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 C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

namespace CSharpSample01
{


    class Program
    {
        static int cnt = 0;
        const int SENTINEL = 2000000000; 

        static void Merge(int[] data_ary, int left_ind, int mid_ind, int right_ind)
        {
            int lenght = data_ary.Length;
            int left_n = mid_ind - left_ind;  //left_indからmid_ind - 1の要素数
            int right_n = right_ind - mid_ind;  //mid_indからright_ind - 1までの要素数

            //番兵を入れるため1つ余分に確保
            int[] left_ary = new int[left_n + 1];
            int[] right_ary = new int[right_n + 1];

            //left_indからleft_ind + left_n - 1まで
            for (int i = 0; i < left_n; i++)
            {
                left_ary[i] = data_ary[left_ind + i];
            }

            //mid_indからmid_ind + right_n - 1まで
            for(int i = 0; i < right_n; i++)
            {
                right_ary[i] = data_ary[mid_ind + i];
            }

            //最後の要素に番兵を入れる
            left_ary[left_n] = SENTINEL;
            right_ary[right_n] = SENTINEL;

            int l = 0;
            int r = 0;

            //比べる回数はright_n - left_n
            //よって、番兵同士が比べれられることはない
            for(int k = left_ind; k < right_ind; k++)
            {
                cnt++;
                if(left_ary[l] <= right_ary[r])
                {
                    data_ary[k] = left_ary[l];
                    l++;
                }
                else
                {
                    data_ary[k] = right_ary[r];
                    r++;
                }
            }
        }

        //対象のインデックス番号はleft_indからright_ind - 1まで
        static void MergeSort(int[] data_ary, int left_ind, int right_ind)
        {
            if (left_ind + 1 < right_ind)
            {             
                int mid_ind = (left_ind + right_ind) / 2;
                MergeSort(data_ary, left_ind, mid_ind);
                MergeSort(data_ary, mid_ind, right_ind);
                Merge(data_ary, left_ind, mid_ind, right_ind);
            }
        }


        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            int[] data_ary = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();

            MergeSort(data_ary, 0, data_ary.Length);

            Console.WriteLine(String.Join(" ", data_ary));
            Console.WriteLine(cnt);
        }
    }
}