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 {
	Scanner sc = new Scanner(System.in);
	
	//配列の要素数
	int n;
	//配列Aの最後の要素を示す変数
	int x;
	//交換のための変数
	int swap;
	//partition発見のための変数
	int i;
	//要素が格納される配列
	int[] A;
	
	public void input() {
		n = sc.nextInt();
		A = new int[n];
		for(int i=0; i<n; i++) A[i] = sc.nextInt();
	}
	
	public void partition() {
		x = A[n-1];
		i = -1;
		for(int j=0; j<n-1; j++) {
			if(A[j] <= x) {
				i++;
				swap = A[i];
				A[i] = A[j];
				A[j] = swap;
			}
		}
		swap = A[i+1];
		A[i+1] = A[n-1];
		A[n-1] = swap;
	}
	
	public void output() {
		for(int j=0; j<n; j++) {
			if(j == n-1) System.out.print(A[j]);
			else if(j == i+1 ) System.out.print("["+A[j]+"] ");
			else System.out.print(A[j]+" ");
		}
		System.out.println();
	}
	
	public static void main(String[] args) {
		Main obj = new Main();
		obj.input();
		obj.partition();
		obj.output();
	}
}


