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)


Notes

Constraints

* n ≤ 500000
* 0 ≤ an element in S ≤ 109

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.

Example

Input

10
8 5 9 2 6 3 7 1 10 4


Output

1 2 3 4 5 6 7 8 9 10
34
import java.util.*;
import java.io.*;
class Main{

	static int count=0; //number of comparisons
	public static void main(String[]args) throws IOException{
		BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
		//Scanner in=new Scanner(System.in);
		PrintWriter out=new PrintWriter(System.out, true);
		int n=Integer.parseInt(in.readLine());
		String str[]=in.readLine().split(" ");
		int a[]=new int[n];
		for(int i=0;i<n;i++)
			a[i]=Integer.parseInt(str[i]);
		merge_sort(a, 0, n-1);
		for(int i=0;i<n;i++){
			if(i==n-1)
				out.printf(a[i]+"\n");
			else
				out.print(a[i]+" ");
		}
		out.println(count);
	}

	public static void merge_sort(int[] arr, int left, int right){
		if(left<right){
			int m=(left+right)/2;

			merge_sort(arr, left, m);
			merge_sort(arr, m+1, right);

			merge(arr, left, m, right);
		}
	}

	public static void merge(int[] arr, int left, int mid, int right){
		int n1=mid-left+1;
		int n2=right-mid;

		int l[]=new int[n1];
		int r[]=new int[n2];

		for(int i=0;i<n1;i++)
			l[i]=arr[left+i];
		for(int j=0;j<n2;j++)
			r[j]=arr[mid+1+j];

		int i=0, j=0;
		
		int k=left;

		while(i<n1 && j<n2){
			if(l[i]<=r[j]){
				arr[k]=l[i];
				i++;
			}else{
				arr[k]=r[j];
				j++;
			}
			k++;
			count++;
		}

		while(i<n1){
			arr[k]=l[i];
			i++;
			k++;
			count++;
		}
		while(j<n2){
			arr[k]=r[j];
			j++;
			k++;
			count++;
		}
	}
}
