#include <bits/stdc++.h>
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)
 
using namespace std;
using LL = long long;
 
int main(void)
{
  LL n;
  cin >> n;
  vector<LL> v(n);
  LL sum=0,once=n*(n+1)/2;
  for(auto &x: v) cin >> x;
  for(auto x:v) sum+=x;
  bool flag = true;
  if(sum%once) flag = false;
  LL times = sum/once;
  REP(i,n) {
    LL diff = v[(i+1)%n] - v[i];
    diff -= times;
    if(diff%n) flag = false;
    if(diff>0) flag = false;
  }
  
  cout << (flag?"YES":"NO") << endl;
  return 0;
}

### 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>
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)
 
using namespace std;
using LL = long long;
 
int main(void)
{
  LL n;
  cin >> n;
  vector<LL> v(n);
  LL sum=0,once=n*(n+1)/2;
  for(auto &x: v) cin >> x;
  for(auto x:v) sum+=x;
  bool flag = true;
  if(sum%once) flag = false;
  LL times = sum/once;
  REP(i,n) {
    LL diff = v[(i+1)%n] - v[i];
    diff -= times;
    if(diff%n) flag = false;
    if(diff>0) flag = false;
  }
  
  cout << (flag?"YES":"NO") << endl;
  return 0;
}

```