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)

{-# 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.IntMap.Strict as IM
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
  imap0 = foldl' op IM.empty as
    where op im a = IM.insertWith (+) a 1 im

  answer = sum $ unfoldr f imap0
    where
    f imap
      | IM.null imap = Nothing
      | x == b       = Just (m `div` 2, IM.delete x imapNxt)
      | otherwise    = fsub (IM.lookup x imap)
      where
      fsub Nothing = Just (0, imapNxt)
      fsub (Just k) | k <= m = Just (k, IM.delete x imapNxt)
                    | otherwise = Just (m, IM.adjust (+ (- m)) x imapNxt)
      ((b, m), imapNxt) = IM.deleteFindMax imap
      x = btox b

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