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 JavaScript (node.js v5.12) (judge verdict: Accepted)


'use strict'

function main(input) {

    input = input.split('\n')
    const n = ~~input[0]
    const x = input[1].split(' ').map(v => ~~v) //.sort((a, b) => a - b)
    const x2 = x.slice(0).sort((a, b) => a - b)
    const mid = x2[n / 2]
    const mid2 = x2[n / 2 - 1]

    let ans = 0
    for (let i = 0; i < n; i++) {
        if (x[i] < mid) ans = mid
        else ans = mid2
        console.log(ans)
    }
}

main(require("fs").readFileSync("/dev/stdin", "utf8"));