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 int count=0;
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n, i;
		n = scan.nextInt();
		int[] s = new int[n];
		for (i = 0; i < n; i++) {
			s[i] = scan.nextInt();
		}
		margesort(s);
		scan.close();
		show(s);
		System.out.println(count);
	}
	public static void margesort(int[] a) {
		if(a.length>1) {
			int m,n;
			m=a.length/2;
			n=a.length-m;
			int[] a1=new int[m];
			int[] a2=new int[n];
			System.arraycopy(a, 0, a1, 0, m);
			System.arraycopy(a, m, a2, 0, n);
			margesort(a1);
			margesort(a2);
			marge(a1,a2,a);
		}
	}
	public static void marge(int[] a1,int[] a2,int[] a) {
		int i=0,j=0;
		while(i<a1.length || j<a2.length) {
			if(j>=a2.length || (i<a1.length && a1[i]<a2[j])) {
				a[i+j]=a1[i];
				i++;
			}
			else {
				a[i+j]=a2[j];
				j++;
			}
			count++;
		}
	}
	public static void show(int[] a) {
		int i;
		for(i=0;i<a.length-1;i++) {
			System.out.print(a[i]+" ");
		}
		System.out.println(a[a.length-1]+"");
	}
}
