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.io.*;
import java.util.*;

public class Main{

    static int count=0;
    
    public static void main(String args[]) throws IOException{
	BufferedReader br=new BufferedReader(new InputStreamReader(System.in));

	int n=Integer.parseInt(br.readLine());
	String str[]=br.readLine().split(" ");
	int a[]=new int[n];
	
	for(int i=0;i<n;i++){
	    a[i]=Integer.parseInt(str[i]);
	}

	mergeSort(a,0,n);

	System.out.print(a[0]);
	for(int i=1;i<n;i++){
	    System.out.print(" "+a[i]);
	}
	System.out.print("\n");
	System.out.println(count);
    }
    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);
	}
    }

    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];

	int i=0;
	int j=0;
	
	for (i = 0;i<n1;i++)
	    L[i] = A[left + i];
	for (i = 0;i<n2;i++)
	    R[i] = A[mid + i];
	L[n1] = Integer.MAX_VALUE;
	R[n2] = Integer.MAX_VALUE;
	i=0;
	j=0;
	for (int k = left; k<right;k++){
	    if (L[i] <= R[j]){
		A[k] = L[i];
		i = i + 1;
	    }else{ 
		A[k] = R[j];
		j = j + 1;
	    }
	    count++;
	}
    }
}

