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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
  declare(strict_types=1);

  fscanf(STDIN, "%i", $n);
  $xs = explode(" ", trim(fgets(STDIN)));

  $solve = function () use ($n, $xs)
  {
      $s = array_sum($xs);
      $t = (int)(($n * $n + $n) / 2);
      if (($s % $t) === 0)
      {
          return "NO";
      }
      
      $k = (int)($s / $t);
      $xs[-1] = $xs[$n - 1];
      for ($i = 0; $i < $n; $i++)
      {
          $d = $xs[$i] - $xs[$i - 1] - $k;
          if ($d > 0 || ($d % $n) !== 0)
              return "NO";
      }

      return "YES";
  };

  echo $solve().PHP_EOL;