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: Accepted)

import Control.Applicative((<$>))
import Control.Monad
import Data.Map ((!))
import qualified Data.Map as M
-- import Data.IntMap ((!))
-- import qualified Data.IntMap as M
import qualified Data.List as L
import Data.Maybe (catMaybes)
-- import qualified Data.Char as C
-- import qualified Data.IntSet as I
import Data.List (sort)
import Debug.Trace
--------------------------------------------
readInt    = read :: String -> Int
getInt     = readInt <$> getLine
getIntList = map readInt . words <$> getLine
int2bin 0 =  []
int2bin n =  n `mod` 2 : int2bin (n `div` 2)
----------------------------------------------

search = aux 0
  where
    aux c m (a:as)
      | c == m    = (a, head as)
      | otherwise = aux (c+1) m as

main :: IO ()
main = do
  n  <- getInt
  t_xs <- getIntList
  let
    xs = sort t_xs
    (n1, n2) = search (n `div` 2 - 1) xs
  forM_ t_xs $ \x ->
    print $ if x <= n1 then n2 else n1