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)

n = gets.chomp.to_i
s = gets.chomp.split(" ").map{ |x| x.to_i }

$count = 0

def merge(a, left, mid, right)
  n1 = mid - left
  n2 = right - mid
  l = (0..n1).to_a
  r = (0..n2).to_a
  (0...n1).each { |i| l[i] = a[left + i] }
  (0...n2).each { |i| r[i] = a[mid + i] }

  l[n1] = r[n2] = 10**9
  i = j = 0

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

def mergeSort(a, left, right)
  
  if left + 1 < right
    mid = (left + right) / 2
    mergeSort(a, left, mid)
    mergeSort(a, mid, right)
    merge(a, left, mid, right)
  end
  return $count, a
end

result = mergeSort(s, 0, n)
puts result[1].join(" ")
puts result[0]