#include<bits/stdc++.h>
#define REP(i,n) for(int i=0;i<(n);i++)
using namespace std;
#define int long long

signed main()
{  
   int N; cin>>N;
   vector<int> a(N);
   REP(i,N) cin>>a[i];
   
   int sum=accumulate(a.begin(),a.end(),0LL);
   int K=N*(N+1)/2;
   
   if(sum%K!=0){
      cout<<"NO"<<endl;
      return 0;
   }
   
   int C=sum/K;
   vector<int> b(N);
   REP(i,N){
      if(C+a[i]-a[(i+1)%N]<0 or (C+a[i]-a[(i+1)%N])%N!=0){
         cout<<"NO"<<endl;
         return 0;
      }
      b[i]=(C+a[i]-a[(i+1)%N])/N;
   }
   cout<<"YES"<<endl;
}

### Prompt

Generate 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 REP(i,n) for(int i=0;i<(n);i++)
using namespace std;
#define int long long

signed main()
{  
   int N; cin>>N;
   vector<int> a(N);
   REP(i,N) cin>>a[i];
   
   int sum=accumulate(a.begin(),a.end(),0LL);
   int K=N*(N+1)/2;
   
   if(sum%K!=0){
      cout<<"NO"<<endl;
      return 0;
   }
   
   int C=sum/K;
   vector<int> b(N);
   REP(i,N){
      if(C+a[i]-a[(i+1)%N]<0 or (C+a[i]-a[(i+1)%N])%N!=0){
         cout<<"NO"<<endl;
         return 0;
      }
      b[i]=(C+a[i]-a[(i+1)%N])/N;
   }
   cout<<"YES"<<endl;
}

```