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.Monad
import Text.Printf
import Control.Applicative
import qualified Data.Vector as V
import qualified Data.List as L (sortOn)

main :: IO()
main = do
  [n] <- map read . words <$> getLine
  x <- map read . words <$> getLine
  printf "%s\n" $ slv n x

slv :: Int -> [Int] -> String
slv n x = unlines $ map (show . snd) $ L.sortOn fst $ V.toList $ V.map (conv (fst(fst left), fst(fst right)) (n `div` 2)) vec
-- slv n x = unlines $ map (show . snd) $ L.sortOn fst $ V.toList $ V.map (conv (fst left, fst right) (n `div` 2) . snd) vec
  where vec = V.fromList $ zip (L.sortOn fst $ zip x [0..]) [0..]
        (left, right) = (vec V.! ((n `div` 2) - 1), vec V.! (n `div` 2))

conv :: (Int, Int) -> Int -> ((Int, Int), Int) -> (Int, Int)
conv (left, right) bIdx ((val, pidx), idx) | bIdx <= idx = (pidx, left)
                                           | otherwise = (pidx, right)