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 OCaml (judge verdict: Accepted)

let cnt = ref 0

let merge a l m r =
  let init_ary n p = Array.init (n + 1) (fun i -> if i = n then max_int else a.(p + i)) in
  let ai = init_ary (m - l) l in
  let aj = init_ary (r - m) m in
  let rec doit = function
    | (_, _, k) when k = r -> ()
    | (i, j, k) ->
      incr cnt;
      if ai.(i) <= aj.(j) then begin
        a.(k) <- ai.(i);
        doit (i + 1, j, k + 1)
      end else begin
        a.(k) <- aj.(j);
        doit (i, j + 1, k + 1)
      end in
  doit (0, 0, l)

let rec merge_sort a l r =
  if (l + 1) < r then begin
    let m = (l + r) / 2 in
    merge_sort a l m;
    merge_sort a m r;
    merge a l m r
  end

let () =
  let n = read_int () in
  let a = Array.init n (fun _ -> Scanf.scanf "%d " (fun i -> i)) in
  merge_sort a 0 n;
  Array.iteri (fun i e -> if i <> 0 then print_string " "; print_int e) a;
  print_newline ();
  Printf.printf "%d\n" !cnt