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.io.StdIn

object Main extends App {
  val n = StdIn.readLine().trim.toInt
  val a = StdIn.readLine().trim.split(' ').map(_.toInt)

  val last = a(n - 1)

  @inline private def swap(from: Int, to: Int) = {
    //println(s"from: $from  to: $to")
    val temp = a(from)
    a(from) = a(to)
    a(to)   = temp
  }
  
  def partition(arr: Array[Int], p: Int, r: Int): Int = {
    var i = p - 1
    (p until r).foreach{ j =>
      while(arr(j) <= last){
        i += 1
        swap(j, i)
      }
    }
    swap(r-1, i+1)
    i+1
  }
  
  val num = partition(a, 0, n)
  val a1 = new Array[Int](num - 1)
  Array.copy(a, 0, a1, 0, num - 1)
  print(a1.mkString(" "))
  print(s" [$last] ")
  val a2 = new Array[Int](n - num)
  Array.copy(a, num, a2, 0, n - num)
  println(a2.mkString(" "))
  
  
}