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 <utility>
#include <vector>

using namespace std;

int partition(vector<int>& vec, int left, int right);

int main()
{
    int n;
    cin >> n;

    vector<int> a(n);
    for (int i = 0; i < n; ++i)
        cin >> a[i];

    int pivot = partition(a, 0, n - 1);
    cout << a[0];
    for (int i = 1; i < n; ++i) {
        if (i == pivot)
            cout << ' ' << "[" << a[i] << "]";
        else
            cout << ' ' << a[i];
    }
    cout << '\n';
}

int partition(vector<int>& vec, int left, int right)
{
    int pivot = vec[right];
    int boundary = left - 1;

    for (int i = left; i < right; ++i) {
        if (vec[i] <= pivot) {
            ++boundary;
            swap(vec[i], vec[boundary]);
        }
    }

    ++boundary;
    swap(vec[boundary], vec[right]);

    return boundary;
}