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 final int MAX = 500000;
	public static final int SENTINEL = (int)Math.pow(10, 9) + 1;
	public static int[] A = new int[MAX];
	public static int[] L = new int[MAX/2+1];
	public static int[] R = new int[MAX/2+1];
	public static int count = 0;

	public static void main(String[] args){
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		for(int i = 0; i < n; i++){
			A[i] = scan.nextInt();
		}
		merge_sort(0,n);
		StringBuilder sb = new StringBuilder();
		for(int i = 0; i < n; i++){
			sb.append(A[i]);
			sb.append(" ");
		}
		System.out.println(sb.toString().trim());
		System.out.println(count);
	}


	public static void merge_sort(int left,int right){
		if(left+1 == right) return;
		int mid = (right + left) / 2;
		merge_sort(left,mid);
		merge_sort(mid,right);

		merge(left,right);
	}

	public static void merge(int left,int right){
		int mid = (right + left) / 2;
		int n1 = mid - left;
		int n2 = right - mid;
		for(int i = 0; i < n1; i++) L[i] = A[left + i];
		for(int y = 0; y < n2; y++) R[y] = A[mid + y];
		L[n1] = R[n2] = SENTINEL;

		int x = 0;
		int y = 0;
		for(int i = left; i < right; i++){
			count++;
			if(L[x] <= R[y]){
				A[i] = L[x++];
			}else{
				A[i] = R[y++];
			}
		}
	}
}