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 [] 2 sl where
    iter ac p [] = iter ac (p*2) sl
    iter ac p (x:xs)
        | p > limit = count ac
        | x > p = iter ac (p*2) sl
        | d > 0 && elem d xs = iter ([x, d]:ac) p xs
        | otherwise = iter ac p xs
        where d = p - x
    limit = 10 ^ 9
    sl = sort l

count :: [[Int]] -> Int
count = iter [] where 
    iter ac [] = length ac
    iter ac ([a, b]:xs)
        | take1 >= drop1 = take1
        | otherwise = drop1
        where
            take1 = iter ([a, b]:ac) (filter (\x -> not (elem a x || elem b x)) xs)
            drop1 = iter ac xs
  
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