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 {
    def main(args: Array[String]): Unit = {
        val len = readInt
        val arr = readLine.split(" ").map(_.toInt)
        val pivot = partition(arr, len)
        val ret = arr.zipWithIndex.map{case (v, i) =>
            if (i == pivot) "[" + v.toString + "]" else v.toString
        }
        println(ret.mkString(" "))
    }
    def partition(arr: Array[Int], len: Int): Int = {
        val pivot = arr(len - 1)
        def go(sep: Int, seek: Int): Int = {
            if (seek == len - 1) {
                swap(arr, sep + 1, seek)
                sep + 1
            } else {
                if (arr(seek) > pivot) {
                    go(sep, seek + 1)
                } else {
                    swap(arr, sep + 1, seek)
                    go(sep + 1, seek + 1)
                }
            }
        }
        go(-1, 0)
    }
    def swap(arr: Array[Int], a: Int, b: Int): Unit = {
        val tmp = arr(a)
        arr(a) = arr(b)
        arr(b) = tmp
    }
}