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 (
	"fmt"
	"sort"
)

func main() {
	var N int
	fmt.Scan(&N)
	all := make([]int, N)
	preall := make([]int, N)
	ReadN(all, 0, N)
	copy(preall, all)
	sort.Ints(all)

	s := all[N/2]
	m := N - 1 - N/2

	for i := 0; i < len(preall); i++ {
		if s > preall[i] {
			fmt.Println(s)
		} else {
			fmt.Println(all[m])
		}
	}
}

func ReadN(all []int, i, n int) {
	if n == 0 {
		return
	}
	if m, err := Scan(&all[i]); m != 1 {
		panic(err)
	}
	ReadN(all, i+1, n-1)

}

func Scan(a *int) (int, error) {
	return fmt.Scan(a)
}

func remove(ints []int, index int) []int {
	result := []int{}
	for i := 0; i < len(ints); i++ {
		if i != index {
			result = append(result, ints[i])
		}
	}
	return result
}