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>
#define N 20000000

int A[N];

int partition(int,int);

main(){
  int k,r,mid;
  int i;

  scanf("%d",&k);

  for(i=0; i<k; i++){

    scanf("%d",&A[i]);

  }

  r = k-1;

  mid = partition(0,r);

  for(i=0; i<mid; i++){

    printf("%d ",A[i]);

  }
  printf("[%d] ",A[mid]);

  for(i=mid+1; i<=r; i++){
    printf("%d",A[i]);
    if(i != r)printf(" ");
  }

  printf("\n");

  return 0;

}


int partition(int p,int r){

int i=0,j,e=0;


for(j=p; j<r; j++){
  if(A[j] <= A[r]){
    
    e = A[i];
    A[i] = A[j];
    A[j] = e;
    i++;
  } 
 }

e = A[r];
A[r] = A[i];
A[i] = e;

return i;
}