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: Time Limit Exceeded)

import Data.List

scan :: [Int] -> Int
scan l = iter 0 sl where
    iter c [] = c
    iter c (x:xs) = case exist (f x) xs of
        Just nl -> iter (c+1) nl
        Nothing -> iter c xs
        where
            exist y = iter [] where
                iter _ [] = Nothing
                iter ac (x:xs)
                    | x == y = Just (join ac xs)
                    | otherwise = iter (x:ac) xs
            f x = iter 2 where
                iter p
                    | x < p = p - x
                    | otherwise = iter (p*2)
            join [] ys = ys
            join (x:xs) ys = join xs (x:ys)
             
    sl = reverse (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