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 {

  private static int partition(int[] array, int p, int r) {
    int pivot = array[r];
    int i = p - 1;
    int j = p;

    while (j < r) {
      if (array[j] <= pivot) {
        i++;
        swap(array, i, j); 
      }   
      j++;
    }   
    swap(array, i + 1, r); 

    return i + 1;
  }

  private static void swap(int[] array, int i, int j) {
    int tmp = array[j];
    array[j] = array[i];
    array[i] = tmp;
  }

  public static void main(String[] args) {
    Scanner scan = new Scanner(System.in);
    String str = scan.next();

    //String[] parsed = args[0].split("\n");
    int N = Integer.valueOf(str);
    //System.out.println(N);

    //String input = parsed[1];
    int[] array = new int[N];
    for (int i = 0; i < N; i++) {
      array[i] = scan.nextInt();
      //System.out.println(array[i]);
    }   

    int part = partition(array, 0, array.length - 1); 

    StringBuilder builder = new StringBuilder();
    for (int i = 0; i < N; i++) {
      if (i == part) {
        builder.append("[" + array[i] + "]");
      } else {
        builder.append(array[i]);
      }   
      builder.append(" ");
    }   
    System.out.println(builder.toString().trim());

  }
}