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.*;

public class Main {
	public static void main(String args[]){
		Scanner sc =new Scanner(System.in);
		int n = sc.nextInt();
		int[] nums = new int[n];
		for(int i=0;i<n;i++){
			nums[i] = sc.nextInt();
		}
		int index = partition(nums,0,nums.length-1);
		for(int i=0;i<n;i++){
			if(i!=index){
				if(i!=0)System.out.print(" "+nums[i]);
				else System.out.print(nums[i]);
			}else{
				System.out.print(" ["+nums[i]+"]");
			}
		}
		System.out.println();
	}
	public static int partition(int[] A,int l,int r){
		int pivot = A[r];
		int left = l; 
		while(l<r){
			if(A[l]<=pivot){
				swap(A,l,left);
				left++;
			}
			l++;
		}
		swap(A,r,left);
		return left ;
		
	}
	public static  void swap(int[] A,int i,int j){
		int tmp = A[i];
		A[i] = A[j];
		A[j] = tmp; 
	}
}