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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#define ll long long
#define rep(i,l,r) for(ll i=(l);i<(r);i++)
#define max(p,q) ((p)>(q)?(p):(q))
#define min(p,q) ((p)<(q)?(p):(q))
#define abs(p) ((p)>=(0)?(p):(-(p)))
int cmp(const void *a, const void *b);
int main(void){
    ll N, X[200005], Xcp[200005];
    scanf("%lld", &N);
    rep(i, 0, N){
        scanf("%lld", X+i);
        Xcp[i] = X[i];
    }
    qsort(X, N, sizeof(ll), cmp);
    rep(i, 0, N){
        if(Xcp[i]<X[N/2])printf("%lld\n", X[N/2]);
        else printf("%lld\n", X[N/2 -1]);
    }
    return 0;
}
int cmp(const void *a, const void *b){
    ll A=*(ll *)a, B=*(ll *)b;
    if(A==B)return 0;
    else return A>B ? 1:-1;//昇順ソート
}