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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;


public class Main {
	static int count=0;
	public static void main(String[] args) throws NumberFormatException, IOException {
		//????????????????????????
		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));

		
		//?????????
		int n = Integer.parseInt(bf.readLine());
		ArrayList<Integer> array=new ArrayList<Integer>();
		String[] list=bf.readLine().split(" ");
		for(int i=0;i<n;i++){
			array.add(Integer.parseInt(list[i]));
		}
		
		
		int q=partition(array, 0, array.size()-1);
		
		for(int i=0;i<array.size();i++){
			if(i!=0){
				System.out.printf(" ");
			}
			if(i==q){
				System.out.printf("[");
			}
			System.out.printf("%d",array.get(i));
			if(i==q){
				System.out.printf("]");
			}

		}
		System.out.println("");
	}
	
	public static int partition(ArrayList<Integer> array,int p,int r){
		int x=array.get(r);
		int i=p-1;
		
		for(int j=p;j<r;j++){
			if(array.get(j)<=x){
				i++;
				int tmp=array.get(i);
				array.set(i, array.get(j));
				array.set(j, tmp);
			}
		}
		
		int tmp=array.get(i+1);
		array.set(i+1, array.get(r));
		array.set(r, tmp);
		
		return i+1;
		
	}

}