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) {
		Scanner s = new Scanner(System.in);
		int arrayCnt = new Integer(s.nextLine()).intValue();
		int[] array = new int[arrayCnt];
		String[] tmpArray = s.nextLine().split(" ");
		for(int i=0 ; i<array.length ; i++) {
			array[i] = new Integer(tmpArray[i]).intValue();
		}
		String result = partition(array);
		System.out.println(result);
	}

	public static String partition(int[] array) {
		int index = 0;
		for(int i=0 ; i<array.length-1 ; i++) {
			if(array[i] <= array[array.length-1]) {
				int tmp = array[index];
				array[index] = array[i];
				array[i] = tmp;
				index++;
			}else {

			}
		}
		int tmp = array[index];
		array[index] = array[array.length - 1];
		array[array.length - 1] = tmp;
		StringBuilder b = new StringBuilder();
		for(int i=0 ; i<array.length ; i++) {
			if(index == i)
				b.append("[").append(array[i]).append("] ");
			else
				b.append(array[i]).append(" ");
		}
		return b.toString().trim();
	}
}