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: Accepted)

import Data.List
import qualified Data.IntMap.Strict as M
import qualified Data.ByteString.Char8 as B

p2s = map (2^) [1..32]
main=do
    _<-getLine
    as<-foldl' (\m a->M.insertWith (+) a 1 m) M.empty.unfoldr (B.readInt.B.dropWhile(==' '))<$>B.getLine
    print $ sum $ unfoldr s as
s as
    | M.null as = Nothing
    | fcc == k  = Just(a`div`2, as')
    | otherwise = case M.lookup fcc as' of
        Nothing -> Just(0, as')
        Just b  -> if b<=a
                    then Just(b, M.delete fcc as')
                    else Just(a, M.insert fcc (b-a) as')
    where
        ((k,a), as') = M.deleteFindMax as
        fc = head $ dropWhile (<k) p2s
        fcc = if fc==k then k else fc-k