Problem:
Partition

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].

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 [  ].

Constraints

1 ≤ n ≤ 100,000

0 ≤ Ai ≤ 100,000

Sample Input 1

12
13 19 9 5 12 8 7 4 21 2 6 11

Sample Output 1

9 5 8 7 4 2 6 [11] 21 13 19 12

Solution in JAVA (judge verdict: Accepted)

import java.io.*;

public class Main
{
  public static void main(String[] args) {
    try{
      BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
      int n = Integer.parseInt(in.readLine());
      String[] arr = in.readLine().split(" ");
      int[] A = new int[n];
      for(int i=0; i<n; i++) {
        A[i] = Integer.parseInt(arr[i]);
      }
      int partitionId = partition(A, 0, n-1);
      StringBuilder sb = new StringBuilder();
      for(int i=0; i<n; i++) {
        if(i == partitionId) {
          sb.append("[").append(A[i]).append("] ");
        } else if(i == n-1) {
          sb.append(A[i]);
        } else {
          sb.append(A[i]).append(" ");
        }
      }
      System.out.println(sb.toString());
    } catch (IOException e) {}

  }

  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 tmp = A[j];
        A[j] = A[i];
        A[i] = tmp;
      }
    }
    A[r] = A[i+1];
    A[i+1] = x;
    return i+1;
  }

}