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.IOException;
import java.util.NoSuchElementException;

import java.io.InputStream;

import java.io.PrintWriter;

import java.util.Arrays;

@SuppressWarnings("unchecked")
public class Main {
    static final int INF = 1000000007;

    // aとbを掛けた値をmodする(a * b mod p)
    static int modmulti(int a, int b) {
        int res = 0;
        int mod = a % INF;
        while (b > 0) {
            if ((b & 1) == 1) {
                res += mod;
                if (res > INF) {
                    res -= INF;
                }
            }
            mod <<= 1;
            if (mod > INF) {
                mod -= INF;
            }
            b >>= 1;
        }
        return res;
    }

    public static void main(String[] args) throws IOException {
        PrintWriter out = new PrintWriter(System.out);

        final int N = nextInt();

        int[] A = new int[N];

        Arrays.fill(A, 0);

        for (int i = 0; i < N; i++) A[nextInt()]++;

        int pos = N % 2 == 1 ? 0 :1;

        boolean flg = true;

        int ans = 1;

        if (pos == 0 && A[0] != 1) flg = false;

        for (int i = 1; i < N; i++) {
            if (!flg) break;
            if (i % 2 == pos && A[i] != 2) flg = false;
        }

        if (flg)
            for (int i = 0; i < N / 2; i++) ans = modmulti(ans, 2);

        out.println(flg ? ans : 0);

        out.flush();
    }

    // FastScanner start
    static final InputStream in = System.in;
    static final byte[] buffer = new byte[1024];
    static int ptr = 0;
    static int buflen = 0;
    static 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;
    }
    static int readByte() {
        if (hasNextByte()) return buffer[ptr++];
        else return -1;
    }
    static boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }
    static boolean hasNext() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
        return hasNextByte();
    }
    static 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();
    }
    static 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();
        }
    }
    static int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
            throw new NumberFormatException();
        return (int) nl;
    }
    static double nextDouble() {
        return Double.parseDouble(next());
    }
    // FastScanner end
}