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 PHP (5.6.30) (judge verdict: Accepted)

<?php
$line = fgets(STDIN);
$line = fgets(STDIN);
$line = rtrim($line, "\r\n");
$aa_list = explode(" ", $line);
$nn = count($aa_list);

$sum = 0;
foreach ($aa_list as $aa) {
  $sum += $aa;
}

$kk = $nn * ($nn + 1) / 2;
if ($sum % $kk != 0) { print 'NO'; exit; }
$div = $sum / $kk;

for ($ii = 1; $ii < $nn; $ii++) {
  $dd = $aa_list[$ii] - $aa_list[$ii - 1] - $div;
  if ($dd > 0) { print 'NO'; exit; }
  if ($dd < 0) {
    if ($dd % $nn != 0) { print 'NO'; exit; }
  }
}
print 'YES';
exit;