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;

namespace ConsoleTest
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.ReadLine();
            var arr = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var idx = Partition(ref arr, 0, arr.Length - 1);
            Console.WriteLine($"{string.Join(" ", arr.Take(idx))} [{arr[idx]}] {string.Join(" ", arr.Skip(idx + 1))}");
        }

        private static int Partition(ref int[] arr, int p, int r)
        {
            var x = arr[r];
            var i = p - 1;
            for(var k = p; k < r; ++k)
            {
                if(arr[k] <= x)
                {
                    ++i;
                    Swap(ref arr[i], ref arr[k]);
                }
            }
            Swap(ref arr[i + 1], ref arr[r]);
            return i + 1;
        }

        private static void Swap(ref int v1, ref int v2)
        {
            var tmp = v1;
            v1 = v2;
            v2 = tmp;
        }
    }
}