀⣤⣶⢶⣶⣻⣽⣟⣯⢿⡽⣿⢶⣶⣦⣤⣴⣶⢾⣟⡿⣽⣯⢿⣯⢿⣻⢯⣟⣿⣻⣷⣤⡀⠀ ⠸⣿⣟⡾⣟⣷⣯⣷⣻⣽⣟⡿⣽⣟⣾⣳⣯⡷⣟⣿⢾⣻⣟⣾⢿⣽⣻⢯⣿⣻⣾⣽⢾⣽⣻⠆ ⠀⠈⠙⠻⠟⠾⣳⣯⣟⣾⣽⣻⣟⠾⠽⠗⠋⠛⠿⢾⣟⡿⣞⣯⣿⣞⡿⣯⣷⣟⣾⡽⡯⠗⠁⠀ ⠀⠀⠀⠀⢀⣼⣿⣳⡿⡽⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡽⣾⡽⣷⡄⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣟⡾⣷⠋⠀⠀⠀⣠⣶⢿⣻⣟⡿⣦⣄⠀⠀⠈⢻⡷⣟⣯⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣟⡾⣟⠃⠀⠀⢠⣾⣟⣯⣿⣻⢾⡿⣽⣻⡆⠀⠀⠀⣿⢿⣽⣞⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⢷⣯⢿⡟⠀⠀⠀⣾⡷⣯⣟⠎⠁⠀⠀⠈⠻⡅⠀⠀⠀⣿⢿⡾⣽⠯⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣯⢿⣾⣻⡇⠀⠀⠀⣿⣽⢯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣯⣟⡿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡾⣟⣷⣯⢿⠀⠀⠀⢹⡾⣟⣷⣻⣦⣀⡀⠀⠀⣀⣤⣾⢿⣽⢯⣿⡝⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡽⣟⣾⡽⣟⣧⠀⠀⠀⠙⣿⣽⣳⣯⣟⣿⣻⢿⣻⣽⢯⣿⢾⣟⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣟⣯⡿⣽⢿⣽⣳⡄⠀⠀⠀⠙⠻⢾⣽⣾⣻⢯⣿⡽⡿⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣯⣷⢿⣻⣟⣾⢯⣿⣳⣄⠀⠀⠀⠀⠀⠁⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⢾⣻⣽⡾⣯⣿⣳⡿⣽⣻⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡟⣯⣷⣿⡟⠚⣷⣿⢻⣷⢻⡞⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⣻⣽⡾⣽⡄⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣟⣾⣽⣟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣯⣷⣟⣾⢯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡷⣯⣟⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣽⣟⣾⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣟⡷⣯⣷⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣯⣟⡿⣞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣽⡾⣯⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣯⢿⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣯⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀