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)

$cnt = 0

def merge(ary, left, mid, right)
  l_ary = ary.slice(left...mid)
  r_ary = ary.slice(mid...right)
  i = j = 0
  (left...right).each { |k|
    l_val = l_ary[i] || 10**10 # because element < 10^9
    r_val = r_ary[j] || 10**10
    if l_val <= r_val
      ary[k] = l_val
      i += 1
    else
      ary[k] = r_val
      j += 1
    end
    $cnt += 1
  }
end

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

# main
n = gets.to_i
ary = gets.split(' ').map(&:to_i)

merge_sort(ary, 0, ary.size)

puts ary.join(' ')
puts $cnt