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;

namespace Practice
{
    public struct Vector2
    {
        public float X;
        public float Y;
        public Vector2(float x, float y)
        {
            X = x;
            Y = y;
        }
        public float Length()
        {
            return (float)Math.Sqrt(X * X + Y * Y);
        }
        public static Vector2 Normalize(Vector2 v)
        {
            float l = v.Length();
            return new Vector2(v.X / l, v.Y / l);
        }
        public static Vector2 operator +(Vector2 a, Vector2 b)
        {
            return new Vector2(a.X + b.X, a.Y + b.Y);
        }
        public static Vector2 operator- (Vector2 a, Vector2 b)
        {
            return new Vector2(a.X - b.X, a.Y -b.Y);
        }
        public static Vector2 operator* (Vector2 a, float f)
        {
            return new Vector2(a.X * f, a.Y * f);
        }
        public static Vector2 operator /(Vector2 a, float f)
        {
            return new Vector2(a.X / f, a.Y / f);
        }
    }

    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());
            string[] szarr = Console.ReadLine().Split(' ');
            int[] s = new int[n];
            for(int i = 0; i < szarr.Length; ++i)
            {
                s[i] = int.Parse(szarr[i]);
            }
            MergeSort(s, 0, s.Length);

            string szresult = "";
            for(int i=0;i<s.Length;++i)
            {
                szresult += s[i].ToString();
                if( i != s.Length - 1)
                {
                    szresult += " ";
                }
            }
            Console.WriteLine(szresult);
            Console.WriteLine(s_compareTotal);
        }

        static void Merge(int[] a , int left, int mid, int right)
        {
            int n1 = mid - left;
            int n2 = right - mid;
            int[] L = new int[n1+1];
            int[] R = new int[n2+1];
            for(int i=0;i<n1;++i)
            {
                L[i] = a[left + i];
            }
            for(int i=0;i<n2;++i)
            {
                R[i] = a[mid + i];
            }
            L[n1] = int.MaxValue;
            R[n2] = 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);
            }
        }
    }

}