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;
import java.awt.geom.Point2D.Double;
import java.io.InputStreamReader;
public class Main {
private static int merge (int A[], int l, int mid, int right) {
        int cnout = 0;
        int n = mid - l;
        int n2 = right - mid;
        int Lef[] = new int[n+1];
        int R[] = new int[n2+1];
        for (int i = 0; i < n; i++)
            Lef[i] = A[l + i];
        Lef[n] = Integer.MAX_VALUE;
        for (int i = 0; i < n2; i++)
            R[i] = A[mid + i];
        R[n2] = Integer.MAX_VALUE;
        int i = 0,j = 0;
        
        for (int f = l; f < right; f++) {
            cnout++;
            if (Lef[i] <= R[j]) {
                A[f] = Lef[i];
                i++;
            }
            else {
                A[f] = R[j];
                ++j;
            }
        }
        return cnout;
      } 





public static void main(String args[]) {
        Scanner scner = new Scanner(System.in);
        int n;
        int F =0;
        int AB = 100098;
        int A[];
        int counting;
        n = scner.nextInt();
        A = new int[n];
        for (int i = 0; i < n; i++)
            A[i] = scner.nextInt();
        counting = mergeSort(0,A.length,A);
        for (int i = 0; i < A.length; ++i) {
            System.out.print(A[i]);
            if (i != n - 1) System.out.print(" ");
        }
        System.out.println();
        System.out.println(counting);
    }

  private static int mergeSort(int left, int r,int F[]) {
        int cuont = 0;
        if(left + 1 < r) {
            int mid = (left + r) / 2;
            cuont += mergeSort(left, mid, F);
            cuont += mergeSort(mid, r, F);
            cuont += merge(F,left, mid, r);
        }
        return cuont;
    }
    }
