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: Wrong Answer)

import Control.Monad
import Text.Printf
import Control.Applicative
import Data.List as L

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 $ map (conv (fst vs, fst v) (n `div` 2) . snd ) tupleList
  where tupleList = sortOn fst $ zip x [1..]
        (_ , v:vs:vss) = splitAt ((n `div` 2) - 1) tupleList

conv :: (Int, Int) -> Int -> Int -> Int
conv (a, b) v1 v2 | v1 < v2 = a
                  | otherwise = b