Problem:
Score : 500 points

Problem Statement

There are N boxes arranged in a circle. The i-th box contains A_i stones.

Determine whether it is possible to remove all the stones from the boxes by repeatedly performing the following operation:

Select one box. Let the box be the i-th box. Then, for each j from 1 through N, remove exactly j stones from the (i+j)-th box. Here, the (N+k)-th box is identified with the k-th box.

Note that the operation cannot be performed if there is a box that does not contain enough number of stones to be removed.

Constraints

1 ≦ N ≦ 10^5

1 ≦ A_i ≦ 10^9

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 … A_N

Output

If it is possible to remove all the stones from the boxes, print YES. Otherwise, print NO.

Sample Input 1

5
4 5 1 2 3

Sample Output 1

YES

All the stones can be removed in one operation by selecting the second box.

Sample Input 2

5
6 9 12 10 8

Sample Output 2

YES

Sample Input 3

4
1 2 3 1

Sample Output 3

NO

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {

	public static void main(String[] args)throws Exception{
		BufferedReader br = new BufferedReader ( new InputStreamReader(System.in));
		int count = Integer.parseInt(br.readLine());
		String []input = br.readLine().split(" ");
		boolean notFlag = false;
		boolean yesFlag = false;
		int num = 0;
		int co = 0;
		for(int i=0;i<count;i++) {
			for(int j=0;j<count;j++) {
				notFlag = false;
				num = Integer.parseInt(input[j]);
				co = i+j+1;
				if(num%co != 0 && co <= count) {
					notFlag = true;
					break;
				}else if(co > count) {
					if(num%(co-count) != 0) {
						notFlag = true;
						break;
					}
				}
			}
			if(!notFlag) {
				yesFlag = true;
				break;
			}
		}
		if(yesFlag) {
			System.out.println("YES");
		}else {
			System.out.println("NO");
		}
	}

}