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.*;
import java.util.*;
public class Main{
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        int n = Integer.parseInt(st.nextToken());
        st = new StringTokenizer(br.readLine());
        int array[] = new int[n + 1];
        long sum = 0;
        for(int i = 1;i <= n;i++){
            int a = Integer.parseInt(st.nextToken());
            array[i] = a;
            sum += a;
        }
        if(sum * 2 % (n * 1L * (n + 1)) != 0){
            System.out.println("NO");
            return;
        }
        long times = sum * 2 / (n * 1L * (n + 1));
        int cnt = 0;
        array[0] = array[n];
        for(int i = 1;i <= n;i++){
            long diff = array[i] - array[i - 1] - times;
            if(diff > 0){
                System.out.println("NO");
                return;
            }
            if(diff < 0){
                if(Math.abs(diff) % n > 0){
                 System.out.println("NO");
                 return;
                }
                cnt += Math.abs(diff)/n;
            }
        }
        if(cnt > n){
            System.out.println("NO");
            return;
        }
        System.out.println("YES");
    }
}