Quick sort is based on the Divide-and-conquer approach. In QuickSort(A, p, r), first, a procedure Partition(A, p, r) divides an array A[p..r] into two subarrays A[p..q-1] and A[q+1..r] such that each element of A[p..q-1] is less than or equal to A[q], which is, inturn, less than or equal to each element of A[q+1..r]. It also computes the index q.

In the conquer processes, the two subarrays A[p..q-1] and A[q+1..r] are sorted by recursive calls of QuickSort(A, p, q-1) and QuickSort(A, q+1, r).

Your task is to read a sequence A and perform the Partition based on the following pseudocode:


Partition(A, p, r)
1 x = A[r]
2 i = p-1
3 for j = p to r-1
4     do if A[j] <= x
5        then i = i+1
6            exchange A[i] and A[j]
7 exchange A[i+1] and A[r]
8 return i+1


Note that, in this algorithm, Partition always selects an element A[r] as a pivot element around which to partition the array A[p..r].

Constraints

* 1 ≤ n ≤ 100,000
* 0 ≤ Ai ≤ 100,000

Input

The first line of the input includes an integer n, the number of elements in the sequence A.

In the second line, Ai (i = 1,2,...,n), elements of the sequence are given separated by space characters.

Output

Print the sorted sequence. Two contiguous elements of the sequence should be separated by a space character. The element which is selected as the pivot of the partition should be indicated by [  ].

Example

Input

12
13 19 9 5 12 8 7 4 21 2 6 11


Output

9 5 8 7 4 2 6 [11] 21 13 19 12
import java.util.Scanner;
public class Main{
    public static void main(String args[]){
	int i,n,j,p,r,hz,x;
	Scanner scat=new Scanner(System.in);
	n=scat.nextInt();
	int A[]=new int[n];
	for(i=0;i<n;i++){
	    A[i]=scat.nextInt();
	}
	p=0;
	r=n-1;
	x=A[r];
	i=p-1;
	for(j=p;j<r;j++){
	    if(A[j]<=x){
		i++;
		hz=A[i];
		A[i]=A[j];
		A[j]=hz;
	    }
	}
	hz=A[i+1];
	A[i+1]=A[r];
	A[r]=hz;
	for(j=0;j<n;j++){
	    if(j!=0) System.out.print(" ");
	    if(j!=i+1){
		System.out.print(A[j]);
	    }else{
		System.out.print("["+A[j]+"]");
	    }
	}
	System.out.println("");
    }
}

