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
#include <iostream>
using namespace std;

int main() {
long long n,a[100000], s=0,m,c=0;
cin>>n;
for(int i=0;i<n;i++){
    cin>>a[i];
    s+=a[i];
}
if(s%(n*(n+1)/2)!=0){
    cout<<"NO"<<endl;
    return 0;
}
m=2*s/(n*(n+1));
for(int i=0;i<n;i++){
    long long d=a[i]-a[(i-1+n)%n];
    if(m-d>=0&&(m-d)%n==0){
        c+=(m-d)/n;
    }else{
        cout<<"NO"<<endl;
        return 0;
    }
}
cout<<"YES"<<endl;
	return 0;
}