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) {
    let cin = new Inputer(input);
    let N = cin.getInt()
    let X = cin.getIntArray(N).map((v, i) => { return { value: v, index: i } });
    X.sort((a, b) => a.value - b.value);
    let P = new Array(N);
    for (let n = 0; n < N; n++) {
        P[X[n].index] = n;
    }
    let c = N / 2;
    for (let n = 0; n < N; n++) {
        let i = P[n] >= c ? c - 1 : c;
        console.log(X[i].value);
    }
}
class Inputer{constructor(t){if(typeof t=='undefined')throw new Error('引数（stdin）を省略できません！');this.cnt=0,this.items=t.split(/\n|\s/)}getInt(){return this.items[this.cnt++]-0}getIntArray(t){if(typeof t=='undefined')throw new Error('引数（1以上）を省略できません！');let r=new Array(t);for(let e=0;e<t;e++)r[e]=this.getInt();return r}getStr(){return this.items[this.cnt++]}getStrArray(t){if(typeof t=='undefined')throw new Error('引数（1以上）を省略できません！');let r=new Array(t);for(let e=0;e<t;e++)r[e]=this.getStr();return r}}
if (typeof window == "undefined") Main(require("fs").readFileSync("/dev/stdin", "utf8"));