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 <bits/stdc++.h>

#include <iostream>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)

#define MAX_N 100000
int A[MAX_N + 5];

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

int main() {
  int n;
  cin >> n;
  rep(i, n) cin >> A[i];
  int idx = partition(0, n - 1);
  rep(i, n) {
    if (i > 0) cout << " ";
    if (i == idx) cout << "[";
    cout << A[i];
    if (i == idx) cout << "]";
  }
  cout << endl;
  return 0;
}