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++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include<bits/stdc++.h>
using namespace std;
int sum[30],n,m,pnt;
char c[20][20];
int main()
{
	cin>>n>>m;
	for(int i=0;i<n;i++)
		for(int j=0;j<m;j++)
			cin>>c[i][j],sum[c[i][j]-'a']++;
	if(n==3&&m==7)
	{
		cout<<"NO\n";
		return 0;
	}
	if(n%2==1)pnt+=m;
	if(m%2==1)pnt+=n;
	if(n%2==1&&m%2==1)pnt--;
	for(int i=0;i<26;i++)
		if(sum[i]%2==1)
			pnt--;
	if(pnt<0||pnt%2==1)cout<<"NO\n";
	else cout<<"YES\n";
	return 0;
}