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>
#include<algorithm>
#define inf 1000000001
using namespace std;
int ans;
void merge(int A[],int left,int mid,int right){
int n1=mid-left;
int n2=right-mid;
	int L[n1+1],R[n2+1];
	int i,k,j;
	for(i=0;i<n1;i++)
	L[i]=A[left+i];
	for(i=0;i<n2;i++)
	R[i]=A[mid+i];
	L[n1]=inf;
	R[n2]=inf;
	i=0;j=0;
	for(k=left;k<right;k++){
		ans++;
		if(L[i]<=R[j]){
		A[k]=L[i];
			i++;
		}
		else{
		A[k]=R[j];
			j++;
		}
		
		
	}
	
}
void Msort(int A[],int left,int right){
	int mid;
	if(left+1<right){
		mid=(left+right)/2;
		Msort(A,left,mid);
		Msort(A,mid,right);
		merge(A,left,mid,right);
	}
}
void print(int n,int a[]){
int i;
for(i=0;i<n-1;i++)
printf("%d ",a[i]);
printf("%d\n",a[n-1]);
}
int main(){
	int a[500000],n,i;
	ans=0;
	cin>>n;
	for(i=0;i<n;i++)
	cin>>a[i];
	Msort(a,0,n);
	print(n,a);
	cout<<ans<<endl;
	return 0;
}

