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

int x[100001];

inline void no() { printf("NO\n"), exit(0); }

int main(){
	int n;
	scanf("%d", &n);
	ll s = 0;
	f(i, 0, n)scanf("%d", x + i), s += x[i];
	x[n] = x[0];
	ll d = (ll)n * (n + 1) >> 1;
	if (s % d)no();
	ll z = s / d, k = 0;
	f(i, 0, n){
		ll t = x[i + 1] - x[i];
		t = z - t;
		if (t % n || t < 0)no();
		k += t / n;
	}
	if (k != z)no();
	printf("YES\n");
}

### Prompt

Your task is to create 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>
using namespace std;
#define ll long long
#define f(i, x, n) for(int i = x; i < (int)(n); ++i)

int x[100001];

inline void no() { printf("NO\n"), exit(0); }

int main(){
	int n;
	scanf("%d", &n);
	ll s = 0;
	f(i, 0, n)scanf("%d", x + i), s += x[i];
	x[n] = x[0];
	ll d = (ll)n * (n + 1) >> 1;
	if (s % d)no();
	ll z = s / d, k = 0;
	f(i, 0, n){
		ll t = x[i + 1] - x[i];
		t = z - t;
		if (t % n || t < 0)no();
		k += t / n;
	}
	if (k != z)no();
	printf("YES\n");
}

```