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: Time Limit Exceeded)

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

int partition(int *,int ,int );

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

  scanf("%d",&n);
  if(n<1 || n>100000) exit(1);

  A = malloc( n*sizeof(int) );
  
  for(i=0; i<n; i++){
    scanf("%d", &A[i]);
    if(A[i]<0 || A[i]>100000) exit(2);
  }
  
  key = partition(A, 0, n-1);

  for(i=0; i<n; i++){
    if(i = key){
      printf("[%d]", A[i]);
      if(i<n-1) printf(" ");
      continue;
    }
    printf("%d", A[i]);
    if(i<n-1) printf(" ");
  }
  printf("\n");
    
  return 0;
}

int partition(int *A, int p, int r){
  int i, j, x, tmp, omp;

  x = A[r];
  i = p-1;
  for(j=p; j<=r-1; j++){
    if(A[j] <= x){
      i++;
      tmp =A[i];
      A[i] = A[j];
      A[j] = tmp;
    }
  }
  omp = A[i+1];
  A[i+1] = A[r];
  A[r] = omp;

  return i+1;
}