#include <bits/stdc++.h>
using namespace std;
bool func() {
	long long N;
	cin >> N;
	vector<long long> A(N);
	for (auto& x : A) cin >> x;
	long long s = 0;
	for (auto x : A) s += x;
	long long m = N * (N+1) / 2;
	if (s % m) return false;
	long long n = s / m;
	vector<long long> B(N);
	B[0] = A[0] - A[N-1] - n;
	for (int i = 1; i < N; ++ i) {
		B[i] = A[i] - A[i-1] - n;
	}
	for (auto x : B) {
		if (x > 0) return false;
		if (-x % N != 0) return false;
	}
	return true;
}
int main() {
	cout << (func() ? "YES" : "NO") << endl;
}

### Prompt

Generate 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;
bool func() {
	long long N;
	cin >> N;
	vector<long long> A(N);
	for (auto& x : A) cin >> x;
	long long s = 0;
	for (auto x : A) s += x;
	long long m = N * (N+1) / 2;
	if (s % m) return false;
	long long n = s / m;
	vector<long long> B(N);
	B[0] = A[0] - A[N-1] - n;
	for (int i = 1; i < N; ++ i) {
		B[i] = A[i] - A[i-1] - n;
	}
	for (auto x : B) {
		if (x > 0) return false;
		if (-x % N != 0) return false;
	}
	return true;
}
int main() {
	cout << (func() ? "YES" : "NO") << endl;
}

```