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[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = sc.nextInt();
        }
        int count = mergeSort(arr,  0, n, 0);

        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < n - 1; i++) {
            sb.append(arr[i]);
            sb.append(" ");
        }
        sb.append(arr[n - 1]);

        System.out.println(sb);
        System.out.println(count);


    }

    static int merge(int[] arr, 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] = arr[left + i];
        }
        for (int i = 0; i < n2; i++) {
            r[i] = arr[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]) {
                arr[k] = l[i];
                i = i + 1;
            } else {
                arr[k] = r[j];
                j = j + 1;
            }
        }
        return count;
    }

    static int mergeSort(int[] arr, int left, int right, int count) {
        if (left + 1 < right) {
            int mid = (left + right) / 2;
            int x = mergeSort(arr, left, mid, count);
            int x2 = mergeSort(arr, mid, right, count);
            count = count + x + x2 + merge(arr, left, mid, right);
        }
        return count;
    }
}
