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>
int a[200005];
void pai(int *a,int n)
{
    int i,j,x,t;
    for(i=0; i<n; i++)
    {
        x=i;
        for(j=i; j<n; j++)
        {
            if(a[x]<=a[j])
                x=j;
        }
        if(x!=i)
        {
            t=a[i];
            a[i]=a[x];
            a[x]=t;
        }
    }
}
int main()
{
    int b[200005];
    int n,i;
    scanf("%d",&n);
    for(i=0; i<n; i++)
    {
        scanf("%d",&a[i]);
    }
    for(i=0; i<n; i++)
    {
        b[i]=a[i];
    }
    pai(b,n);
    for(i=0;i<n;i++)
    {
        if(a[i]<=b[n/2])
        {
            printf("%d\n",b[n/2-1]);
        }
        else if(a[i]>=b[n/2-1])
            printf("%d\n",b[n/2]);
    }

    return 0;
}