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.*;
import java.io.*;
public class Main {

    int count = 0;
    public static void main(String[] args) {
        new Main().runner();
    }

    public void runner() {
        Scanner in = new Scanner(System.in);
        int n=Integer.parseInt(in.next());
        int A[] = new int[n];
        for(int i=0; i<n; i++) {
            A[i] = Integer.parseInt(in.next());
        }
        MergeSort(A, 0, n);
        System.out.print(A[0]);
        for (int i = 1; i < n; i++) {
            System.out.print(" " +A[i]);
        }
        System.out.println();
        System.out.println(count);
        
    }

    public 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 L = 0;
        int R = 0;
        for (int k = left; k < right; k++) {
            if (l[L] <= r[R]) {
                A[k] = l[L++];
            } else {
                A[k] = r[R++];
            }
            count++;
        }
    }


    public 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);
        }
    }
}
