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 <iostream>
#include <stdio.h>

using namespace std;
#define MAX_N 100000

void swap(int* x, int* y) {
  int tmp = *x;
  *x = *y;
  *y = tmp;
}

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

int main() {
  int n;
  cin >> n;
  int A[MAX_N];
  for(int i=0; i<n; i++) {
    cin >> A[i];
  }

  int q = partition(A, 0, n-1);
  for(int i=0; i<q; i++) {
    printf("%d", A[i]);
    if(i != q-1) {
      printf(" ");
    }
  }
  printf(" [%d] ", A[q]);

  for(int i=q+1; i<n; i++) {
    printf("%d", A[i]);
    if(i != n-1) {
      printf(" ");
    }
  }
  printf("\n");
}