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
$N = trim(fgets(STDIN));
$A = explode(" ",trim(fgets(STDIN)));
$max = max($A);
 
if($max < $N){
    echo "NO";
}else{
$ans = 0;
$min = 1;
$c = $N - 1;
$s = array_search($max,$A);
while($N < $max){
    $max = 0;
    $b = 0;
    $i = 1;
    while($i <= $N){
        $d = $s + $i;
        if($d >= $N){
            $d -= $N;
        }
        $A[$d] -= $i;
        if($A[$d] > $max){
            $max = $A[$d];
            $t = $d;
        }elseif($A[$d] < 0){
            ++$ans;
            break;
        }elseif($A[$d] <= $min){
            ++$b;
        }
        ++$i;
    }
    if($b > 1){
        ++$ans;
        break;
    }
    $s = $t;
    $t = 0;
}
if($ans != 0){
    echo "NO";
}else{
    echo "YES";
}
}
?>