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.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Collections;
using Pair = System.Tuple<long, long>;
using System.Linq.Expressions;
using static _20200213.Cin;
using static _20200213.Util;

namespace _20200213
{
    public class Program
    {
        public static void Main(string[] args)
        {
            // ABC085_D(); 45m
            ARC066_C();
        }

        public static void ARC066_C()
        {
            long N = rl;
            long[] A = rla;

            bool even = N % 2 == 0;
            long cnt = 0;
            HashMap<long, long> hm = new HashMap<long, long>();
            for (int i = 0; i < N; i++)
            {
                if (even && A[i] % 2 != 1)
                {
                    Console.WriteLine(0);
                    return;
                }
                else if (!even && A[i] % 2 != 0)
                {
                    Console.WriteLine(0);
                    return;
                }

                hm[A[i]]++;
                if(hm[A[i]] == 2)
                {
                    if (A[i] == 0)
                    {
                        Console.WriteLine(0);
                        return;
                    }
                    cnt++;
                }
                else if (hm[A[i]] > 2)
                {
                    Console.WriteLine(0);
                    return;
                }
            }

            if(cnt != (int)N / 2)
            {
                Console.WriteLine(0);
                return;
            }

            long ans = 1;
            for (int i = 0; i < cnt; i++)
            {
                ChModMul(ref ans, 2);
            }

            Console.WriteLine(ans);
        }

        /// <summary>
        /// D - Katana Thrower
        /// </summary>
        public static void ABC085_D()
        {
            long N = rl;
            long H = rl;
            long[] A, B;
            ReadCols(out A, out B, N);

            SortDecend(B);
            long max = A.Max();
            long count = 0;
            for (int i = 0; i < N; i++)
            {
                if (B[i] > max)
                {
                    H -= B[i];
                    count++;
                    if (H <= 0)
                    {
                        Console.WriteLine(count);
                        return;
                    }
                }
                else
                {
                    break;
                }
            }

            count += (H + max - 1) / max;
            Console.WriteLine(count);
        }
    }

    public class HashMap<K,V>:Dictionary<K,V>{V i;static Func<V>j=Expression.Lambda<Func<V>>(Expression.New(typeof(V))).Compile();public HashMap(){}public HashMap(V a){i=a;}new public V this[K a]{get{V b;if(TryGetValue(a,out b))return b;else return base[a]=i!=null?i:j();}set{base[a]=value;}}}public static class Util{public static readonly long INF=(long)1e17;public readonly static long MOD=(long)1e9+7;public static void DontAutoFlush(){var a=new StreamWriter(Console.OpenStandardOutput()){AutoFlush=false};Console.SetOut(a);}public static void Flush(){Console.Out.Flush();}public static T[]Sort<T>(T[]a){Array.Sort<T>(a);return a;}public static T[]SortDecend<T>(T[]a){Array.Sort<T>(a);Array.Reverse(a);return a;}public static void Swap<T>(ref T a,ref T b){T c=a;a=b;b=c;}public static int GCD(int a,int b){return(b==0)?a:GCD(b,a%b);}public static void ChMax(ref long a,long b){if(a<b)a=b;}public static void ChMin(ref long a,long b){if(a>b)a=b;}public static long ModAdd(long a,long b){long c=a+b;if(c>=MOD)return c%MOD;return c;}public static long ModMul(long a,long b){long c=a*b;if(c>=MOD)return c%MOD;return c;}public static void ChModAdd(ref long a,long b){a+=b;if(a>=MOD)a%=MOD;}public static void ChModMul(ref long a,long b){a*=b;if(a>=MOD)a%=MOD;}public static void FillArray<T>(T[]a,T b){int c=a.Length;for(int d=0;d<c;d++)a[d]=b;}public static void FillArray<T>(T[,]a,T b){int c=a.GetLength(0);int d=a.GetLength(1);for(int e=0;e<c;e++)for(int f=0;f<d;f++){a[e,f]=b;}}public static void FillArray<T>(T[,,]a,T b){int c=a.GetLength(0);int d=a.GetLength(1);int e=a.GetLength(2);for(int f=0;f<c;f++)for(int g=0;g<d;g++){for(int h=0;h<e;h++){a[f,g,h]=b;}}}public static long[]Accumulate(long[]a){long[]b=new long[a.Length+1];for(int c=0;c<a.Length;c++)b[c+1]=b[c]+a[c];return b;}public static double[]Accumulate(double[]a){double[]b=new double[a.Length+1];for(int c=0;c<a.Length;c++)b[c+1]=b[c]+a[c];return b;}}public static class Cin{public static long rl{get{return ReadLong();}}public static long[]rla{get{return ReadLongArray();}}public static double rd{get{return ReadDouble();}}public static double[]rda{get{return ReadDoubleArray();}}public static string rs{get{return ReadString();}}public static int ReadInt(){return int.Parse(k());}public static long ReadLong(){return long.Parse(k());}public static double ReadDouble(){return double.Parse(k());}public static string ReadString(){return k();}public static int[]ReadIntArray(){i=null;return Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);}public static long[]ReadLongArray(){i=null;return Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);}public static double[]ReadDoubleArray(){i=null;return Array.ConvertAll(Console.ReadLine().Split(' '),double.Parse);}public static void ReadCols(out long[]a,out long[]b,long c){a=new long[c];b=new long[c];for(int d=0;d<c;d++){a[d]=ReadLong();b[d]=ReadLong();}}public static void ReadCols(out long[]a,out long[]b,out long[]c,long d){a=new long[d];b=new long[d];c=new long[d];for(int e=0;e<d;e++){a[e]=ReadLong();b[e]=ReadLong();c[e]=ReadLong();}}public static int[][]ReadIntTable(int a){i=null;int[][]b=new int[a][];for(int c=0;c<a;c++)b[c]=ReadIntArray();return b;}public static long[][]ReadLongTable(long a){i=null;long[][]b=new long[a][];for(long c=0;c<a;c++)b[c]=ReadLongArray();return b;}static string[]i{get;set;}static int j{get;set;}static string k(){if(i==null||i.Length<=j){i=Console.ReadLine().Split(' ');j=0;}return i[j++];}}
}