jewelry

May. 15, 2011 You don't need to understand the economics of a generating plant in order to intelligently buy electricity. If your neighbor is an expert on that subject and you are a neophyte, your electric rates will be identical. But jewelry purchases are different. What you pay for an item vs. what your neighbor pays for a comparable item can be, and often is, widely different. Understanding the economics of the business will tell you why. To begin with, all jewelers turn their inventory very slowly, and that ties up a lot of capital. A once-a-year turn is par for the course. The reason is

Sherlock has a new girlfriend (so unlike him!). Valentine's day is coming and he wants to gift her some jewelry. He bought n pieces of jewelry. The i -th piece has price equal to i  + 1, that is, the prices of the jewelry are 2, 3, 4, ... n  + 1. Watson gave Sherlock a challenge to color these jewelry pieces such that two pieces don't have the same color if the price of one piece is a prime divisor of the price of the other piece. Also, Watson asked him to minimize the number of different colors used. Help Sherlock complete this trivial task. Input The only line contains single integer n ( 1 ≤