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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.*;
import java.util.*;
import java.math.BigInteger;

class Main{

    void solve(){
        int N = ni();
        int[] a = new int[N];
        int[] count = new int[N];
        for (int i = 0; i < N; i++) {
            int ai = ni();
            a[i] = ai;
            count[ai] ++;
        }
        int[] pow2 = new int[N+1];
        pow2[0] = 1;
        for (int i = 1; i < pow2.length; i++) {
            pow2[i] = pow2[i-1]*2%MOD;
        }
        boolean feasible = true;
        int ans = 0;
        // System.out.println(Arrays.toString(count));
        if(N%2==0){
            for (int i = 0; i < N; i++) {
                if(i%2==0 && count[i]!=0) feasible = false;
                else if(i%2==1 && count[i]!=2) feasible = false;
            }
            if(feasible) ans = pow2[N/2];
        }else{
            for (int i = 0; i < N; i++) {
                if(i==0 && count[i]!=1) feasible = false;
                if(i!=0 && i%2==0 && count[i]!=2) feasible = false;
                if(i%2==1 && count[i]!=0) feasible = false;
            }
            if(feasible) ans = pow2[(N-1)/2];
        }
        if(feasible){
            out.println(ans);
        }
        else{
            out.println(0);
        }
        out.flush();
    } 


    public static void main(String[] args){
        Main m = new Main();
        m.solve();
    }

    Main(){
        this.scan = new FastScanner();
        this.out = new PrintWriter(System.out);
    }

    private FastScanner scan;
    private PrintWriter out;
    private final int MOD = 1_000_000_007;
    private final int INF = 2_147_483_647;
    private final long LINF = 9223372036854775807L;

    // Scanner
    int ni(){ return scan.nextInt();}
    int[] ni(int n){int[] a = new int[n]; for(int i = 0; i < n; i++){a[i] = ni();} return a;}
    int[][] ni(int y, int x){int[][] a = new int[y][x];
        for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = ni();}} return a;}
    long nl(){return scan.nextLong();}
    long[] nl(int n){long[] a = new long[n]; for(int i = 0; i < n; i++){a[i] = nl();} return a;}
    long[][] nl(int y, int x){long[][] a = new long[y][x];
        for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = nl();}} return a;}
    String ns(){return scan.next();}
    String[] ns(int n){String[] a = new String[n]; for(int i = 0; i < n; i++){a[i] = ns();} return a;}
    String[][] ns(int y, int x){String[][] a = new String[y][x];
        for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = ns();}} return a;}
}
class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() { return Double.parseDouble(next());}
}