Problem:
Merge Sort

Write a program of a Merge Sort algorithm implemented by the following pseudocode. You should also report the number of comparisons in the Merge function.

Merge(A, left, mid, right)
n1 = mid - left;
n2 = right - mid;
create array L[0...n1], R[0...n2]
for i = 0 to n1-1
do L[i] = A[left + i]
for i = 0 to n2-1
do R[i] = A[mid + i]
L[n1] = SENTINEL
R[n2] = SENTINEL
i = 0;
j = 0;
for k = left to right-1
if L[i] <= R[j]
then A[k] = L[i]
i = i + 1
else A[k] = R[j]
j = j + 1

Merge-Sort(A, left, right){
if left+1 < right
then mid = (left + right)/2;
call Merge-Sort(A, left, mid)
call Merge-Sort(A, mid, right)
call Merge(A, left, mid, right)

Input

In the first line n is given. In the second line, n integers are given.

Output

In the first line, print the sequence S. Two consequtive elements should be separated by a space character.

In the second line, print the number of comparisons.

Constraints

n ≤ 500000

0 ≤ an element in S ≤ 109

Sample Input 1

10
8 5 9 2 6 3 7 1 10 4

Sample Output 1

1 2 3 4 5 6 7 8 9 10
34

Notes

Solution in Scala (judge verdict: Accepted)

object Main extends App {

  val SENTINEL = 10000000001L

  def sliceAndTerminate(a: Array[Long], from: Int, until: Int) = {
    val n = until - from
    val ret = new Array[Long](n + 1)
    compat.Platform.arraycopy(a, from, ret, 0, n)
    ret(n) = SENTINEL
    ret
  }

  def merge(a: Array[Long], left: Int, mid: Int, right: Int) = {
    val l = sliceAndTerminate(a, left, mid)
    val r = sliceAndTerminate(a, mid, right)

    def loop(i: Int, j: Int, k: Int): Unit = {
      if (k < right) {
        if (l(i) <= r(j)) {
          a(k) = l(i)
          loop(i+1, j, k+1)
        } else {
          a(k) = r(j)
          loop(i, j+1, k+1)
        }
      }
    }

    loop(0, 0, left)
    right - left
  }

  def mergeSort(a: Array[Long], left: Int, right: Int): Int = {
    if (left + 1 < right) {
      val mid = (left + right) / 2
      mergeSort(a, left, mid) +
      mergeSort(a, mid, right) +
      merge(a, left, mid, right)
    } else 0
  }


  val sc = new java.util.Scanner(Console.in)

  def readInt() = sc.next().toInt
  def readLong() = sc.next().toLong

  val ary = Array.fill(readInt())(readLong())
  val n = mergeSort(ary, 0, ary.length)
  println(ary mkString " ")
  println(n)
}