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.Arrays;
import java.util.Scanner;

public class Main{
	static int num = 0;
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int[] a = new int[scanner.nextInt()];

		
		for(int i = 0; i < a.length; i++) {
			a[i] = scanner.nextInt();
		}
		
		int[] b = sortlist(a);
		for(int i = 0; i < a.length - 1; i++) {
			System.out.print(b[i]+" ");
		}
		System.out.print(b[a.length - 1]);
		System.out.println();
		System.out.println(num);
		scanner.close();
	}
	
	private static int[] sortlist(int[] i) {
		if(i.length == 1) {
			return i;
		}else {
			
			int[] a = sortlist(Arrays.copyOfRange(i,0,i.length/2));
			int[] b = sortlist(Arrays.copyOfRange(i, i.length/2, i.length));
			int j = 0, k = 0;
			while(j < a.length && k < b.length) {
				num += 1;
				if(a[j] > b[k]) {
					i[j+k] = b[k];
					k++;
				}else {
					i[j+k] = a[j];
					j++;
				}
			}
			if(j == a.length) {
				while(k < b.length) {
					num += 1;
					i[j+k] = b[k];
					k++;
				}
			}else {
				while(j < a.length) {
					num+= 1;
					i[j+k] = a[j];
					j++;
				}
			}
			return i;
		}
	}
}
