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 100000

/*
    2019 5.11
    7.2 Partition
*/

int A[MAX], n;

int partition(int p, int r) {
    int x, i, j, t;
    /*
    i は x = A[r] 以下のグループの最後尾，
    つまり　以下のグループの要素の個数（1オリジン）.
    Switchするたびに，i++ してる.
    */
    x = A[r];
    i = p - 1;
    for (j = p; j < r; j++){
        if (A[j] <= x){
            /*
            A A A | B B A B x
                i       j
            A A A   A | B B B x
                    i+1
            */
            i++;
            t = A[i]; A[i] = A[j]; A[j] = t;
        }
    }
    t = A[i+1]; A[i+1] = A[r]; A[r] = t;
    // 最後に，A[r]とそれより大きいグループの先頭を入れ替えている
    return i+1;
}

int main(){
    int i, q;

    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) printf(" ");
        if(i == q) printf("[");
        printf("%d", A[i]);
        if(i == q) printf("]");
    }
    printf("\n");

    return 0;
}