Problem:
Score : 600 points

Problem Statement

Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i.
He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2.
Note that a ball cannot belong to multiple pairs.
Find the maximum possible number of pairs that can be formed.

Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.

Constraints

1 \leq N \leq 2\times 10^5

1 \leq A_i \leq 10^9

A_i is an integer.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.

Sample Input 1

3
1 2 3

Sample Output 1

1

We can form one pair whose sum of the written numbers is 4 by pairing the first and third balls.
Note that we cannot pair the second ball with itself.

Sample Input 2

5
3 11 14 5 13

Sample Output 2

2

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

n=gets.chomp.to_i
if n == 1
  puts 0
  exit
end
ary=gets.chomp.split(' ').map(&:to_i)
cary = ary.combination(2)
tary = []
30.times do |i|
  i += 1
  tary << 2**i
end
cdt = []
cary.each do |c|
  cdt << c if tary.any? { |t| t == (c[0] + c[1]) }
end
pr = cdt
f_pr = pr.flatten
hsh = {}
pr.each_with_index do |pa, i|
  if hsh[pa[0]]
    a0 = hsh[pa[0]]
  else
    a0 = f_pr.count(pa[0])
    hsh[pa[0]] = a0
  end
  if hsh[pa[1]]
    a1 = hsh[pa[1]]
  else
    a1 = f_pr.count(pa[1])
    hsh[pa[1]] = a1
  end
  if a0 > 1 && a1 > 1
  	pr.delete_at(i)
    f_pr.delete_at(f_pr.index(pa[0]))
    f_pr.delete_at(f_pr.index(pa[1]))
    hsh[pa[0]] -= 1
    hsh[pa[1]] -= 1
  end
end
pr.each_with_index do |pa, i|
  if hsh[pa[0]]
    a0 = hsh[pa[0]]
  else
    a0 = f_pr.count(pa[0])
    hsh[pa[0]] = a0
  end
  if hsh[pa[1]]
    a1 = hsh[pa[1]]
  else
    a1 = f_pr.count(pa[1])
    hsh[pa[1]] = a1
  end
  if a0 > 1 || a1 > 1
  	pr.delete_at(i)
    f_pr.delete_at(f_pr.index(pa[0]))
    f_pr.delete_at(f_pr.index(pa[1]))
    hsh[pa[0]] -= 1
    hsh[pa[1]] -= 1
  end
end
puts pr.size