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 JAVA (judge verdict: Time Limit Exceeded)

import java.io.*;

public class Main{

	private static int merge(int A[], int left, int mid, int right){
		int cnt = 0;
		int n1 = mid - left; // ????????¨??????????´???°
		int n2 = right - mid; // ????????¨??????????´???°
		int[] L = new int[n1+1], R = new int[n2+1];
		for(int i = 0; i < n1; i++)
			L[i] = A[left + i]; // ????????¨??????????????????????????????mid???????????????
		L[n1] = Integer.MAX_VALUE; // ?????§????????????
		for(int i = 0; i < n2; i++)
			R[i] = A[mid + i]; // ????????¨??????????????????????????????mid????????????right???????????????
		R[n2] = Integer.MAX_VALUE; // ?????§????????????
		int i = 0;
		int j = 0;
		for(int k = left; k < right; k++){ //?????????????´??????????????????\???????????????

			if(L[i] <= R[j]){ // ????????¨??????????´????????????¨??????????´????????°????????????°
				A[k] = L[i]; // ?°???????????????¨??????????´???????????????????
				i++; // ????????¨?????????????????????????????????
			}else{
				A[k] = R[j]; // ?°???????????????¨??????????´???????????????????
				j++; // ????????¨????????????????????????????????????
			}
			cnt++; // ???????????°????????????
		}
		return cnt;
	}

	private static int mergeSort(int A[], int left, int right){
		int cnt = 0;
		if(left + 1 < right){ // ?????????????????????????¬???????????????????????????§???????????°
			int mid = (left + right) / 2; // ???????????????????????????mid????????????
			cnt += mergeSort(A, left, mid); // ?????°???????????????????????¨?????????????????????
			cnt += mergeSort(A, mid, right); // ?????°???????????????????????¨??????????????????
			cnt += merge(A, left, mid, right); // ??±?????????
		}
		return cnt;
	}

	public static void main(String[] args) throws IOException{

		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n, cnt;
		int[] A;
		n = Integer.parseInt(br.readLine());
		A = new int[n];
		String[] in = br.readLine().split(" ");
		for(int i = 0; i < n; i++)
			A[i] = Integer.parseInt(in[i]);
		cnt = mergeSort(A, 0, A.length);
		for(int i = 0; i < n; i++)
			System.out.printf(i != n-1? "%d " : "%d\n", A[i]);
		System.out.printf("%d\n", cnt);
		
	}
}