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 in=new Scanner(System.in);
		int n=in.nextInt(),A[]=new int[n];

		for(int i=0;i<n;i++)A[i]=Integer.parseInt(in.next());

		int stdIndex=partition(A,n,A[n-1]);

		for(int i=0;i<n-1;i++) {
			if(i==stdIndex) {
				System.out.print("["+A[i]+"] ");
			}
			else System.out.print(A[i]+" ");
		}
		if(n-1==stdIndex) {
			System.out.println("["+A[n-1]+"]");
		}
		else System.out.println(A[n-1]);
	}

	static int partition(int A[],int n,int std) {
		int i=0;
		do {
			while(i<n && A[i]<=std)i++;
			if(i==n)return i-1;

			int j=i;
			while(j<n && A[j]>std)j++;

			int tmp=A[i];
			A[i]=A[j];
			A[j]=tmp;

			if(j==n-1)return i;
		}while(true);
	}

}

