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.split.map(&:to_i)
h = Hash.new(0)
a.sort!.reverse!
a.each{|t| h[t]+=1}

def f(x)
  res = 1
  while x>0
    x /= 2
    res *= 2
  end
  res
end

ans = 0
a.each{|t|
  r = f(t)
  p [t,r-t]
  if t==r-t
    if h[t]>=2
      h[t]-=2
      ans+=1
    end
  else
    if h[r-t]>=1 && h[t]>=1
      h[t]-=1
      h[r-t]-=1
      ans+=1
    end
  end
}

p ans