#include <bits/stdc++.h>
#define ll long long
using namespace std;
ll n,sum,a[100005],cnt,t;
int main(){
    cin >> n;
    for(int i=0;i<n;i++){
        cin >> a[i];
        sum += a[i];
    }
    if (sum % (n * (n+1)/2)) return printf("NO"),0;
    cnt = t = sum / (n*(n+1)/2);
    for(int i=0;i<n;i++){
        ll delta = - a[(i- 1+n)%n] + a[i] - t;
        if (delta > 0) return printf("NO"),0;
        if (delta % n != 0) return printf("NO"),0;
        cnt += delta / n;
    }
    if (cnt) return printf("NO"),0;
    printf("YES");
}

### Prompt

Your challenge is to write a CPP solution to the following problem:

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`.

Examples

Input

5
4 5 1 2 3


Output

YES


Input

5
6 9 12 10 8


Output

YES


Input

4
1 2 3 1


Output

NO

### Response

```cpp
#include <bits/stdc++.h>
#define ll long long
using namespace std;
ll n,sum,a[100005],cnt,t;
int main(){
    cin >> n;
    for(int i=0;i<n;i++){
        cin >> a[i];
        sum += a[i];
    }
    if (sum % (n * (n+1)/2)) return printf("NO"),0;
    cnt = t = sum / (n*(n+1)/2);
    for(int i=0;i<n;i++){
        ll delta = - a[(i- 1+n)%n] + a[i] - t;
        if (delta > 0) return printf("NO"),0;
        if (delta % n != 0) return printf("NO"),0;
        cnt += delta / n;
    }
    if (cnt) return printf("NO"),0;
    printf("YES");
}

```