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: Wrong Answer)

import java.util.ArrayList;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        int total;

        Scanner inp = new Scanner(System.in);
        total = inp.nextInt();

        int a[] = new int[total];

        for (int k = 0; k < total; k++) {
            a[k] = inp.nextInt();
        }

        int part = partition(a, 0, total-1);

        StringBuilder s = new StringBuilder();
        for (int i = 0; i < total; i++) {
            if (part == i) {
                s.append("[" + a[i] + "]");
            } else {
                s.append(a[i]);
            }

            if (i != total-1) {
                s.append(" ");
            }
        }

        System.out.print(s + "\n");
    }

    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 = i+1;
                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;
    }
}