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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {

  public static void main(String[] args) {
  
    new Main().run();
  }

  public void run() {

    try(BufferedReader br = new BufferedReader(new InputStreamReader(System.in))) {

      int n = Integer.parseInt(br.readLine());
      int[] seq = new int[n];
      int i=0;
      for (String var : br.readLine().split(" "))
        seq[i++] = Integer.parseInt(var);

      int q = partition(seq, 0, n-1);
      dispIntArrayPartition(seq, q);
    }
    catch(IOException e) {
      System.out.println("IOException!");
    }
  }

  public int partition(int[] seq, int p, int r) {

    int x = seq[r];
    int i = p-1;
    int t;

    for(int j=p; j<r; j++) {
      if(seq[j] <= x) {
        t = seq[++i]; seq[i] = seq[j]; seq[j] = t;
      }
    }
    t = seq[i+1]; seq[i+1] = seq[r]; seq[r] = t;

    return i+1;
  }

public void dispIntArrayPartition(int[] target, int q) {
  StringBuilder s = new StringBuilder();
  int l=target.length-1;

  for (int i=0; i<q; i++) { s.append(target[i]).append(" "); }
  s.append("[").append(target[q]).append("] ");
  for (int i=q+1; i<l; i++) { s.append(target[i]).append(" "); }
  s.append(target[l]);

  System.out.println(s);
  }
}
