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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
)

func solve() {
	n := getInt()
	xs := getIntSlice(n)
	b1, b2 := func() (int, int) {
		tmp := make([]int, n)
		copy(tmp, xs)
		sort.Ints(tmp)
		return tmp[(n-1)/2], tmp[(n-1)/2+1]
	}()

	for _, x := range xs {
		ans := 0
		if x <= b1 {
			ans = b2
		} else {
			ans = b1
		}
		fmt.Fprintln(wr, ans)
	}
}

// -----------------------------------------

const (
	inf = 1 << 60
	// mod = 1000000007
)

var (
	sc = bufio.NewScanner(os.Stdin)
	wr = bufio.NewWriter(os.Stdout)
)

func main() {
	maxBufSize := int(1e8)
	sc.Buffer(make([]byte, 4096), maxBufSize)
	sc.Split(bufio.ScanWords)
	solve()
	wr.Flush()
}

func getInt() (ret int) {
	sc.Scan()
	ret, err := strconv.Atoi(sc.Text())
	if err != nil {
		panic(err)
	}
	return
}

func getIntSlice(n int) (ret []int) {
	ret = make([]int, n)
	for i := range ret {
		ret[i] = getInt()
	}
	return
}

func getString() (ret string) {
	sc.Scan()
	ret = sc.Text()
	return
}

func getRunes() (ret []rune) {
	ret = []rune(getString())
	return
}