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: Time Limit Exceeded)

import java.io.*;
import java.util.*;
public class Main {
  public static int array[];
  public static int minId;
  public static int minVal;
  public static void main(String[] args) throws Exception {
    String line = null;
    int res = 0;
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    line = br.readLine();
    line = br.readLine();
    String data[] = line.split(" ");
    array = new int[data.length];

    minVal = Integer.parseInt(data[0]);
    for (int i = 0; i < data.length; i ++) {
      int num = Integer.parseInt(data[i]);
      array[i] = num;
      if (num < minVal) {
        minVal = num;
        minId = i;
      }
    }

    while (true) {
      res = doSubtract();
      if (res == -1) {
        System.out.println("NO");
        return;
      } else if (res == 0) {
        System.out.println("YES");
        return;
      }
    }
  }

  public static int doSubtract() {
    int i = minId;
    int res = 0;
    minVal = array[0];
    minId = 0;
    for (int j = 0; j < array.length; j++) {
      array[i] = array[i] - (j + 1);
      if (array[i] < 0) {
        return -1;
      } else if (array[i] > 0) {
        res = 1;
      }
      int v = array[i];
      if (v < minVal) {
        minVal = v;
        minId = i;
      }
      if (i == (array.length - 1)) {
        i = 0;
      } else {
        i = i + 1;
      }
    }
    return res;
  }

}