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 sc = new Scanner(System.in);
   int n = sc.nextInt();
   int[] A = new int[n];
   for(int i = 0;i < n;i++) A[i] = sc.nextInt();

   int p = 0;
   int r = n - 1;
   int x = A[r];
   int i = p - 1;
   int tmp,tmp2;
   for(int j = p;j < r;j++){
     if(A[j] <= x){
      i++; 
      tmp = A[i];
      A[i] = A[j];
      A[j] = tmp;
    }    
   }
   tmp2 = A[i + 1];
   A[i + 1] = A[r];
   A[r] = tmp2;
   int par = i + 1; 
   for(int j = 0;j < n;j++){
    if(j == par) System.out.print("["+A[j]+"]");
    else System.out.print(A[j]);
    if(j != n - 1) System.out.print(" ");
   }
   System.out.println();
  }
}
