#include <cstdio>
#define repi(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,a) repi(i,0,a)

constexpr int MAX_N = 100000;

using ll = long long;

ll N;
ll A[MAX_N];
ll d[MAX_N], S;

int main()
{
  scanf( "%lld", &N );
  rep( i, N )
    scanf( "%lld", A+i ), S += A[i];

  if( S % (N*(N+1)/2) )
  {
    puts("NO");
    
    return 0;
  }

  ll k = S / (N*(N+1)/2);

  rep( i, N-1 )
    d[i] = A[i+1]-A[i];

  bool fl = true;
  rep( i, N-1 )
  {
    fl &= d[i] <= k;
    fl &= (d[i]-k)%N == 0;
  }

  puts( fl ? "YES" : "NO" );

  return 0;
}
### Prompt

Your challenge is to write 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 <cstdio>
#define repi(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,a) repi(i,0,a)

constexpr int MAX_N = 100000;

using ll = long long;

ll N;
ll A[MAX_N];
ll d[MAX_N], S;

int main()
{
  scanf( "%lld", &N );
  rep( i, N )
    scanf( "%lld", A+i ), S += A[i];

  if( S % (N*(N+1)/2) )
  {
    puts("NO");
    
    return 0;
  }

  ll k = S / (N*(N+1)/2);

  rep( i, N-1 )
    d[i] = A[i+1]-A[i];

  bool fl = true;
  rep( i, N-1 )
  {
    fl &= d[i] <= k;
    fl &= (d[i]-k)%N == 0;
  }

  puts( fl ? "YES" : "NO" );

  return 0;
}
```