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 int partition(int[] a, int p, int r) {
    int x = a[r];
    int i = p - 1;
    for (int j = p; j < r; j++) {
      if (a[j] <= x) {
        i++;
        int temp = a[i];
        a[i] = a[j];
        a[j] = temp;
      }
    }
    int temp = a[i+1];
    a[i+1] = a[r];
    a[r] = temp;
    return i+1;
  }

  public static void main(String[] args) {
    Scanner s = new Scanner(System.in);
    int n = s.nextInt();
    int[] A = new int[n];
    for (int i = 0; i < n; i++) {
      A[i] = s.nextInt();
    }
    s.close();
    int result = partition(A, 0, n-1);
    for (int i = 0; i < n; i++) {
      if (i == result)
        System.out.print("[");
      System.out.print(A[i]);
      if (i == result)
        System.out.print("]");
      if (i != n-1)
        System.out.print(" ");
    }
    System.out.println();
  }
}
