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: Time Limit Exceeded)

<?php
fscanf(STDIN, "%d", $n);
$line = fgets(STDIN);
$arr = explode(" ", $line);
$flag = 0;

$max = 0;
foreach ($arr as $v) {
    if ($v > $max) {
        $max = $v;
    }
}

while ($max >= $n) {
    $max = 0;
    $m = array_search(max($arr), $arr);
    for ($i = 1; $i <= $n; $i++) {
        if ($arr[($i + $m) % $n] < $i) {
            break 2;
        } else {
            $arr[($i + $m) % $n] -= $i;
            if ($arr[($i + $m) % $n] > $max) {
                $max = $arr[($i + $m) % $n];
            }
        }
    }
}

if (array_sum($arr) == 0) {
    echo "YES";
} else {
    echo "NO";
}