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>
//小さい順にソート
int c[200002];
void merge(int i,int j,int *s){
  if(i!=j){
    merge(i,(i+j)/2,s);
    merge((i+j)/2+1,j,s);
    int a=i,b=(i+j)/2+1;
    int d;
    for(d=i;d<=j;d++){
      if((i+j)/2<a){
        c[d]=s[b];
        b++;
      }
      else if(j<b){
        c[d]=s[a];
        a++;
      }
      else if(s[a]<s[b]){
        c[d]=s[a];
        a++;
      }
      else{
        c[d]=s[b];
        b++;
      }
    }
    for(d=i;d<=j;d++)
      s[d]=c[d];
  }
}

int main(){
  int n,i;
  scanf("%d",&n);
  int x[n+1],b[n+1];
  for(i=0;i<n;i++){
    scanf("%d",&x[i]);
    b[i]=x[i];
  }
  merge(0,n-1,x);
  for(i=0;i<n;i++){
    if(b[i]<x[n/2])
      printf("%d\n",x[n/2]);
    else
      printf("%d\n",x[n/2-1]);
  }
  return 0;
}