⣿⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻ ⣿⣞⡿⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⢿ ⣿⣞⣿⣽⢾⣟⣯⡷⣿⣻⣽⢾⣟⣯⡷⣿⣻⣽⢾⣟⣯⡷⣿⣻⣽⢾⣟⣯⡷⣿⣻⣽⢾⣟⣯⡷⣿⣻⣽⢾⣟⣯⡷⣿⣻⣽⢾⣟⣯⣿ ⣿⣞⡿⣞⣯⡿⣞⣿⣳⡿⣽⣻⡾⣯⣟⣷⢿⣽⣻⡾⣯⣟⣷⢿⣽⣻⡾⣯⣟⣷⢿⣽⣻⡾⣯⣟⣷⢿⣽⡿⢾⣯⣿⢷⣻⣽⢿⣞⡿⣾ ⣿⣞⣿⣻⣽⣻⢯⣷⢿⣽⣟⡷⣿⣽⣻⣾⣯⣟⡷⣿⣽⣻⢾⣯⣟⡷⣿⣽⣻⢾⣯⣟⡷⣿⣽⣻⢾⣿⣏⠙⢦⡙⢿⠿⣿⣽⣻⡾⣿⣽ ⣿⢾⡽⣷⣻⣽⢿⣽⣻⣾⣽⣻⢷⡿⠋⢻⣷⣻⢿⣽⢾⣻⣯⡷⣟⣿⣽⢾⣻⣯⡷⣟⣿⣽⢾⣻⣯⣿⣿⣧⡈⢷⠈⣧⠹⣿⣳⣿⣳⣿ ⣿⢯⣿⢯⣟⣾⢿⣽⣳⡿⣞⣿⡟⠁⠀⠈⢿⣟⡿⣾⣻⣟⣾⣽⢿⡾⣽⣻⡷⣯⣟⡿⣾⣽⠟⢁⣠⣤⣌⠙⠃⠈⠃⠹⠂⢹⣿⡾⣽⣾ ⣿⢯⣟⣯⡿⣽⣻⡾⣯⣟⣿⣏⣀⣀⣠⣤⣈⣿⣿⣽⣷⣯⣟⣾⢿⡽⣟⣷⢿⣯⢿⣽⣯⣿⡦⠾⣿⣟⣿⡇⠀⠀⠀⠀⠀⠘⣿⣽⣟⣾ ⣿⢯⣟⣷⡿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⢿⣿⡾⣟⣾⣟⡷⣯⣿⣧⣀⠈⢉⣉⡄⠀⠀⠀⠀⠀⠀⣿⣿⣞⣿ ⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣿⣻⣽⢾⣻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣷⢿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣟⠋⠉⠁⠀⣾⡿⣽⣧⠀⠀⠀⠀⢀⣿⣯⢿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢰⣿⣟⡿⣿⠀⠀⠀⠀⢸⣿⣯⢿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣼⣿⢾⣻⣿⡁⠀⠀⠀⣸⣿⡽⣟⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠈⢿⣿⣻⡽⣿⠃⠀⠀⠀⣿⡿⣽⣻⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⣠⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠘⣿⣯⢿⣿⠀⠀⠀⢸⣿⢿⣽⢯⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣀⣀⣀⢀⣀⣈⣳⣤⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣻⡟⠀⠀⢀⣿⣿⣻⢾⡿⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⡏⠉⠉⠉⠁⠀⠉⠛⢶⣤⣤⣠⣤⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⣼⣿⣳⡿⣯⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⣸⣿⢯⣷⣟⣯⢿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⣰⣿⣟⣯⡷⣿⡽⣟⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⣴⣿⣟⣾⢯⣟⣷⢿⣻⣽ ⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣼⣿⣟⣾⢯⣿⣻⢾⣟⣯⢿ ⠀⠀⠀⢻⡄⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⣾⣿⣻⣞⣯⣿⣳⢿⣻⡾⣯⣿ ⠀⠀⠀⠀⢷⡀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣿⣿⣳⡿⣽⣳⣯⣟⡿⣽⣻⢷⣻ ⠀⠀⠀⠀⠈⢳⣄⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⡾⣷⣟⡿⣽⡾⣯⣟⡿⣽⣟⣿ ⠀⠀⠀⠀⠀⠀⠉⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣟⣾⣟⣷⣻⣽⢿⡽⣷⣻⢿⣽⣾⣻

⣻⣾⣽⢿⣻⣷⡽⢿⣽⣻⣷⣟⣾⣟⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⠉⠀⠀⠀⠀⠀⠀ ⣿⣟⣽⡿⣟⣯⡾⣽⡿⣟⣷⡾⣟⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣄⢳⠈⠀⠀⠀⠀ ⣻⢷⣻⣽⡿⣟⣯⣳⣽⡿⣳⣿⣿⣯⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⡀⢷⠀⠀⠀⠀ ⣿⣯⡾⣻⢿⣳⣿⣯⣞⣻⣿⣾⢁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⡄⢻⠀⠀⠀ ⢿⣯⣟⢾⣻⣿⢯⣾⣟⣿⣼⠀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⠀⠀⠀⠀⠀⠀⠀ ⣽⣻⢿⣷⣟⢯⣾⣟⣿⣴⠀⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠶⠤⠦⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣟⡽⣿⡷⣯⣟⣿⣰⠀⠀⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡼⢀⠀⠀⠀⠀⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⢿⣯⣟⣷⢯⣿⣸⠀⠀⡏⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣟⣯⡿⣳⣿⣼⠀⠀⠃⣿⣿⢸⠀⠀⠀⠀⠀⠀⠆⣤⣠⣤⣤⢶⠛⠉⠀⠁⠉⠉⠉⡏⠩⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣽⡿⢾⣻⣿⣿⢀⠀⠀⡟⣻⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠞⣤⣤⣳⣈⣀⢀⣀⣀⣀⣤⠷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢯⣽⢿⣿⢸⠀⠀⠀⣿⢿⣯⣿⠘⠀⠀⠀⠀⠁⠛⠈⠀⠀⠀⣠⠀⠀⠀⠀⣆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣽⣻⣽⡿⣿⠀⠀⠀⠃⣿⡽⣻⣿⢿⠈⠀⠀⠀⡄⣶⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣟⡽⣿⣸⠀⠀⠀⡁⣿⣻⢾⣿⣼⢧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⢿⣯⣿⢸⠀⠀⠀⠀⣿⡿⣟⣿⢰⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⢿⣯⣿⢀⠀⠀⠀⠀⣧⣽⡿⣾⠀⠁⠉⠋⣟⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⢿⣷⣿⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣻⢾⣽⣻⣿⢷⠻⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿ ⣿⣞⣿⣿⠀⠀⠀⠀⠀⠀⡄⣉⢉⠈⣀⣧⣿⣯⡷⣟⣾⣟⡾⣿⢿⠿⠛⠛⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠛⠛⠿⡿⣷⣟⢯⣿ ⣾⣟⣽⣿⠘⠀⠀⠀⠀⠀⡇⣿⣟⣿⠾⡦⣿⣯⣽⢿⣯⢿⣷⣟⡽⢿⣾⣟⣯⣷⣽⣿⣿⣈⣤⣠⣀⣀⣏⣿⣟⣯⡾⣻⣽⡿⣯⣟⢯⣿ ⣾⣽⡾⣿⢹⠂⠹⠃⠈⠃⠙⣌⣤⣠⢁⠟⣽⣾⡿⣟⣯⡷⣻⣽⡾⢿⣽⣾⣟⣻⣾⡿⣟⢿⠈⠀⠁⡟⣿⣞⡿⣳⣽⢿⣾⣟⢯⣿⢯⣿ ⣿⣳⣿⣳⣿⠹⣧⠈⢷⡈⣧⣿⣿⣯⣻⢾⣽⣿⣟⡷⣯⣻⢾⣽⣿⣟⡷⣯⣻⢾⣽⢿⣻⣷⢻⠋⡿⢷⣻⣽⣾⣻⣽⢿⣽⣻⣷⡽⢾⣿ ⣽⣿⡾⣻⣽⣿⠿⢿⡙⢦⠙⣏⣿⢾⣻⣽⣿⡷⣟⣯⢾⣻⣽⣿⡷⣟⣯⢾⣻⣽⣿⡷⣟⣯⣾⣻⣽⣿⡷⣟⣽⢿⣷⢯⣻⣽⣻⣿⣞⣿ ⣾⡿⣞⢿⣽⣻⢷⣿⣯⢾⡿⣽⢿⣷⣟⣯⡾⣻⣽⢿⣷⣟⣯⡾⣻⣽⢿⣷⣟⣯⡾⣻⣽⢿⣷⣟⣯⡾⣻⣽⡿⣳⣿⣞⡿⣯⣞⡿⣞⣿ ⣿⣯⣟⢾⣽⣻⣿⡷⣯⣟⢾⣽⣻⣿⡷⣯⣟⢾⣽⣻⣿⡷⣯⣟⢾⣽⣻⣿⡷⣯⣟⢾⣽⣻⣿⡷⣯⣟⢾⣽⣻⣿⡷⣯⣟⢾⣽⣿⣞⣿ ⢿⣻⢿⣷⣯⣟⡾⣽⣻⢿⣷⣯⣟⡾⣽⣻⢿⣷⣯⣟⡾⣽⣻⢿⣷⣯⣟⡾⣽⣻⢿⣷⣯⣟⡾⣽⣻⢿⣷⣯⣟⡾⣽⣻⢿⣷⣯⡿⣞⣿ ⣻⢿⣻⣿⣟⡿⣟⣻⢿⣻⣿⣟⡿⣟⣻⢿⣻⣿⣟⡿⣟⣻⢿⣻⣿⣟⡿⣟⣻⢿⣻⣿⣟⡿⣟⣻⢿⣻⣿⣟⡿⣟⣻⢿⣻⣿⣟⡿⣟⣿