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 a,c,ans:array[0..2050000]of longint;
    i:longint;
    n:longint;
procedure qs(l,r:longint);
var i,j,m,t:longint;
begin
  i:=l;
  j:=r;
  m:=a[(l+r)>>1];
  repeat
    while a[i]<m do inc(i);
    while a[j]>m do dec(j);
    if i<=j then
    begin
      t:=a[i];a[i]:=a[j];a[j]:=t;
      t:=c[i];c[i]:=c[j];c[j]:=t;
      inc(i);
      dec(j);
    end;
  until i>j;
  if l<j then qs(l,j);
  if i<r then qs(i,r);
end;
begin
  read(n);
  for i:=1 to n do
  begin
    read(a[i]);
    c[i]:=i;
  end;
  qs(1,n);
  for i:=1 to n do
  if i>n div 2 then ans[c[i]]:=a[n div 2] else ans[c[i]]:=a[n div 2+1];
  for i:=1 to n do
  writeln(ans[i]);
end.