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)

{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TupleSections #-}
import qualified Data.ByteString.Lazy.Char8 as B
import Data.Maybe
import Data.List
import Data.Bits
import qualified Data.IntSet as IS
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
-- import Control.Monad
-- import Control.Monad.ST
-- import Debug.Trace

solve :: Int -> [Int] -> Int
solve n as = answer
  where
  iset0 = IS.fromList as

  answer = sum $ unfoldr f iset0
    where
    f iset
      | IS.null iset = Nothing
      | IS.member x iset = Just (1, IS.delete x isetNxt)
      | otherwise        = Just (0, isetNxt)
      where (b, isetNxt) = IS.deleteFindMax iset
            x = btox b

btox b = setBit 0 (64 - (countLeadingZeros (b-1))) - b

readBInt :: B.ByteString -> Int
readBInt = fst . fromJust . B.readInt

tmain :: B.ByteString -> Int
tmain cont =
  let remLines0 = map B.words (B.lines cont)
      [bs_n]:remLines1 = remLines0
      n = readBInt bs_n
      line2:remLines2 = remLines1
      as = map readBInt line2
  in solve n as

outAnswer :: Int -> IO ()
outAnswer = putStrLn . show

main :: IO ()
main = outAnswer . tmain =<< B.getContents