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.to_i
a = gets.chomp.split(" ").map(&:to_i)
a = a.sort
ans = 0
two = []
for i in 1..40
  two.push(2**i)
  if 2**i > 10**9
    two.delete_at(-1)
    break
  end
end
for i in 1..two.length
  min = 0
  max = a.length-1
  for j in 1..a.length-1
    if a[min] + a[max] > two[-i]
      max -= 1
    elsif a[min] + a[max] < two[-i]
      min += 1
    elsif a[min] + a[max] == two[-i]
      ans += 1
      a.delete_at(min)
      a.delete_at(max)
      max -= 2
    end
    if min >= max
      break
    end
  end
end
puts ans