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<bits/stdc++.h>
using namespace std;

int n,a[500105],m;
long long inf=2e9;
void Merge( int left , int mid , int rigth ){
	int n1=mid-left, n2=rigth-mid;
	int l[n1],r[n2];
	for(int i=0 ; i<n1 ; i++){
		l[i]=a[left+i];
	}
	for(int i=0 ; i<n2 ; i++){
		r[i]=a[mid+i];
	}
	l[n1]=inf;
	r[n2]=inf;
	int x=0,y=0;
	for(int i=left ; i<rigth ; i++){
		if(l[x]>r[y]){
			a[i]=r[y];
			y++;
		}
		else{
			a[i]=l[x];
			x++;
		}
	
		m++;
	}
}

void mergesort( int l, int r ){
	if( l+1<r ){
		int mid=(l+r)/2;
		mergesort( l , mid );
		mergesort( mid , r );
		Merge( l , mid , r );
	}
}

int main(){
	
	cin >> n;
	for(int i=0 ; i<n ; i++){
		cin >> a[i];
	}
	
	mergesort( 0 , n );
	
	for(int i=0 ; i<n ; i++){
		cout << a[i];
		if(i!=n-1) printf(" ");
	}
	cout << endl;
	cout << m << endl;
}


/*

*/
