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# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
public class Box {
    public static void Main() {
        long N = long.Parse(Console.ReadLine());
        string[] read = new string[N];
        read = Console.ReadLine().Split(' ');
        int[] A = new int[N];
        long sum = 0;
        long sumlo = 0;
        for (int i = 0; i < N; i++) {
            sumlo += i + 1;
        }
        for (int i = 0; i < N; i++) {
            A[i] = int.Parse(read[i]);
            sum += A[i];
        }
        if (sum % sumlo != 0) {
            Console.WriteLine("NO");
        } else {
            long loop = sum / sumlo;
            bool NO = false;
            //long check = 0;
            for (int i = 0; i < N; i++) {
                /*if (i == N - 1) {
                    check = A[0] - A[N - 1];
                } else {
                    check = A[i + 1] - A[i];
                }
                NO = true;
                if ((check - loop) % N == 0) {
                    if (loop != 0) {
                        if ((check - loop) / loop >= -1 * N) {
                            NO = false;
                        }
                    } else {
                        NO = false;
                    }
                }*/



                for (int j = 0; j <= loop; j++) {
                    NO = true;
                    if (i == N - 1) {
                        if (A[0] - A[N-1] == loop - j * N) {
                            NO = false;
                            break;
                        }
                    } else {
                        if (A[i + 1] - A[i] == loop - j * N) {
                            NO = false;
                            break;
                        }
                    }
                }

                if (NO) {
                    break;
                }
            }
            if (NO) {
                Console.WriteLine("NO");
            } else {
                Console.WriteLine("YES");
            }
        }


    }
}