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 {

    static int SENTINEL = 2000000000;
    static int MAX = 500000;
    static int[] A = new int[MAX];
    static int[] L = new int[MAX/2 + 1];
    static int[] R = new int[MAX/2 + 1];
    static int cnt;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        for(int i = 0 ; i < n; i++){
            A[i] = sc.nextInt();
        }

        mergeSort(A,n,0,n);

        for(int i = 0 ; i < n; i ++){
            System.out.print(A[i]);
            if(i < n - 1){
                System.out.print(" ");
            }
        }
        System.out.println();
        System.out.println(cnt);
    }


    static void mergeSort(int[] A,int n,int left,int right){
        if(left + 1 < right){
            int mid = (left + right) / 2;
            mergeSort(A,n,left,mid);
            mergeSort(A,n,mid,right);
            merge(A,n,mid,left,right);
        }
    }

    static void merge(int[] A,int n,int mid,int left,int right){
        int n1 = mid - left;
        int n2 = right - mid;
        for(int i = 0;i < n1;i++){
            L[i] = A[left + i];
        }
        for(int i = 0;i < n2;i++){
            R[i] = A[mid + i];
        }

        L[n1] = R[n2] = SENTINEL;

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

}

