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 Python3 (judge verdict: Accepted)

def partition(li, p, r):
    """Separate li with a value of li[r].
    Returns index of the partition value.

    >>> ax = [13, 19, 9, 5, 12, 8, 7, 4, 21, 2, 6, 11]
    >>> partition(ax, 0, 11)
    7
    >>> ax
    [9, 5, 8, 7, 4, 2, 6, 11, 21, 13, 19, 12]
    """
    x = li[r]
    i = p - 1
    for j in range(p, r):
        if li[j] <= x:
            i += 1
            li[i], li[j] = li[j], li[i]

    i += 1
    li[i], li[r] = li[r], li[i]

    return i


def run():
    c = int(input())
    ax = [int(n) for n in input().split()]

    p = partition(ax, 0, c-1)
    for (i, a) in enumerate(ax):
        if i == p:
            val = '[{}]'.format(a)
        else:
            val = str(a)

        if i < c-1:
            print(val, end=" ")
        else:
            print(val)


if __name__ == '__main__':
    run()