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.IntMap.Strict (IntMap,Key)
import qualified Data.IntMap.Strict as IM

main = do
  getLine
  as <- map read.words<$>getLine
  print $ solve as

solve as = go ims where
  ims = IM.fromListWith (+) $ zip as $ repeat 1
  go :: IntMap Int -> Int
  go ims
    | IM.null ims = 0
    | otherwise = case IM.lookup d ims of
      Nothing -> go newIms
      Just 1 -> 1 + go (IM.delete d newIms)
      Just n -> 1 + go (IM.adjust pred d newIms)
    where
    newIms = case mn of
      1 -> IM.delete m ims
      _ -> IM.adjust pred d ims
    (m,mn) = IM.findMax ims
    d = 2^ceiling(logBase 2 $ fromIntegral m)-m