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;

namespace AOJ.ALDS
{
    public class MergeSort
    {
        private static int compare;

        private static int[] Sort(int[] array, int left, int right)
        {
            if (left + 1 < right)
            {
                int mid = (left + right) / 2;
                var l_array = Sort(array, left, mid);
                var r_array = Sort(array, mid, right);
                return Merge(l_array, r_array);
            }
            else
            {
                return new int[] { array[left] };
            }
        }

        // 2つの配列をマージする
        private static int[] Merge(int[] a, int[] b)
        {
            int[] ret = new int[a.Length + b.Length];
            int a_cnt = 0;
            int b_cnt = 0;
            for (int i = 0; i < a.Length + b.Length; i++)
            {
                if (a_cnt >= a.Length)
                {
                    ret[i] = b[b_cnt];
                    b_cnt++;
                }
                else if (b_cnt >= b.Length)
                {
                    ret[i] = a[a_cnt];
                    a_cnt++;
                }
                else
                {
                    if (a[a_cnt] <= b[b_cnt])
                    {
                        ret[i] = a[a_cnt];
                        a_cnt++;
                    }
                    else
                    {
                        ret[i] = b[b_cnt];
                        b_cnt++;
                    }
                }
                compare++;
            }

            return ret;
        }

        public static void Main()
        {
            int length = int.Parse(Console.ReadLine());
            int[] array = new int[length];
            var input = Console.ReadLine().Split(' ');
            for (int i = 0; i < length; i++) { array[i] = int.Parse(input[i]); }

            // ソート
            compare = 0;
            var ret = Sort(array, 0, length);

            // 出力
            string output = "";
            for (int i = 0; i < length; i++) { output += " " + ret[i]; }
            output = output.Trim();
            Console.WriteLine(output);
            Console.WriteLine(compare);
        }
    }
}