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.*;

public class Main{
    static int SENTINEL=1000000001;
    static int cnt=0;
    public static void main (String args[]){


      
        //初期処理
        Scanner sc=new Scanner(System.in);
        int n=Integer.parseInt(sc.nextLine());
        String[] sElementArray=sc.nextLine().split(" ");
        int[] array=Arrays.stream(sElementArray).mapToInt(Integer::parseInt).toArray();
        // BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    //    try{
    //         n= Integer.parseInt(br.readLine());
    //         sElementArray = br.readLine().split(" ");
    //         array = Arrays.stream(sElementArray).mapToInt(Integer::parseInt).toArray();
    //     }catch(IOException e){e.printStackTrace();}

            mergeSort(array,n,0,n);
            String[] ss=Arrays.stream(array).mapToObj(Integer::toString).toArray(s->new String[s]);
            String str=String.join(" ",ss);
            System.out.println(str);
            System.out.println(cnt);
        
    }

    public static void mergeSort (int[] array,int n,int left,int right){
        if(left+1<right){
            int mid=(right+left)/2;
            
            mergeSort(array, n, left, mid);
            mergeSort(array, n, mid, right);
            merge(array,n,left,mid,right);
        }
    }
    
    public static void merge(int[] array,int n,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 i=0;i<n1;i++){L[i]=array[left+i];}
        for(int i=0;i<n2;i++){R[i]=array[mid+i];}
        L[n1]=SENTINEL;
        R[n2]=SENTINEL;

        int i=0;
        int j=0;
        for(int k=left;k<right;k++){
            if(L[i]<=R[j]){
                array[k]=L[i];
                i++;
            }else if(L[i]>R[j]){
                array[k]=R[j];
                j++;
            }
            cnt++;
        }

    }
}

