#include<bits/stdc++.h>
using namespace std;

int N , A[100003];

int main(){
	cin >> N; long long sum = 0; for(int i = 1 ; i <= N ; ++i){cin >> A[i]; sum += A[i];}
	long long num = N * (N + 1ll) / 2; if(sum % num){puts("NO"); return 0;}
	sum /= num; A[N + 1] = A[1]; long long cnt = 0;
	for(int i = 2 ; i <= N + 1 ; ++i){
		if(A[i - 1] + sum < A[i] || (A[i - 1] + sum - A[i]) % N){puts("NO"); return 0;}
		cnt += (A[i - 1] + sum - A[i]) / N;
	}
	puts(sum == cnt ? "YES" : "NO");
	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>
using namespace std;

int N , A[100003];

int main(){
	cin >> N; long long sum = 0; for(int i = 1 ; i <= N ; ++i){cin >> A[i]; sum += A[i];}
	long long num = N * (N + 1ll) / 2; if(sum % num){puts("NO"); return 0;}
	sum /= num; A[N + 1] = A[1]; long long cnt = 0;
	for(int i = 2 ; i <= N + 1 ; ++i){
		if(A[i - 1] + sum < A[i] || (A[i - 1] + sum - A[i]) % N){puts("NO"); return 0;}
		cnt += (A[i - 1] + sum - A[i]) / N;
	}
	puts(sum == cnt ? "YES" : "NO");
	return 0;
}

```