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
#include <bits/stdc++.h>
using i64 = long long;

int main() {
    i64 n, s = 0;
    std::cin >> n;
    std::vector<i64> a(n);
    for (auto &e : a) {
        std::cin >> e;
        s += e;
    }
    i64 m = n * (n + 1) / 2;
    if (s % m) {
        std::cout << "NO" << std::endl;
        return 0;
    }
    i64 k = s / m;
    for (int i = 0; i < n; i++) {
        auto d = a[(i + 1) % n] - a[i] - k;
        if (d > 0 || d % n != 0) {
            std::cout << "NO" << std::endl;
            return 0;
        }
    }

    std::cout << "YES" << std::endl;

    return 0;
}
