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;
int n,*a,cnt = 0;
void Merge(int left,int mid,int right)
{
	int n1 = mid-left,n2 = right-mid;
	int *L,*R;
	L = new int [n1+1]; R = new int [n2+1];
	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] = R[n2] = 1e9+1;
	int i = 0,j = 0;
	for(int k = left;k < right;k++)
	{
		cnt++;
		if(L[i] <= R[j]) a[k] = L[i++];
		else a[k] = R[j++];
	}
}
void Merge_Sort(int left,int right)
{
	if(right-left <= 1) return ;
	int mid = (left+right)/2;
	Merge_Sort(left,mid);
	Merge_Sort(mid,right);
	Merge(left,mid,right); 
}
int main(void)
{

	scanf("%d",&n); a = new int [n];
	for(int i = 0;i < n;i++) scanf("%d",&a[i]);
	Merge_Sort(0,n);
	for(int i = 0;i < n;i++) printf("%d%c",a[i],(i == n-1)?'\n':' ');
	printf("%d\n",cnt);
	return 0;
}
