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: Time Limit Exceeded)

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

namespace Practice
{
    class Program
    {
        static void Main(string[] args)
        {
            SolveA(args);
            //SolveB(args);
            //SolveC(args);
            //SolveD(args);


        }
        private static int s_compareTotal = 0;
        static void SolveA(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            int[] s = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            L = new List<int>(n + 1);
            R = new List<int>(n + 1);
            MergeSort(s, 0, s.Length);

     
            Console.WriteLine(string.Join(" ", Array.ConvertAll(s, a=>a.ToString())));
            Console.WriteLine(s_compareTotal);
        }
        private static List<int> L = null;
        private static List<int> R = null;
        static void Merge(int[] a , int left, int mid, int right)
        {
            int n1 = mid - left;
            int n2 = right - mid;

            L.Clear();
            R.Clear();
            for(int i=0;i<n1;++i)
            {
                //L[i] = a[left + i];
                L.Add(a[left + i]);
            }
            for(int i=0;i<n2;++i)
            {
                //R[i] = a[mid + i];
                R.Add(a[mid + i]);
            }
            //L[n1] = int.MaxValue;
            //R[n2] = int.MaxValue;
            L.Add(int.MaxValue);
            R.Add(int.MaxValue);

            {
                int i = 0;
                int j = 0;
                for(int k=left;k<right;++k)
                {
                    s_compareTotal++;
                    if (L[i] <= R[j])
                    {
                        a[k] = L[i];
                        i = i + 1;
                    }
                    else
                    {
                        a[k] = R[j];
                        j = j + 1;
                    }
                }
            }
        }
        static void MergeSort(int[] a, int left, int right)
        {
            if( left + 1 < right)
            {
                int mid = (left + right) / 2;
                MergeSort(a, left, mid);
                MergeSort(a, mid, right);
                Merge(a, left, mid, right);
            }
        }
    }

}