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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        new Main().solve();
    }

    void solve() {
        try (Scanner in = new Scanner(System.in)) {
            int n = in.nextInt();
            int a[] = new int[n];
            for (int i = 0; i < n; ++i) {
                a[i] = in.nextInt();
            }
            int x = (n + 1) * n / 2, y = min(a), z = a[y] / x;
            for (int i = 0; i < n; ++i) {
                a[i] -= n * z;
            }
            System.out.println(ok(n, a) ? "YES" : "NO");
        }
    }

    boolean ok(int n, int a[]) {
        while (true) {
            int i = min(a);
            if (a[i] < 0) return false;
            if (a[i] == 0) return true;
            for (int j = 0; j < n; ++j) {
                a[(i + j) % n] -= j + 1;
            }
        }
    }

    int min(int a[]) {
        int index = -1, value = Integer.MAX_VALUE;
        for (int i = 0; i < a.length; ++i) {
            if (value > a[i]) {
                value = a[i];
                index = i;
            }
        }
        return index;
    }

    void tr(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }
}