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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Data.List

scan :: [Int] -> Int
scan l = iter 0 2 sl where
    iter c p [] = iter c (p*2) sl
    iter c p (x:xs)
        | p > limit = c
        | x > p = iter c (p*2) sl
        | d > 0 && elem d xs = iter (c+1) (p*2) sl  
        | otherwise = iter c p xs
        where d = p - x
    limit = 10 ^ 9
    sl = sort l
  
readData :: IO [Int]
readData = do
    line1 <- getLine
    let xs = map (\x -> read x :: Int) (words line1)
    return xs

main :: IO() 
main = do
    n  <- readLn :: IO Int
    la <- readData
    let ans = scan la
    print ans