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 Scala (judge verdict: Accepted)

object Main extends App {
  val n: Int = io.StdIn.readLine().toInt
  val arr: Array[Int] = io.StdIn.readLine().split(" ") map(_.toInt)

  def partition(arr: Array[Int], i: Int, p: Int, r:Int): (Array[Int], Int) = {
    val a: Array[Int] = arr.clone()
    var p: Int = 0

    for(i <- 0 until r) {
      val (ai, ap, ar) = (a(i), a(p), a(r))
      if (i == p) {if (ai <= ar) p += 1}
      else {if (ai <= ar && ai < ap) {a(i) = ap; a(p) = ai; p += 1}}
    }
    val ap = a(p)
    a(p) = a(r); a(r) = ap
    
    (a,p)
  }

  val (pa, i): (Array[Int], Int) = partition(arr, 0, 0, n-1)
  println(pa.slice(0, i).mkString(" ") + " [" + pa(i) + "] " + pa.slice(i+1, n).mkString(" "))
}