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 JAVA (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

class Main{
    public static void main(String[] args) throws IOException{
        final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        final StringBuilder sb = new StringBuilder();
        final int n = Integer.parseInt(br.readLine());
        final StringTokenizer in = new StringTokenizer(br.readLine(), " ");
        final int[] A = new int[n];
        for(int i = 0; i<n; i++)
            A[i] = Integer.parseInt(in.nextToken());
        final int x = partition(A, 0, n-1);
        for(int i = 0; i<x; i++)
            sb.append(A[i]).append(' ');
        sb.append('[').append(A[x]).append(']');
        for(int i = x+1; i<n; i++)
            sb.append(' ').append(A[i]);
        System.out.println(sb);
    }
    private static int partition(int[] A, int p, int r){
        final int x = A[r];
        int i = p;
        int t;
        for(int j = p; j<r; j++){
            if(A[j]<=x){
                t = A[i];
                A[i] = A[j];
                A[j] = t;
                i++;
            }
        }
        A[r] = A[i];
        A[i] = x;
        return i;
    }
}