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 Ruby (2.3.3) (judge verdict: Wrong Answer)

# value に一致する値を持つインデクスを返却する
def get_indexes(nums, value)
   nums.each_with_index.select {|x| x[0] == value}.map { |x| x[1]+1 }
end

def get_center_index(nums)
    ret = []
    if (N % 2) == 0
        ret = get_indexes(nums, 1)
        return 0 unless ret.size == 2
    else
        ret = get_indexes(nums, 0)
        return 0 if ret.empty? # 奇数のとき、必ず真ん中に位置する数が存在する
    end
    ret
end

N = gets.to_i
arr = gets.split(' ').map(&:to_i)

hasi = get_indexes(arr, N-1)

unless hasi.size == 2
  STDOUT.puts 0
  exit
end

center = []
if (N % 2) == 0
    center = get_indexes(arr, 1)
    unless center.size == 2
      STDOUT.puts 0
      exit
    end
else
    center = get_indexes(arr, 0)
    if center.empty? # 奇数のとき、必ず真ん中に位置する数が存在する
        STDOUT.puts 0
        exit
    end
end

STDOUT.puts 2 ** (N/2)