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, q;

	Scanner s = new Scanner(System.in);
	int n = s.nextInt();
	int A[]= new int[n];
	    
	for(i=0; i<n; i++){
	    A[i] = s.nextInt();
	}
  
	q = partition(A, 0, n-1);

	for(i=0; i<n; i++){
	    if(i!=0) System.out.print(" ");
	    if(i==q) System.out.print("[");
	    System.out.print(A[i]);
	    if(i==q) System.out.print("]");
	}
	System.out.println();
    }
    
    public static int partition(int A[], int p, int r){
	int x, i, j, t;
	x = A[r];
	i = p-1;
	for(j=p; j<r; j++){
	    if(A[j]<=x){
		i++;
		t = A[i]; A[i] = A[j]; A[j] = t;
	    }
	}
	t = A[i+1]; A[i+1] = A[r]; A[r] = t;
	return i+1;
    }
}