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.*;
import java.util.*;
public class Main {

	public static void main(String[] args) {
		Scanner in=new Scanner(System.in);
		
		int n=in.nextInt();List<Integer> A=new ArrayList<>();
		for(int i=0;i<n;i++) {
			//A[i]=Integer.parseInt(in.next());
			A.add(Integer.parseInt(in.next()));
		}
		
		
		PrintWriter out=new PrintWriter(System.out);
		A=partition(A);int r=A.get(A.size()-1);
		for(int i=0;i<A.size()-2;i++) {
			if(i==r)out.print("["+A.get(i)+"] ");
			else out.print(A.get(i)+" ");
		}
		out.println(A.get(A.size()-2));
		out.flush();

	}
	
	static List<Integer> partition(List<Integer> A){
		int r=A.size()-1,x=A.get(r),i=-1;
		
		if(A.get(0)<=x)i++;
		for(int j=1;j<r;j++) {
			if(A.get(j)<=x) {
				i++;
				Collections.swap(A, i, j);
			}
		}
		
		i++;
		
		if(i<r && A.get(i)>x) {
			Collections.swap(A, i, r);
		}
		A.add(i);
		return A;
	}

}

