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 Ruby (judge verdict: Accepted)

class MergeSort
  def initialize
    @cnt = 0
    @sentinel = 2000000000
  end

  def solve
    n = gets.chomp.to_i
    s = gets.scan(/\d+/).map(&:to_i)

    merge_sort(s, 0, n)
    return [s.join(" "), @cnt]
  end

  def merge_sort(a, left, right)
    if left + 1 < right
      mid = (left + right) / 2
      merge_sort(a, left, mid)
      merge_sort(a, mid, right)
      merge(a, left, mid, right)
    end
  end

  def merge(a, left, mid, right)
    n1 = mid - left
    n2 = right - mid

    l = Array.new(n1+1)
    r = Array.new(n2+1)

    (0...n1).each do |i|
      l[i] = a[left + i]
    end

    (0...n2).each do |i|
      r[i] = a[mid + i]
    end

    l[n1] = @sentinel
    r[n2] = @sentinel

    i = 0
    j = 0

    (left...right).each do |k|
      if l[i] <= r[j]
        a[k] = l[i]
        i += 1
      else
        a[k] = r[j]
        j += 1
      end
      @cnt += 1
    end
  end
end

if $0 == __FILE__
  puts MergeSort.new.solve
end