Problem:
Score : 300 points

Problem Statement

There are N people, conveniently numbered 1 through N.
They were standing in a row yesterday, but now they are unsure of the order in which they were standing.
However, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person.
According to their reports, the difference above for person i is A_i.

Based on these reports, find the number of the possible orders in which they were standing.
Since it can be extremely large, print the answer modulo 10^9+7.
Note that the reports may be incorrect and thus there may be no consistent order.
In such a case, print 0.

Constraints

1≦N≦10^5

0≦A_i≦N-1

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the number of the possible orders in which they were standing, modulo 10^9+7.

Sample Input 1

5
2 4 4 0 2

Sample Output 1

4

There are four possible orders, as follows:

2,1,4,5,3

2,5,4,1,3

3,1,4,5,2

3,5,4,1,2

Sample Input 2

7
6 4 0 2 4 0 2

Sample Output 2

0

Any order would be inconsistent with the reports, thus the answer is 0.

Sample Input 3

8
7 5 1 1 7 3 5 3

Sample Output 3

16

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;

class LiningUp {
    static void Main() {
        const int mystery_coefficient = 1000000007; // Math.Pow(10, 9)+7 
        string input = Console.ReadLine();

        int person_count = int.Parse(input);

        input = Console.ReadLine();

        // 自分が中央にいたと申告している人数を取得
        int center_person_count = input.Split(' ')
                                       .Where(s => s == "0")
                                       .Count();
        
        // 申告に矛盾があれば0を、そうでなければ組み合わせ数を謎の係数で割った余りを返す
        if (IsContradiction(center_person_count, person_count)) {
            Console.WriteLine(0);
        } else {
            Console.WriteLine(Math.Pow(person_count / 2, 2) % mystery_coefficient);
        }
    }

    // 報告に矛盾が含まれる場合はtrueを返すメソッド
    private static bool IsContradiction(int center_person_count, int person_count) {

        // 自分が中央だっていう人が2人以上いる場合、または偶数人なのに中央の人間がいる場合はtrue
        if (center_person_count >= 2) {
            return true;
        } else if (person_count % 2 == 0 && center_person_count >= 1) {
            return true;
        } else {
            return false;
        }
    }
}