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 (7.4.4) (judge verdict: Wrong Answer)

<?php

list($boxCount) = getSingleLine();
$boxes = getSingleLine();

$sumStones = array_sum($boxes);
$k = $sumStones/(($boxCount + 1) * $boxCount / 2);
$diffList = [];

for ($i = 0; $i < $boxCount; $i++) {
    $nextBoxIndex = ($i + 1) % $boxCount;
    $diffList[] = $boxes[$nextBoxIndex] - $boxes[$i];
}

$validated = [];


for ($i = 0; $i < $boxCount; $i++) {
    $diffSum = array_sum($diffList);
    if ($diffList[$i] < $k && $k % $boxCount === 0) {
        $validated[] = true;
    }else{
        $validatedp[] = false;
        }
}

if (in_array(false,$validated,true)) {
    echo 'YES';
} else {
    echo 'NO';
}


/**
 * @return array
 */
function getSingleLine():array
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}