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.ArrayList;
import java.util.Scanner;

public class Main {
    static int counter = 0;

    public static void main(String[] args) {
        Scanner inp = new Scanner(System.in);
        int total = inp.nextInt();

        int[] list = new int[total];

        for (int k = 0; k < total; k++) {
            list[k] = inp.nextInt();
        }

        merge_sort(list, 0, total);

        StringBuilder pInt = new StringBuilder();
        
        int place = 0;
        for(int n : list) {
            if (place != 0) {
                pInt.append(" ").append(n);

            } else {
                pInt.append(n);
            }

            place++;
        }

        System.out.println(pInt);

        System.out.println(counter);
    }

    public 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];

        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] = Integer.MAX_VALUE;
        r[n2] = Integer.MAX_VALUE;

        int i = 0;
        int j = 0;

        for (int k = left; k < right; k++) {
            if (l[i] <= r[j]) {
                a[k] = l[i++];
            } else {
                a[k] = r[j++];
            }
            counter++;
        }
    }

    public static void merge_sort(int[] a, int left, int right) {
        if (left + 1 < right) {
            int mid = (left + right) / 2;
            merge_sort(a, left, mid);
            merge_sort(a, mid, right);
            merge(a, left, mid, right);
        }
    }
}
