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"
)

type rec struct {
	v, idx int
}
type recs []rec

func (r recs) Len() int {
	return len(r)
}
func (r recs) Swap(i, j int) {
	r[i], r[j] = r[j], r[i]
}

type byIdx struct {
	recs
}
type byValue struct {
	recs
}

func (b byIdx) Less(i, j int) bool {
	return b.recs[i].idx < b.recs[j].idx
}
func (b byValue) Less(i, j int) bool {
	return b.recs[i].v < b.recs[j].v
}

func main() {
	var N int
	fmt.Scan(&N)
	X := make([]rec, N)
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	for i := range X {
		sc.Scan()
		X[i].v, _ = strconv.Atoi(sc.Text())
		X[i].idx = i
	}
	sort.Sort(byValue{X})
	m1 := X[len(X)/2-1].v
	m2 := X[len(X)/2].v
	sort.Sort(byIdx{X})
	for i := 0; i < len(X); i++ {
		if X[i].v <= m1 {
			fmt.Println(m2)
		} else {
			fmt.Println(m1)
		}
	}
}