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: Accepted)

using System;
using System.Collections.Generic;
using System.Text;

class Program
{
    public void Proc()
    {
        int num = int.Parse(Console.ReadLine());
        string[] inpt = Console.ReadLine().Split(' ');
        // inpt = "13 19 9 5 12 8 7 4 21 2 6 11".Split(' ');
        int[] arr = new int[num];
        for (int i = 0; i < num; i++)
        {
            arr[i] = int.Parse(inpt[i]);
        }
        int idx = this.Partition(arr, 0, num - 1);
        StringBuilder ans = new StringBuilder();
        for (int i = 0; i < arr.Length; i++)
        {
            if (ans.Length > 0)
            {
                ans.Append(" ");
            }
            if (i == idx)
            {
                ans.Append("[" + arr[i] + "]");
            }
            else
            {
                ans.Append(arr[i]);
            }
        }
        Console.WriteLine(ans.ToString());
    }

    private int Partition(int[] A, int p, int r)
    {
        /*
         * 1 partition(A, p, r)
            2   x = A[r]
            3   i = p-1
            4   for j = p to r-1
            4     if A[j] <= x
            5       i = i+1
            6       A[i] ??¨ A[j] ?????????
            7   A[i+1] ??¨ A[r] ?????????
            8   return i+1
         **/

        int x = A[r];
        int i = p - 1;
        for (int j = p; j <= r - 1; j++)
        {
            if (A[j] <= x)
            {
                i++;
                int tmp = A[i];
                A[i] = A[j];
                A[j] = tmp;
            }
        }
        int tmp2 = A[i + 1];
        A[i + 1] = A[r];
        A[r] = tmp2;
        return i + 1;
    }


    static void Main(string[] args)

    {

        Program prg = new Program();
        prg.Proc();

    }
}