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 Kotlin (judge verdict: Accepted)

fun main(args: Array<String>) {
    readLine()
    val array = readLine()
        ?.split(" ".toRegex())
        ?.map(Integer::parseInt)
        ?.toIntArray()
        ?: intArrayOf()
    val mid = array.partition(0, array.lastIndex)
    println(array.mapIndexed { index, value ->
        if (index == mid) {
            "[$value]"
        } else {
            value.toString()
        }
    }.joinToString(" "))
}

fun IntArray.partition(p: Int, r: Int): Int {
    val x = this[r]
    var i = p - 1
    for (j in p until r) {
        if (this[j] <= x) {
            i++
            swap(i, j)
        }
    }
    swap(i + 1, r)
    return i + 1
}

fun IntArray.swap(i: Int, j: Int) {
    val tmp = this[i]
    this[i] = this[j]
    this[j] = tmp
}