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.IO;
using System.Linq;

namespace Sort_II
{
    class AOJ_Partition
    {
        static void Main(string[] args)
        {
            Console.ReadLine();
            var A = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            var p = 0;
            var r = A.Length - 1;

            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            var index = Partition(A, p, r);

            for (int i = 0; i < A.Length - 1; i++)
                if (i == index) Console.Write("[" + A[i] + "] ");
                else Console.Write(A[i] + " ");
            if (index == A.Length - 1) Console.WriteLine("[" + A.Last() + "]");
            else if (index == A.Length - 1) Console.WriteLine(A.Last());

            Console.Out.Flush();
        }

        static public int Partition(int[] A, int p, int r)
        {
            var x = A[r];
            var i = p - 1;
            for (int j = p; j < r; j++)
                if (A[j] <= x)
                {
                    i++;
                    var temp = A[i];
                    A[i] = A[j];
                    A[j] = temp;
                }
            var tmp = A[i + 1];
            A[i + 1] = A[r];
            A[r] = tmp;

            return i + 1;
        }
    }
}