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 {
	static int cnt=0;
	public static void Merge(int a[],int start,int end){
		if (start>=end) return;
		int center=(start+end)/2;
		Merge(a,start,center);
		Merge(a,center+1,end);
		int n1=center-start+1;
		int n2=end-center;
		int[] L=new int[n1];
		int[] R=new int[n2];
		for (int i=0;i<n1;i++){L[i]=a[start+i];}
		for (int i=0;i<n2;i++){R[i]=a[center+1+i];}
		int i=0; int j=0;
		for (int k=start;k<=end;k++){
			cnt++;
			if (i==n1) a[k]=R[j++];
			else if (j==n2) a[k]=L[i++];
			else if (L[i]<=R[j]) a[k]=L[i++];
			else a[k]=R[j++];
		}
	}
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
	    int n = in.nextInt();
	    int[] A = new int[n];
	    for (int i = 0; i<n; i++) {
	      A[i] = in.nextInt();
	    }
		Merge(A,0,n-1);
		for (int i=0;i<n;i++){
			System.out.print(A[i]);
			if (i<n-1) System.out.print(" ");
		}
		System.out.println();
		System.out.println(cnt);
	}
}