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.Linq;
using System.IO;
using System.Text;
using System.Collections;
using System.Collections.Generic;
 
class Program{
    static void Main(){
        int n = int.Parse(Console.ReadLine());
        int[] A = Console.ReadLine().Split(' ')
                                    .Select(val => int.Parse(val))
                                    .ToArray();
        int q = Partition(ref A, 0, A.Length - 1);
        //Console.WriteLine(string.Join(" ", A));
        for (int i = 0; i < n; i++)
        {
            if(i != 0) Console.Write(" ");
            if(i == q) Console.Write("[");
            Console.Write(A[i]);
            if(i == q) Console.Write("]");
        }
        Console.WriteLine();
    }

    static int Partition(ref 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++;
                Swap(ref A, i, j);
            }
        }
        Swap(ref A, i + 1, r);
        return i + 1;
    }

    static void Swap(ref int[] A, int i, int j){
        try{
            int tmp = A[i];
            A[i] = A[j];
            A[j] = tmp;
        }
        catch(IndexOutOfRangeException ex){
            Console.Error.WriteLine(ex.Message);
        }
    }
}