#include<bits/stdc++.h>
using namespace std;

void no() {
    cout<<"NO"<<endl;
    exit(0);
}

const int N = 1e5+7;
int a[N];

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);

    int n;
    cin>>n;

    long long sum = 0, B = 1LL*n*(n+1)/2;
    for (int i=1; i<=n; i++) {
        int x;
        cin>>x;
        sum += x;
        a[i] = x;
    }
    a[0] = a[n];

    if (sum%B)  no();
    long long K = sum/B;

    for (int i=1; i<=n; i++) {
        long long D = a[i] - a[i-1];
        if ((K-D)%n || K-D<0)    no();
    }
    cout<<"YES\n";
}

### Prompt

Create a solution in CPP for 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>
using namespace std;

void no() {
    cout<<"NO"<<endl;
    exit(0);
}

const int N = 1e5+7;
int a[N];

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);

    int n;
    cin>>n;

    long long sum = 0, B = 1LL*n*(n+1)/2;
    for (int i=1; i<=n; i++) {
        int x;
        cin>>x;
        sum += x;
        a[i] = x;
    }
    a[0] = a[n];

    if (sum%B)  no();
    long long K = sum/B;

    for (int i=1; i<=n; i++) {
        long long D = a[i] - a[i-1];
        if ((K-D)%n || K-D<0)    no();
    }
    cout<<"YES\n";
}

```