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.Scanner;
public class Main {
    public static void main(String [] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int [] S = new int[n];
        int opt = 0;
        for(int i=0;i<n;i++) S[i] = sc.nextInt();
        opt = mergesort(S,opt,0,n);
        for(int i=0;i<n;i++){
            System.out.print(S[i]);
            if(i!=n-1) System.out.print(" ");
        }
        System.out.println();
        System.out.println(opt);
    }
    public static int  mergesort(int [] S,int sum,int left,int right){
        if(left+1<right){
            int mid = (left+right)/2;
            sum=mergesort(S,sum,left,mid);
            sum=mergesort(S,sum,mid,right);
            sum=merge(S,left,right,mid,sum);
        }
        return sum;
    }
    public static int merge(int [] S,int left,int right,int mid,int sum){
        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] = S[left+i];
        for(int i=0;i<n2;i++)R[i] = S[mid+i];
        L[n1]=999999999;
        R[n2]=999999999;
        int i=0,j=0;
        for(int k=left;k<right;k++){
            if(L[i]<=R[j]){
                S[k] = L[i];
                i++;
                sum++;
            }
            else{
                S[k] = R[j];
                j++;
                sum++;
            }
        }
        return sum;
    }
}
