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: Accepted)

using System;
using System.Diagnostics;
using System.IO;
using System.Text;
using System.Linq;
using System.Collections.Generic;
using System.Text.RegularExpressions;

class Program
{
    const string Yes = "Yes";
    const string No = "No";
    const char White = '.';
    const char Black = '#';
    const long Mod = 1000000007;

    static void Main(string[] args) {
#if DEBUG
        MyDebugger.Test(process, "../TextFile1.txt");
#else
        object ret = process(new StreamReader(Console.OpenStandardInput()));
        Console.WriteLine(ret);
#endif
    }

    static Dictionary<int, int> dic;

    static object process(TextReader input) {
        var n = int.Parse(input.ReadLine());
        var ary = ToIntArray(input.ReadLine(), n);

        var dic = new DefaultDectionary<int, int>(0);


        foreach(var a in ary) {
            dic[a] += 1;
        }

        for(int i= n-1; i >= 1; i-=2) {
            if(dic[i] == 2) {
            } else {
                return 0;
            }
        }

        if(n % 2 == 1) {
            if(dic[0] == 0) return 0;
        }

        return ModPow(2, n/2);
    }

    static long ModPow(long x1, long x2) {
        long ans = 1;
        while (x2 > 0) {
            if (x2 % 2 == 1) {
                ans = (ans * x1) % Mod;
            }
            x1 = (x1 * x1) % Mod;
            x2 /= 2;
        }
        return ans % Mod;
    }

    static int[] ToIntArray(string strs, int n) {
        var ret = new int[n];
        var spl = strs.Split(' ');
        for (int i = 0; i < n; i++)
            ret[i] = int.Parse(spl[i]);
        return ret;
    }

    class DefaultDectionary<Tkey, TValue> : Dictionary<Tkey, TValue>
    {
        TValue DefaultValue;
        public DefaultDectionary(TValue defaultvalue) {
            this.DefaultValue = defaultvalue;
        }
        public new TValue this[Tkey key] {
            get {
                if (this.ContainsKey(key)) return base[key];
                else return DefaultValue;
            }
            set {
                base[key] = value;
            }
        }
    }


}