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 Data.List
import Data.Ord
import Data.Function

type Index = Int

numberingSort :: [Int] -> [(Index, Int)]
numberingSort = sortBy (comparing snd) . zip [1..]

deleteIndex :: Index -> [(Index, Int)] -> [(Index, Int)]
deleteIndex i = deleteBy ((==) `on` fst) (i,0)

manyMedians n xs = [takeMedian i | i <- [1..n]]
    where
        sorted = numberingSort xs
        middleIndex = (n - 1) `div` 2
        takeMedian i = snd $ genericIndex (deleteIndex i sorted) middleIndex

main :: IO ()
main = do
    n <- read <$> getLine
    xs <- map read . words <$> getLine
    putStrLn . unwords . map show $ manyMedians n xs