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 C# (judge verdict: Wrong Answer)

using System;
using System.Linq;
using System.Text;

namespace ALDS1_6_B_Partition
{
	class Program
	{
		static void Main ( string[] args )
		{
			//input
			int dataCount = int.Parse (Console.ReadLine ());
			int[] numArray = new int[dataCount];
			numArray = Console.ReadLine ().Split (' ').Select (int.Parse).ToArray ();

			//process
			int index = Partition (numArray, 0, numArray.Length - 1);

			//output
			string result = string.Join (
				" ", Array.ConvertAll (numArray, num => num.ToString ())
				);

			string replace = numArray[index].ToString ();
			result = result.Replace (replace, "[" + replace + "]");

			Console.WriteLine (result);
		}

		static int Partition ( int[] numArray, int firstIndex, int lastIndex )
		{
			int lastItem = numArray[lastIndex];
			int index = firstIndex - 1;

			for (int lp = firstIndex; lp < lastIndex; lp++)
			{
				if (numArray[lp] <= lastItem)
				{
					index++;

					var tmp = numArray[index];
					numArray[index] = numArray[lp];
					numArray[lp] = tmp;
				}
			}

			var tmp2 = numArray[index + 1];
			numArray[index + 1] = numArray[lastIndex];
			numArray[lastIndex] = tmp2;

			return index + 1;
		}
	}
}