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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {

    void solve() throws IOException {
        int n = ni();
        long[] a = nla(n);

        long sum = 0;
        for (int i = 0; i < n; i++) {
            sum += a[i];
        }

        if (sum % (n * (n + 1) / 2) != 0) {
            out.println("NO");
            return;
        }

        long m = sum / (n * (n + 1) / 2);
        long cnt = 0;

        for (int i = 1; i < n; i++) {
            if ((a[i] - a[i - 1] - m) % n != 0) {
                out.println("NO");
                return;
            }
            if (a[i] - a[i - 1] - m < 0) {
                cnt += Math.abs(a[i] - a[i - 1] - m) / n;
            }
        }
        if ((a[0] - a[n - 1] - m) % n != 0) {
            out.println("NO");
            return;
        }
        if (a[0] - a[n - 1] - m < 0) {
            cnt += Math.abs(a[0] - a[n - 1] - m) / n;
        }

        if (cnt > m) {
            out.println("NO");
            return;
        }

        out.println("YES");
    }

    String ns() throws IOException {
        while (!tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine(), " ");
        }
        return tok.nextToken();
    }

    int ni() throws IOException {
        return Integer.parseInt(ns());
    }

    long nl() throws IOException {
        return Long.parseLong(ns());
    }

    double nd() throws IOException {
        return Double.parseDouble(ns());
    }

    String[] nsa(int n) throws IOException {
        String[] res = new String[n];
        for (int i = 0; i < n; i++) {
            res[i] = ns();
        }
        return res;
    }

    int[] nia(int n) throws IOException {
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            res[i] = ni();
        }
        return res;
    }

    long[] nla(int n) throws IOException {
        long[] res = new long[n];
        for (int i = 0; i < n; i++) {
            res[i] = nl();
        }
        return res;
    }

    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer tok;

    public static void main(String[] args) throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        tok = new StringTokenizer("");
        Main main = new Main();
        main.solve();
        out.close();
    }
}