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: Time Limit Exceeded)


#include<stdio.h>
#include<string.h>

void sort(int data[], int n){
    int temp;
    for(int i = 0; i < n; i++){
        for(int j = i + 1; j < n; j++){
            if(data[i] < data[j]){
                temp = data[i];
                data[i] = data[j];
                data[j] = temp;
            }
        }
    }
}

int main(void){
    int n;
    scanf("%d", &n);
    int data1[n], data2[n];
    for(int i = 0; i < n; i++){
        scanf("%d", &data1[i]);
    }
    for(int i = 0; i < n; i++){
        memcpy(data2, data1, sizeof(data1));
        data2[i] = 0;
        sort(data2, n);
        printf("%d\n", data2[n / 2 - 1]);
    }
    return 0;
}