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.*;
public class Main {
	
	static int cmp=0;
	public static void main(String[] args) {
		Scanner in=new Scanner(System.in);
		int n=in.nextInt(),A[]=new int[n];
		
		for(int i=0;i<n;i++)A[i]=Integer.parseInt(in.next());
		
		margeSort(A,0,A.length-1);
		for(int i=0;i<n-1;i++)System.out.print(A[i]+" ");
		System.out.println(A[n-1]);
		System.out.println(cmp);
	}
	
	static void margeSort(int A[],int left,int right) {
		int middle=(left+right)/2;
		if(left<right) {
			margeSort(A,left,middle);
			margeSort(A,middle+1,right);
		}
		else return;
		
		int k=left,l=middle+1,cnt=0,B[]=new int[right-left+1];
		while(k<=middle && l<=right) {
			if(A[k]<=A[l])B[cnt++]=A[k++];
			else B[cnt++]=A[l++];
			cmp++;
		}
		
		while(k<=middle) { 
			B[cnt++]=A[k++];
			cmp++;
		}
		while(l<=right) {
			B[cnt++]=A[l++];
			cmp++;
		}
		
		for(int i=0;i<B.length;i++)A[left+i]=B[i];
	}

}


