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 <bits/stdc++.h>
using namespace std;
using ll=long long;
void NO(){cout<<"NO"<<endl;exit(0);}
int main(){
ll n;cin>>n;ll x[100001];ll s=0;for(int i=0;i<n;++i)cin>>x[i],s+=x[i];
ll n2=n*(n+1)/2;ll k=s/n2;if(n2*k!=s)NO();
ll j=0;for(int i=0;i<n;++i){ll d=x[(i+1)%n]-x[i];if((k-d)%n!=0||k-d<0)NO();j+=(k-d)/n;}
if(j!=k)NO();cout<<"YES"<<endl;
return 0;}