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: Time Limit Exceeded)

n = gets.to_i
s = gets.split.map(&:to_i)
co = 0

merge = ->(left, mid, right) {
  n1, n2 = mid - left, right - mid
  l = s[left, n1] + [Float::INFINITY]
  r = s[mid , n2] + [Float::INFINITY]
  i = j = 0
  co += right - left
  left.upto(right - 1) do |k|
    if l[i] <= r[j]
      s[k] = l[i]
      i += 1
    else
      s[k] = r[j]
      j += 1
    end
  end
}

merge_sort = ->(left, right) {
  if left < right - 1
    mid = (left + right) / 2
    merge_sort.(left, mid)
    merge_sort.(mid, right)
    merge.(left, mid, right)
  end
}

merge_sort.(0, n)
puts s.join(" ")
puts co