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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

public class Main{
    
    public static void main(String[] args) throws IOException {
        int N = in.nextInt();
        HashMap<Integer, Integer> map = new HashMap();
        for(int i = 0; i < N; i++){
            int a = in.nextInt();
            map.put(a, map.getOrDefault(a, 0) + 1);
        }
        int mod = (int) 1e9 + 7;
        boolean flag = true;
        if(N % 2 == 0){
            // all keys should be odd with count 2
            for(int a: map.keySet()){
                if(a % 2 == 0 ||  map.get(a) != 2){
                    flag = false;
                    break;
                }
            }
        }
        else{
            // all keys should be even with count 2 except 0
            for(int a: map.keySet()){
                if(a == 0){
                    if(map.get(a) != 1){
                        flag = false;
                        break;
                    }
                }
                else if(a % 2 == 1 || map.get(a) != 2){
                    flag = false;
                    break;
                }
            }
        }

        if(flag){
            long ans = powerMOD(2, N/2, mod);
            println(ans);
        }
        else{
            println(0);
        }
        
        in.close();
        out.close();
    }


    public static long powerMOD(long a, int n, int mod){
        long res = 1;
        while(n-->0){
            res = res*a;
            res = res % mod;
        }

        return res;
    }

    static int MIN = Integer.MIN_VALUE;
    static int MAX = Integer.MAX_VALUE;
    static Reader in = new Reader();
    static PrintWriter out = new PrintWriter(System.out);
    static void read(int arr[], int N) throws IOException{ for(int i = 0; i < N; i++){ arr[i] = in.nextInt(); } }
    static void read(long arr[], int N) throws IOException{ for(int i = 0; i < N; i++){ arr[i] = in.nextLong(); } }
    static void read(String arr[], int N) throws IOException{ for(int i = 0; i < N; i++){ arr[i] = in.next(); } }
    static void print(Object O){ out.print(O); }
    static void println(Object O){ out.println(O); }
    static void print(int arr[]){ for(int i = 0; i < arr.length; i++){ print(arr[i]+" "); } println(""); }
    static void print(int arr[][]){ for(int i = 0; i < arr.length; i++){ print(arr[i]); } }
    static void debug(Object O){ System.out.println(O); }
}

class Reader {
    BufferedReader reader;
    StringTokenizer tokenizer;

    Reader() {
        reader = new BufferedReader(new InputStreamReader(System.in));
        tokenizer = new StringTokenizer("");
    }

    String next() throws IOException {
        while (!tokenizer.hasMoreTokens() ) { 
            tokenizer = new StringTokenizer(reader.readLine()); 
        }
        return tokenizer.nextToken();
    }

    int nextInt() throws IOException { 
        return Integer.parseInt(next()); 
    }
    
    double nextDouble() throws IOException { 
        return Double.parseDouble(next());
    }
    
    long nextLong() throws IOException { 
        return Long.parseLong(next()); 
    }
    
    String nextLine() throws IOException { 
        return reader.readLine(); 
    }
    
    void close() throws IOException { 
        reader.close(); 
    }
}