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.IOException;
import java.util.Scanner;

class Main {

	static long changecount = 0;
   public static void main(String args[]) throws IOException{

	   Scanner sc = new Scanner(System.in);

	   int n = sc.nextInt();


	   int[] A = new int[n];
	   for(int i = 0;i < n; i++){
		   A[i] = Integer.parseInt(sc.next());
	   }

	   int q = partition(A , 0 , n-1);
	   for(int i = 0;i < n; i++){

		   //System.out.print(A[i]);

		   if(i != q){
		      System.out.print(A[i]);
		   }else{
			   System.out.print( "["+ A[i]+"]" );
		   }


		   if(i < n-1 ){
			   System.out.print(" ");
		   }
	   }
	   System.out.println("");
	   sc.close();
   }

   public static int partition(int[] A, int p, int r){

	  int i = p-1;
      int x = A[r];



      for(int j = p; j < r; j++){

    	  if(A[j] <= x){
    		  i++;
    		  int tmp = A[i];
    		  A[i] = A[j];
    		  A[j] = tmp;
    	  }

      }


      int tmp = A[i+1];
	  A[i+1] = A[r];
	  A[r] = tmp;

	  return i+1;
   }


}