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.Collections.Generic;

namespace ConsoleApp_CS
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = CIn.ReadLong();
            var a = CIn.ReadLongArray(n);
            var ans = (long)1;

            Array.Sort(a);
            for(var i = a.Length % 2; i < n; i += 2)
            {
                if (a[i] == a[i + 1])
                {
                    ans *= 2;
                }
                else
                {
                    ans = 0;
                }
            }

            Console.WriteLine(ans);
            
        }
    }

    class CIn
    {
        private static readonly Queue<string> fieldBuffer = new Queue<string>();

        public static string Read()
        {
            if (fieldBuffer.Count == 0)
            {
                foreach (var field in Console.ReadLine().Split())
                {
                    fieldBuffer.Enqueue(field);
                }
            }
            return fieldBuffer.Dequeue();
        }

        public static int ReadInt() => int.Parse(Read());
        public static long ReadLong() => long.Parse(Read());
        public static double ReadDouble() => double.Parse(Read());

        public static string[] ReadStringArray(long n)
        {
            var array = new string[n];
            for (var i = 0; i < n; i++)
            {
                array[i] = Read();
            }
            return array;
        }

        public static int[] ReadIntArray(long n)
        {
            var array = new int[n];
            for (var i = 0; i < n; i++)
            {
                array[i] = ReadInt();
            }
            return array;
        }

        public static long[] ReadLongArray(long n)
        {
            var array = new long[n];
            for (var i = 0; i < n; i++)
            {
                array[i] = ReadLong();
            }
            return array;
        }

        public static double[] ReadDoubleArray(long n)
        {
            var array = new double[n];
            for (var i = 0; i < n; i++)
            {
                array[i] = ReadDouble();
            }
            return array;
        }
    }
}