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>
int compare(const void* a, const void* b){
    return *(int*)a - *(int*)b;
}

int main(void){
    int n;
    scanf("%d", &n);
    int x[n][2];
    for(int i=0; i<n; i++){
        scanf("%d", &x[i][0]);
        x[i][1] = i;
    }

    qsort(x, n, sizeof(int)*2, compare);

    int ans[n];
    for(int i=0; i<(n/2); i++){
        ans[x[i][1]] = x[n/2][0];
    }
    for(int i=n/2; i<n; i++){
        ans[x[i][1]] = x[(n/2)-1][0];
    }

    for(int i=0; i<n; i++){
        printf("%d\n", ans[i]);
    }

    return 0;

}