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 count = 0;

    public static void main(String[] args) {

        Scanner scanner = new Scanner(System.in);

        int n = scanner.nextInt();

        int[] s = new int[n];

        for (int i = 0; i < n; i++) {

            s[i] = scanner.nextInt();

        }

        

        mergeSort(s, 0, n);

        

        for (int i = 0; i < n - 1; i++) {

            System.out.print(s[i] + " ");

        }

        System.out.println(s[n-1]);

        

        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[] aL = new int[n1 + 1];

        int[] aR = new int[n2 + 1];

        for (int i = 0; i < n1; i++) {

            aL[i] = a[left + i];

        }

        for (int i = 0; i < n2; i++) {

            aR[i] = a[mid + i];

        }

        

        aL[n1] = Integer.MAX_VALUE;

        aR[n2] = Integer.MAX_VALUE;

        

        int i = 0;

        int j = 0;

        for (int k = left; k < right; k++) {

            count++;

            if (aL[i] <= aR[j]) {

                a[k] = aL[i];

                i++;

            } else {

                a[k] = aR[j];

                j++;

            }

        }

    }

}


