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)

// きりみんちゃんの配信からきました
// 答えは2種類ぽくなりそう（いまみてるのが全体の中央値以外なら中央値になるし、そうじゃない==中央値自身ならばひとつずれる）

package main

import (
	"fmt"
	"sort"
)

var n int
var x []int

func main() {
	fmt.Scan(&n)
	x = make([]int, n)
	for i := 0; i < n; i++ {
		var j int
		fmt.Scan(&j)
		x[i] = j
	}
	tmp := append([]int{}, x...)
	sort.Ints(tmp)
	one, two := tmp[n/2-1], tmp[n/2]
	for i := 0; i < n; i++ {
		if x[i] <= one {
			fmt.Println(two)
		} else {
			fmt.Println(one)
		}
	}
}