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)

import scala.io.StdIn.{readInt, readLine}

object Main extends App {
  val n = readInt
  val A = readLine.split(" ").map(_.toInt)
  val p = partition(A, 0, n - 1)
  println(A.zipWithIndex.map{ case(e, i) => { if (i == p) s"[$e]" else e }}.mkString(" "))

  def partition(A: Array[Int], p: Int, r: Int): Int = {
    val x = A(r)
    var i = p - 1
    for (j <- p to r - 1) {
      if (A(j) <= x) {
        i += 1
        swap(A, i, j)
      }
    }
    swap(A, i + 1, r)
    i + 1
  }

  def swap(A: Array[Int], i: Int, j: Int): Unit = {
    if (i == j) {
      return
    }
    A(i) = A(i) ^ A(j)
    A(j) = A(i) ^ A(j)
    A(i) = A(i) ^ A(j)
  }
}