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: Wrong Answer)

import scala.annotation.tailrec

object Main {
  def main(args: Array[String]): Unit = {
    val (n, s) = (io.StdIn.readLine().toInt, io.StdIn.readLine().split(' ').map(_.toInt).toStream)

    @tailrec
    def partition(r: Int, list: Stream[Int], acc: (Stream[Int], Stream[Int]) = (Stream(), Stream())): (Stream[Int], Stream[Int]) = list match {
      case Stream() => acc
      case x #:: list if x < r => partition(r, list, (x #:: acc._1, acc._2))
      case x #:: list if x >= r => partition(r, list, (acc._1, x #:: acc._2))
    }
    val (last, list) = (s.last, s.init)
    val (smaller, larger) = partition(last, list)
    println(s"${smaller.mkString(" ")} [${last}] ${larger.mkString(" ")}")
  }
}