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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
	n,i,ma,mb:Longint;
	a:array[1..200000]of Longint;
function f(c:Longint):Longint;
var L,R,M,cnt,i:Longint;
begin
	L:=0;
	R:=1000000001;
	while R-L>1 do begin
		M:=(L+R)div 2;
		cnt:=0;
		for i:=1 to n do if a[i]<=M then inc(cnt);
		if cnt>=c then R:=M else L:=M;
	end;
	f:=R;
end;
begin
	read(n);
	for i:=1 to n do read(a[i]);
	ma:=f(n div 2+1);
	mb:=f(n div 2);
	for i:=1 to n do if a[i]<ma then writeln(ma)else writeln(mb);
end.