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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program main
	implicit none
    integer::n,i
    real(8)::t
    integer,allocatable::x(:),y(:)
    read(*,*) n
    allocate(x(n))
    allocate(y(n))
    
    read(*,*) x
    y=x
    call heapsort(n,y)
    
    t=(real(y(n/2),kind=8)+real(y(n/2 +1),kind=8))/2.0_8
    
    do i=1,n
    	if(real(x(i),8)<t)then
        	write(*,*) y(n/2 +1)
        else
        	write(*,*) y(n/2)
        end if
    end do
    
    deallocate(x)
    deallocate(y)
    
    
    stop
contains
	subroutine heapsort(n,array)
        implicit none
        integer,intent(in) :: n
        integer,intent(inout) :: array(1:n)
       
        integer ::i,k,j,l
        double precision :: t
       
        if(n.le.0)then
           write(6,*)"Error, at heapsort"; stop
        endif
        if(n.eq.1)return
      
        l=n/2+1
        k=n
        do while(k.ne.1)
           if(l.gt.1)then
              l=l-1
              t=array(L)
           else
              t=array(k)
              array(k)=array(1)
              k=k-1
              if(k.eq.1) then
                 array(1)=t
                 exit
              end if
           end if
           i=l
           j=l+l
           do while(j.le.k)
              if(j.lt.k)then
                 if(array(j).lt.array(j+1))j=j+1
              end if
              if (t.lt.array(j))then
                 array(i)=array(j)
                 i=j
                 j=j+j
              else
                 j=k+1
              endif
           end do
           array(i)=t
        end do
      
        return
    end subroutine heapsort
end program main