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.Scanner;
public class Main {
private static Scanner s = new Scanner(System.in);
static int[] a = new int[100001];
public static void main(String[] args) {
	int n = s.nextInt();

	StringBuilder sb = new StringBuilder();

	for(int i = 0;i < n;i++) {
		a[i] = s.nextInt();
	}
	int j = partition(a,0,n);
	for(int i = 0;i < n-1;i++) {
		if(i == j-1) {
			sb.append("[" + a[i] + "] ");
		}else {
		sb.append(a[i]+" ");
		}
	}
	System.out.println(sb.toString() + a[n-1]);
}

public static int partition(int[] a,int p,int r) {
int x = a[r-1];
int i = p-1;

for(int j = p;j < r;j++) {
	if(a[j] <= x) {
		i++;
		int tmp;
		tmp = a[i];
		a[i] = a[j];
		a[j] = tmp;
	}else {
		int tmp;
	tmp = a[i+1];
	a[i + 1] = a[r];
	a[r] = tmp;
	}
}
return i+1;
}
}