When cutting carrots into small pieces, you are deciding whether to use a knife and cutting board or a food processor. Each carrot chopped by hand takes 45 seconds. Each carrot chopped in a food processor takes 12 seconds. It takes 35 seconds to clean off a knife and cutting board. It takes 8 minutes to clean your food processor. What is the minimum number of carrots to cut up for which it will be faster to use a food processor than the knife and cutting board? (Factor in both the cutting time and the cleaning time. Your final answer should be an integer.)