Problem:
Score : 300 points

Problem Statement

When l is an odd number, the median of l numbers a_1, a_2, ..., a_l is the (\frac{l+1}{2})-th largest value among a_1, a_2, ..., a_l.

You are given N numbers X_1, X_2, ..., X_N, where N is an even number.
For each i = 1, 2, ..., N, let the median of X_1, X_2, ..., X_N excluding X_i, that is, the median of X_1, X_2, ..., X_{i-1}, X_{i+1}, ..., X_N be B_i.

Find B_i for each i = 1, 2, ..., N.

Constraints

2 \leq N \leq 200000

N is even.

1 \leq X_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
X_1 X_2 ... X_N

Output

Print N lines.
The i-th line should contain B_i.

Sample Input 1

4
2 4 4 3

Sample Output 1

4
3
3
4

Since the median of X_2, X_3, X_4 is 4, B_1 = 4.

Since the median of X_1, X_3, X_4 is 3, B_2 = 3.

Since the median of X_1, X_2, X_4 is 3, B_3 = 3.

Since the median of X_1, X_2, X_3 is 4, B_4 = 4.

Sample Input 2

2
1 2

Sample Output 2

2
1

Sample Input 3

6
5 5 4 4 3 3

Sample Output 3

4
4
4
4
4
4

Solution in Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Control.Applicative ((<$>))
import Data.ByteString.Char8 (ByteString)
import qualified Data.ByteString.Char8 as B
import Data.List
import Data.Function (on)
import Data.Char (isSpace)

main :: IO ()
main = do
  n <- readLn
  solve n <$> getl (readil B.readInt) >>= mapM_ print

solve :: Int -> [(Int,Int)] -> [Int]
solve n xs = map f [1..n]
  where
    ls = sortBy (compare `on` snd) xs
    lm = snd $ ls !! (n `div` 2 - 1)
    rm = snd $ ls !! (n `div` 2)
    ll = map fst $ take (n `div` 2) ls
    f i | i `elem` ll = rm
        | otherwise = lm
    
getl :: (ByteString -> a) -> IO a
getl f = f <$> B.getLine

readil :: Integral a =>  (ByteString -> Maybe (a, ByteString)) -> ByteString -> [(Int,a)]
readil f x = unfoldr g (1, x)
  where
    g (i, s) = do
      (n, s') <- f s
      return ((i,n), (i+1, B.dropWhile isSpace s'))