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 <stdio.h>
#define MAX (int)1e5+1

int A[MAX];

void swap(int *a, int *b) { int tmp = *a; *a = *b; *b = tmp; }

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

int main() {
    int i, q, n;

    scanf("%d", &n);

    for (i = 0; i < n; i++) {
        scanf("%d", &A[i]);
    }

    q = partition(0, n - 1);

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

    return 0;
}