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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
fscanf(STDIN, "%d", $n);
$Aarray = explode(' ', trim(fgets(STDIN))); # Aiの配列
$count = array_count_values($Aarray);   # Aiの要素 => 登場回数 の配列
$count_0 = $count[0];   # Aiの中での0の登場回数
unset($count[0]);    # 0を 「Aiの要素 => 登場回数 の配列」 から削除する。unset()はindexを変更しない。
$isodd = array_map('odd', $Aarray); # Aiが奇数ならtrue、偶数ならfalseの配列
$istwo = array_map('two', $count); # 0を除くAiが2回登場するならtrue、そうでないならfalseの配列
$tr = array(TRUE);
$fl = array(0); # FALSEを指定すると配列が空になる
$allodd = array_diff($isodd, $tr);  # Aiが全て奇数なら空の配列
$alleven = array_diff($isodd, $fl); # Aiが全て偶数なら空の配列 
$alltwo = array_diff($istwo, $tr);  # 0を除くAiが全て2回登場するなら空の配列

if($n & 1){
    if((! $alleven) && ($count_0 === 1) && (! $alltwo)){
        print (2**(($n-1)/2)) % ((10**9)+7);
    }else{
        print 0;
    }
}else{
    if((! $allodd) && (! $count_0) && (! $alltwo)){
        print (2**($n/2)) %  ((10**9)+7);
    }else{
        print 0;
    }

}

function odd($var)
{
    // 渡された整数が奇数かどうかを返します
    return($var & 1);
}

function two($var)
{
    // 渡された整数が2かどうかを返します
    return($var === 2);
}