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.*;
class Main{
  public static void main(String args[]){
    StringBuilder bl = new StringBuilder();
    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 i = partition(A,0,A.length-1);
    if(0==i)bl.append('[').append(A[0]).append(']');
    else bl.append(A[0]);
    for(int j = 1; j<A.length; j++){
      if(j==i)bl.append(' ').append('[').append(A[j]).append(']');
      else bl.append(' ').append(A[j]);
    }
    System.out.println(bl);

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