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)

//  Merge_Sort.cs

using System;

class Merge_Sort {

	static int count = 0;

	public static void Main() {

		int n = int.Parse(Console.ReadLine());
		string[] S_s = Console.ReadLine().Split(' ');
		int[] S = new int[n];
		for(int i = 0; i < n; i++) {
			S[i] = int.Parse(S_s[i]);
		}
		int left = 0, right = n;
		mergeSort(S, left, right);

		string ans = "";
		foreach(int num in S) {
			ans += num.ToString();
			ans += " ";
		}

		ans = ans.TrimEnd();
		Console.WriteLine(ans + "\n{0}", count);

	}

	static void merge(int[] S, 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 j = 0; j < n1; j++) {
			L[j] = S[left + j];
		}
		for(int j = 0; j < n2; j++) {
			R[j] = S[mid + j];
		}
		L[n1] = int.MaxValue;
		R[n2] = int.MaxValue;

		for(int k = left, i = 0, j = 0; k < right; k++) {
			if(L[i] <= R[j]) {
				S[k] = L[i];
				count++;
				i++;
			} else {
				S[k] = R[j];
				count++;
				j++;
			}
		}

	}
 
	static void mergeSort(int[] S, int left, int right) {
	
		if(left + 1 < right) {
			int mid = (right + left) / 2;
			mergeSort(S, left, mid);
			mergeSort(S, mid, right);
			merge(S, left, mid, right);
		}

	}

}