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
public class Main{
  public void run(java.io.InputStream in, java.io.PrintStream out){
    java.util.Scanner sc = new java.util.Scanner(in);
/*answer*/
    int n;
    int[] a;
    int i, p;

    n = sc.nextInt();
    a = new int[n];
    for(i = 0;i < n;i++){
      a[i] = sc.nextInt();
    }

    p = partition(a, n);

    for(i = 0;i < (n - 1);i++){
      if(i == p){
        System.out.print("[" + a[i] + "] ");
      }else{
        System.out.print(a[i] + " ");
      }
    }
    if(i == p){
      System.out.println("[" + a[i] + "]");
    }else{
      System.out.println(a[i]);
    }



/*fin*/
    sc.close();
  }
  public static void main(String[] args){
    (new Main()).run(System.in, System.out);
  }

  private static int partition(int[] a, int n){
    int tmp, k, j;

    for(k = -1;;){
      for(j = k + 1;j < n;j++){
        if(a[j] <= a[n - 1]){
          k++;
          tmp = a[k];
          a[k] = a[j];
          a[j] = tmp;
          if(j == n - 1)return k;
          break;
        }
      }
    }
  }
}