⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣽⣾⣳⢿⣞⣷⣻⢾⣳⡿⣞⣷⣻⢾⣳⡿⣞⣷⣻⢾⣳⡿⣞⣷⣻⢾⣳⡿⣞⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠳⢿⣟⣾⢯⣟⡿⣽⣻⣽⢯⣟⡿⣽⣻⣽⢯⣟⡿⣽⣻⣽⢯⣟⡿⣽⡿⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠻⢯⣿⣽⣻⣽⢾⣻⣽⣻⣽⣟⡾⣿⣽⣻⡽⣟⣾⣿⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣾ ⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠾⠿⢯⣷⣟⣷⣯⣿⣷⠯⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣼⡿⣽ ⣿⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⢿⣽ ⣿⣞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡽⣿⣞ ⣿⣞⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣻⢷⣻ ⣿⢾⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢷⣻⢿⣽ ⣿⣻⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⡽⣟⣾ ⣿⣽⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⢉⠁⠠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⠈⡉⠒⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣟⡿⣽ ⣿⢾⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢁⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⢈⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢯⣟⡿ ⣿⣻⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⢿⣽ ⣿⣳⠇⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⠀⠁⠀⢠⣶⠟⠛⠉⠓⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠉⠙⠳⣆⡀⠀⠊⡳⡀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣿⢾ ⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⠎⠠⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠙⢾⣟ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⢘⠐⠁⠀⠀⢰⡿⠿⣇⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⢀⡼⠿⣧⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⢹ ⡏⠢⢀⠀⠀⠀⠀⠀⠀⡗⠁⠀⠀⠀⢸⡁⠀⢸⣷⣤⣤⣴⠾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⢶⣶⣶⣿⡀⠀⣸⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣀⠔⣺ ⡇⠀⠀⠍⠒⠤⠄⢀⣀⡇⠀⠀⠀⠀⠘⣿⣶⠟⠛⣿⣿⣿⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣾⣿⡟⠉⢻⣿⡏⠀⠀⠀⠀⢸⣀⡀⠠⠤⠒⠉⠀⠀⣼ ⡇⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⢿⣷⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣶⡾⠟⠁⠀⡀⡀⠄⠘⠀⠀⠀⠁⠀⠀⠀⠀⣸ ⡇⠀⠀⠀⠀⠀⠀⠀⠈⠜⡄⠀⠀⠀⠀⢀⡠⠜⠭⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⡩⠔⠤⡀⠀⠀⠀⠀⡆⡄⠀⠀⠀⠀⠀⠀⠀⢼ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⡀⠀⠀⡰⠊⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠎⠀⠀⠀⠈⢢⡀⠀⡘⠐⠀⠀⠀⠀⠀⠀⠀⠀⢺ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢄⡘⠁⠀⠀⠀⠀⠀⠸⡀⠀⠰⢋⡠⠤⠤⠄⣀⠠⠄⡀⠤⠤⠤⠼⠃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠱⡘⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⣹ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡘⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢱⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⢼ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢢⠇⠐⡀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣀⡇⠀⠀⠀⠀⠀⠀⠀⠄⠈⡇⠃⠀⠀⠀⠀⠀⠀⠀⣹ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⡘⠀⠀⠀⡀⠀⠀⠀⠀⠀⣸⡏⢳⠒⠳⠤⠤⠤⢄⠠⢠⠤⠤⠤⠼⠓⠒⠉⡛⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠀⠀⠀⠀⠀⠀⠀⢼ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⠈⠀⠂⠀⢐⣾⣿⡇⢸⢀⠀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⡇⢸⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⡇⡄⠀⠀⠀⠀⠀⠀⢺ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⢣⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣸⠡⠀⠀⠀⠀⠀⠀⠀⣹ ⡇⠀⠀⠀⠀⠀⠀⠀⡀⢌⣰⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡚⢁⠀⠀⠀⠀⠀⠀⠀⠀⢼ ⣧⣠⣄⣠⣄⣠⣔⣨⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣀⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣦⣁⣠⣠⣀⣤⣀⣤⣀⣾