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.util.*;
 
public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int np = n*(n+1)/2;
		int k = 0;
		long[] a = new long[n];
		long[] d = new long[n];

		a[0] = sc.nextLong();
		long sum = a[0];
		for(int i=1; i<n; i++){
			a[i] = sc.nextLong();
			d[i-1] = a[i]-a[i-1];
			sum += a[i];
			k += sum/np;
			sum %= np;
		}
 		d[n-1] = a[0]-a[n-1];

		if( sum != 0){
			System.out.println("NO");
			return;
		}

		for(int i=0; i<n; i++){
			d[i] -= k;
			if( d[i] > 0 || d[i]%n != 0 ){
				System.out.println("NO");
				return;
			}
		}
		System.out.println("YES");
		return;
	}
}