#include<bits/stdc++.h>
using namespace std;
const int maxn = 1e5+7;
int n;
long long a[maxn],b[maxn],sum;
int main()
{
    scanf("%d",&n);
    for(int i=0;i<n;i++)
        scanf("%lld",&a[i]),sum+=a[i];
    long long t=1ll*n*(n+1)/2;
    if(sum%t){
        cout<<"NO"<<endl;
        return 0;
    }
    long long cnt = sum/t;
    for(int i=0;i<n;i++){
        b[i]=(a[(i+1)%n]-a[i]-cnt);
    }
    bool flag = true;
    for(int i=0;i<n;i++){
        if(b[i]>0||(-b[i])%n)
            flag = false;
    }
    puts(flag?"YES":"NO");
}

### Prompt

In cpp, your task is to solve 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;
const int maxn = 1e5+7;
int n;
long long a[maxn],b[maxn],sum;
int main()
{
    scanf("%d",&n);
    for(int i=0;i<n;i++)
        scanf("%lld",&a[i]),sum+=a[i];
    long long t=1ll*n*(n+1)/2;
    if(sum%t){
        cout<<"NO"<<endl;
        return 0;
    }
    long long cnt = sum/t;
    for(int i=0;i<n;i++){
        b[i]=(a[(i+1)%n]-a[i]-cnt);
    }
    bool flag = true;
    for(int i=0;i<n;i++){
        if(b[i]>0||(-b[i])%n)
            flag = false;
    }
    puts(flag?"YES":"NO");
}

```