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 cnt=0;
	public static int[] L=new int[500000/2+2];
	public static int[] R=new int[500000/2+2];
	public static void main(String[] args) {
		// TODO Auto-generated method stub

		Scanner scan =new Scanner(System.in);
		int n=scan.nextInt();
		int[] arr=new int[n];
		for(int i=0;i<n;i++){
			arr[i]=scan.nextInt();
		}
		mergeSort(arr,n,0,n);
		arrPrint(arr);
		System.out.println(cnt);
	}

	private static void mergeSort(int[] arr, int n, int low, int high) {
		// TODO Auto-generated method stub
		if(low+1<high){
			int mid=(low+high)/2;
			mergeSort(arr, n, low, mid);
			mergeSort(arr, n, mid, high);
			merge(arr, n, low, mid,high);
		}
	}

	private static void merge(int[] arr, int n, int low, int mid,int high){
		// TODO Auto-generated method stub
		int n1=mid-low;
		int n2=high-mid;
		for(int i=0;i<n1;i++) L[i]=arr[low+i];
		for(int i=0;i<n2;i++) R[i]=arr[mid+i];
		L[n1]=R[n2]=2000000000;
		int i=0,j=0;
		for(int k=low;k<high;k++){
			cnt++;
			if(L[i]<=R[j]){
				arr[k]=L[i++];
				
			}
			else{
				arr[k]=R[j++];
			}
		}
	}

	public static void arrPrint(int[] arr){
		int i=0;
		for(i=0;i<arr.length-1;i++)
			System.out.print(arr[i]+" ");
		System.out.println(arr[i]);
	}
}

