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.io.InputStream;
import java.util.*;
import java.util.function.IntFunction;
import java.util.function.Supplier;
import java.util.stream.IntStream;
import java.util.stream.Stream;


public class Main {
    static int x;
    public static void main(String[] args) {
        Scanner scanner = new Scanner();
        int n=scanner.nextInt();
        int[] a=new int[n];
        for(int i=0;i<n;i++){
            a[i]=scanner.nextInt();
        }
        Arrays.sort(a);
        if(n%2==0){
            for(int i=0;i<n;i++){
                if(a[i]!=i/2*2+1){
                    put(0);
                    return;
                }
            }
        }else{
            if(a[0]!=0){
                put(0);
                return;
            }
            for(int i=1;i<n;i++){
                if(a[i]!=(i+1)/2*2){
                    put(0);
                    return;
                }
            }
        }
        long result=1;
        for(int i=0;i<n/2;i++){
            result*=2;
            result%=(1000_000_000+7);
        }
        put(result);

    }


    public static int max(int a,int b){
        return Math.max(a,b);
    }
    public static long max(long a,long b){
        return Math.max(a,b);
    }
    public static int abs(int a){
        return Math.abs(a);
    }
    public static long abs(long a){
        return Math.abs(a);
    }
    public static void print(Object object){
        System.out.print(object);
    }
    public static void put(Object object) {
        System.out.println(object);
    }
    public static void put(){
        System.out.println();
    }
    public static String format(String string, Object... args) {
        return String.format(string, args);
    }
}

final class Scanner {
    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 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());
    }
}
final class Pair {
    final public int x, y;
    Pair(int x, int y) {
        this.x = x;
        this.y = y;
    }

    @Override
    public int hashCode() {
        return x+y;
    }

    @Override
    public boolean equals(Object obj) {
        boolean result=super.equals(obj);
        if(obj.getClass()!=this.getClass()){
            return false;
        }
        Pair pair=(Pair)obj;
        if(this.x==pair.x&&this.y==pair.y) return true;
        return false;
    }

    @Override
    public String toString() {
        return String.format("(%d,%d)", x, y);
    }
}
final class Tuple<T,V>{
    //immutabl1でないことに注意(T,Vがmutableの場合変更可能)
    final private T t;
    final private V v;
    Tuple(T t,V v){
        this.t=t;
        this.v=v;
    }

    public T getT() {
        return t;
    }

    public V getV() {
        return v;
    }

    @Override
    public int hashCode() {
        return (t.hashCode()+v.hashCode());
    }

    @Override
    @SuppressWarnings("unchecked")
    public boolean equals(Object obj) {
        if(obj.getClass()!=this.getClass()){
            return false;
        }
        Tuple<T,V> tuple=(Tuple<T, V>) obj;
        return tuple.t.equals(this.t)&&tuple.v.equals(this.v);
    }

    @Override
    public String toString() {
        return String.format("<Tuple>=<%s,%s>",t,v);
    }
}
final class LowerBoundComparator<T extends Comparable<? super T>>
        implements Comparator<T>
{
    public int compare(T x, T y)
    {
        return (x.compareTo(y) >= 0) ? 1 : -1;
    }
}

final class UpperBoundComparator<T extends Comparable<? super T>>
        implements Comparator<T>
{
    public int compare(T x, T y)
    {
        return (x.compareTo(y) > 0) ? 1 : -1;
    }
}
final class Util {
    static long gcd(long a,long b){
        if(a%b==0)return b;
        return gcd(b,a%b);
    }
    static long lcm(long a,long b){
        long gcd=gcd(a,b);
        long result=b/gcd;
        return a*result;
    }
    static long kaijoMod(int n,int mod){
        if(n<1) return -1;
        long result=1;
        for(int i=n;i>1;i--){
            result*=i;
            result%=mod;
        }
        return result;
    }
    static <T extends Comparable<T>> Map<T,Integer> count(List<T> list){
        //副作用
        Collections.sort(list);
        Map<T,Integer> result=new HashMap<>();
        int l=0,r=0;
        while(l<list.size()){
            while(r<list.size()-1&&list.get(r).equals(r+1)){
                r++;
            }
            result.put(list.get(r),r-l+1);
            r++;
            l=r;
        }
        return result;

    }
    static Map<Integer,Integer> count(int[] array){
        //副作用
        Arrays.sort(array);
        Map<Integer,Integer> result=new HashMap<>();
        int l=0,r=0;
        while(l<array.length){
            while(r<array.length-1&&array[r]==array[r+1]){
                r++;
            }
            result.put(array[l],r-l+1);
            r++;
            l=r;
        }
        return result;
    }
    static <T> String toStringBWS(Iterable<T> iterable){
        Iterator<T> ite=iterable.iterator();
        return toStringBWS(ite);
    }
    static <T> String toStringBWS(Iterator<T> ite){
        StringBuilder sb=new StringBuilder();
        sb.append(ite.next());
        while(ite.hasNext()){
            sb.append(" ");
            sb.append(ite.next());
        }
        return sb.toString();
    }
    static String toStringBWS(int[] array){
        StringBuilder sb=new StringBuilder();
        for(int i=0;i<array.length-1;i++){
            sb.append(array[i]);
            sb.append(" ");
        }
        sb.append(array[array.length-1]);
        return sb.toString();
    }
    static String toStringBWS(long[] array){
        StringBuilder sb=new StringBuilder();
        for(int i=0;i<array.length-1;i++){
            sb.append(array[i]);
            sb.append(" ");
        }
        sb.append(array[array.length-1]);
        return sb.toString();
    }
}