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: Accepted)

n=gets.to_i
a=gets.split.map &:to_i
a.sort!
c=0
31.downto(1){|s|
  i=0
  j=a.size-1
  while i<j
    if !a[i]
      i+=1
    elsif !a[j]
      j-=1
    else
      k=a[i]+a[j]-2**s
      if k<0
        i+=1
      elsif k>0
        j-=1
      else
        c+=1
        a[i]=a[j]=nil
        i+=1
        j-=1
      end
    end
  end
}
p c