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)

SENTINEL=10**9+1
$count=0

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

  # create array left_array[0...n1], right_array[0...n2]
  left_array=Array.new(n1+1)
  right_array=Array.new(n2+1)
  (n1).times do |i|
    left_array[i] = array[left+i]
  end
  (n2).times do |i|
    right_array[i] = array[mid+i]
  end
  left_array[n1] = SENTINEL
  right_array[n2] = SENTINEL

  i = 0
  j = 0
  for k in left..(right-1)
    $count += 1
    if left_array[i] <= right_array[j]
      array[k] = left_array[i]
      i += 1
    else
      array[k] = right_array[j]
      j += 1
    end
  end
  return array
end

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

n = STDIN.gets.to_i
S = STDIN.gets.split(" ").map { |i| i.to_i }


print "#{merge_sort(S, 0, n).join(' ')}\n"
print "#{$count}\n"