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;
					
public class my
{
	public static void Main()
	{
		var n = my.GetInt();
		var A = my.GetIntArray(n);
		
		var pivotIdx = my.Partition(A, 0, n-1);
		
		for(int i = 0; i<n; i++) {
			if(i == pivotIdx)	Console.Write("[");
			Console.Write(A[i]);
			if(i == pivotIdx)	Console.Write("]");
			
			if(i != n-1)	Console.Write(" ");
			else	Console.WriteLine();
		}
		
	}
	
	private static 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) {
				my.Swap(A, ++i, j);
			}
		}
		my.Swap(A, i+1, r);
		
		return i+1;	// pivot index
	}
	
	private static void Swap(int[] A, int i, int j)
	{
		int tmp = A[i];
		A[i] = A[j];
		A[j] = tmp;
	}
	
	private static int GetInt()
	{
		return int.Parse(Console.ReadLine());
	}
	
	private static int[] GetIntArray()
	{
		return Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
	}

	private static int[] GetIntArray(int n)
	{
		var A = new int[n];
		var s = Console.ReadLine().Split(' ');

		for(int i = 0; i < n; i++) {
			A[i] = int.Parse(s[i]);
		}
		return A;
	}
	
	private static int[] GetIntArray(int n, string t)
	{
		var A = new int[n];
		var s = t.Split(' ');

		for(int i = 0; i < n; i++) {
			A[i] = int.Parse(s[i]);
		}
		return A;
	}

	private static int[] GetIntArray(char c)
	{
		return Array.ConvertAll(Console.ReadLine().Split(c), int.Parse);
	}
	
	private static int[] GetIntArray(char c, string s)
	{
		return Array.ConvertAll(s.Split(c), int.Parse);
	}
	
	private static int[] GetIntArray(string s)
	{
		return Array.ConvertAll(s.Split(' '), int.Parse);
	}
	
	private static double[] GetDoubleArray()
	{
		return Array.ConvertAll(Console.ReadLine().Split(' '), double.Parse);
	}
	
	public static string Reverse(string s)
	{
		var c = s.ToCharArray();
		Array.Reverse(c);
		
		return new String(c);
	}
	
	private static void WriteArray(int[] a)
	{
		Console.WriteLine(string.Join(" ", Array.ConvertAll( a, x=>x.ToString() ) ) );
	}

	private static void WriteArray(long[] a)
	{
		Console.WriteLine(string.Join(" ", Array.ConvertAll( a, x=>x.ToString() ) ) );
	}
	
	private static void WriteVector(Vector v)
	{
		Console.WriteLine(string.Format("{0:f8} {1:f8}", v.X, v.Y));
	}
}

public struct Vector
{
	public double X,Y;
}