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
#include<iostream>
using namespace std;
const int MAXN = 500000+5;
int n,nu[MAXN],an[MAXN],tt(0);
void init(){
	cin>>n;
	for(int i=0;i<n;i++)
	    cin>>nu[i];
}
void sor(int l,int r){
	if(r-l>1){
	    int m(l+(r-l)/2),p(l),q(m),i(l);//l - m-1,m - r
		sor(l,m);
		sor(m,r);
		//cout<<"lmr  p="<<p<<"   m="<<m<<"  r="<<r<<endl;
		while(p<m||q<r){
			if(q>=r||(p<m&&nu[p]<=nu[q])) an[i++]=nu[p++];
			else an[i++]=nu[q++];
			tt++;
			//cout<<"p="<<p<<"   q="<<q<<endl;
			//cout<<an[i-1]<<' ';
	        //system("pause");
		}
		//cout<<endl;
		for(i=l;i<r;i++)
		    nu[i]=an[i];
		//cout<<"l="<<l<<"   r="<<r<<endl;for(i=l;i<r;i++) cout<<nu[i]<<' ';cout<<endl;
	}
}
int main(){
	init();
	sor(0,n);
	for(int i=0;i<n-1;i++)
	   cout<<nu[i]<<' ';
	cout<<nu[n-1]<<endl<<tt<<endl;
	return 0;
}