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 {
    private int count;

    public Main() {
        this.count = 0;
    }

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[] num = new int[n];
        for (int i = 0; i < n; i++) {
            num[i] = in.nextInt();
        }
        Main test = new Main();
        test.mergeSort(num, 0, n);

        for (int i = 0; i < n; i++) {
            System.out.print(num[i]);
            if (i != n - 1) {
                System.out.print(" ");
            } else {
                System.out.println();
            }
        }
        System.out.println(test.count);
    }

    public void merge(int[] num, int left, int mid, int right) {
        int n1 = mid - left;
        int n2 = right - mid;
        int[] L = new int[n1];
        int[] R = new int[n2];
        for (int i = 0; i < n1; i++) {
            L[i] = num[left + i];
        }
        for (int i = 0; i < n2; i++) {
            R[i] = num[mid + i];
        }
        int i = 0, j = 0, k = left;
        while (i < n1 && j < n2) {
            count++;
            if (L[i] <= R[j]) {
                num[k++] = L[i++];
            } else {
                num[k++] = R[j++];
            }
        }
        while (i < n1) {
            count++;
            num[k++] = L[i++];
        }
        while (j < n2) {
            count++;
            num[k++] = R[j++];
        }
//        for (int k = left; k < right; k++) {
//            count ++;
//            if (L[i] <= R[j]) {
//                num[k] = L[i++];
//            } else {
//                num[k] = R[j++];
//            }
//        }

    }

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

