Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

5
4 5 1 2 3

Sample Output 1

YES

All the stones can be removed in one operation by selecting the second box.

Sample Input 2

5
6 9 12 10 8

Sample Output 2

YES

Sample Input 3

4
1 2 3 1

Sample Output 3

NO

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>

using namespace std;
#define int long long
#define double long double
#define rep(i, n) for(int i=0;i<(n);++i)
#define INF (1ll<<60)
#define FI first
#define SE second
typedef pair<int, int> pii;
#define l_b lower_bound
#define u_b upper_bound

int N;
int A[100100];
int d[100100];

signed main() {
    cin >> N;
    int s = 0;
    rep(i, N) {
        cin >> A[i];
        s += A[i];
    }
    if (s % (N * (N + 1) / 2) != 0) {
        cout << "NO" << endl;
        return 0;
    }
    int k = s / (N * (N + 1) / 2);
    rep(i, N - 1) {
        int d = A[i + 1] - A[i] - k;
        if (d > 0 || d % N != 0) {
            cout << "NO" << endl;
            return 0;
        }
    }
    cout << "YES" << endl;
}