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"
)

type Num struct {
	Num   int
	Index int
}

type Nums []Num

func (n Nums) Len() int {
	return len(n)
}

func (n Nums) Swap(i, j int) {
	n[i], n[j] = n[j], n[i]
}

func (n Nums) Less(i, j int) bool {
	return n[i].Num < n[j].Num
}

func main() {
	var N int
	fmt.Scan(&N)
	nums := scanNums(N)
	_nums := Nums{}
	for _, num := range nums {
		_nums = append(_nums, num)
	}
	sort.Sort(nums)
	half := (N + 1) / 2
	numMap := map[int]int{}
	for i := 0; i < N; i++ {
		_half := half
		if i >= half {
			_half = half - 1
		}
		numMap[nums[i].Num] = nums[_half].Num
	}
	for _, num := range _nums {
		fmt.Println(numMap[num.Num])
	}
}

func scanNums(len int) (nums Nums) {
	var num int
	for i := 0; i < len; i++ {
		fmt.Scan(&num)
		nums = append(nums, Num{Num: num, Index: i})
	}
	return nums
}