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.Scanner;

public class Main{
	
	public static void part(int [] arr, int p, int r) {
		int x = arr[r];
		int i = p - 1;
		
		for(int j = p; j < r; j++) {
			if(arr[j] <= x) {
				i++;
				int temp = arr[i];
				arr[i] = arr[j];
				arr[j] = temp;
				
			}
			
			
		
		}
		int temp = arr[i + 1];
		arr[i + 1] = arr[r];
		arr[r] = temp;
		
	
		
		for(int k = 0; k < arr.length; k++) {
			if(arr[k] == x && k == arr.length - 1) {
				System.out.print("[" + x + "]\n");
			}
			
			else if(k == i + 1) {
				System.out.print("[" + x + "] ");
			}
			
			else if(k == arr.length - 1) {
				System.out.print(arr[k] + "\n");
			}
			
			else {
				System.out.print(arr[k] + " ");
			}
		}
	}
	
	public static void main(String [] args) {
		Scanner in = new Scanner(System.in);
		
		int n = in.nextInt();
		int [] arr = new int [n];
		
		for(int i = 0; i < n; i++) {
			arr[i] = in.nextInt();
		}
		
		part(arr, 0, arr.length - 1);
	}

}

