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>
using namespace std;
#define MAX 100000

int A[MAX], L[MAX], R[MAX];

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

int main(){
    int n, center;
    
    cin >> n;
    for(int i = 0; i < n; i++) cin >> A[i];
    
    center = partition(0, n-1);
    
    for(int i = 0; i < n; i++){
        if(i) cout << " ";
        
        if(i != center) cout << A[i];
        else cout << "[" << A[i] << "]";
    }
    cout << endl;
    
    return 0;
}