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)

#include <stdio.h>
#include <stdlib.h>

void swap(int *, int *);
int partition(int A[], int, int);

int main()
{
  int i, n, *A, q;

  scanf("%d", &n);
  A = (int *)malloc( sizeof(int) * n );    /* 数列Aの領域を動的に確保 */
  
  for( i = 0; i<n; i++ )
    scanf("%d", &A[i]);

  q = partition(A, 0, n-1);

  for( i = 0; i<n; i++ )
    {
      if( i == q )
	printf("[%d]", A[i]);
      else
	printf("%d", A[i]);

      if( i != n-1 )
	printf(" ");
    }
  printf("\n");

  return 0;
}

/* int型の aとbを交換する関数 */
void swap(int *a, int *b)
{
  int tmp;

  tmp = *a;
  *a = *b;
  *b = tmp;
}

/* 配列 A[ p..r ] を A[ p..q − 1] の各要素が A[q] 以下で、A[ q +1.. r ] の各要素が A[ q ] より大きい   A[ p..q − 1] と A[q + 1..r ] に分割する関数 
   戻り値： インデックスq */
int partition(int A[], int p, int r)
{
  int i, j , x;

  x = A[r];
  i = p-1;

  for( j = p; j<r; j++ )
    {
      if( A[j] <= x )
	{
	  i++;
	  swap(&A[i], &A[j]);
	}
    }
  swap(&A[i+1], &A[r]);
  return i+1;
}