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.Arrays;
import java.util.Scanner;

public class Main {

    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();

        int count = mergeSort(s, n, 0, n);

        System.out.println(Arrays.toString(s).replaceAll("[\\[\\],]", ""));
        System.out.println(count);
    }

    private static int mergeSort(int[] s, int n, int left, int right) {
        if (left + 1 >= right) return 0;
        int count = 0;
        int mid = (left + right) / 2;
        count += mergeSort(s, n, left, mid);
        count += mergeSort(s, n, mid, right);
        count += merge(s, n, left, mid, right);
        return count;
    }

    private static int merge(int[] s, 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] = s[left + i];
        for (int i = 0; i < n2; i++) r[i] = s[mid + i];
        l[n1] = Integer.MAX_VALUE;
        r[n2] = Integer.MAX_VALUE;
        int i = 0;
        int j = 0;
        int count = 0;
        for (int k = left; k < right; k++) {
            count++;
            if (l[i] <= r[j]) {
                s[k] = l[i++];
            } else {
                s[k] = r[j++];
            }
        }
        return count;
    }
}

