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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <cstdio>
typedef long long ll;
#define N 100050
int n;ll a[N],s;
int main() {
	scanf("%d",&n); int i;
	for(i=1;i<=n;i++) scanf("%lld",&a[i]),s+=a[i]; a[n+1]=a[1];
	ll t=n*(n+1)/2;
	if(s%t) {puts("NO");return 0;}
	s/=t;
	for(i=1;i<=n;i++) {
		t=a[i]-a[i+1]+s;
		if(t%n||t<0) {puts("NO");return 0;}
	}puts("YES");
}