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


#define MAXN (500000+50)

#include<iostream>

using namespace std;

int arr[MAXN];
int exc[MAXN];

int N;
int T(0);

void msort(int l,int r)
{
	int mid((l+r)>>1);
	if(r-l<=1)
		return;
	msort(l,mid);
	msort(mid,r);
	int p1(mid-1),p2(r-1);
	for(int i=r-1;i>=l;--i)
	{//++T;
		if(p1<l)
		{
			exc[i]=arr[p2--];
			continue;
		}
		if(p2<mid)
		{
			exc[i]=arr[p1--];
			continue;
		}
		if(arr[p1]<arr[p2])
			exc[i]=arr[p1--];
		else
			exc[i]=arr[p2--];
	}
	for(int i=l;i<r;++i)
	{
		++T;
		arr[i]=exc[i];
	}
}
int main()
{
	cin>>N;
	for(int i=0;i<N;++i)
		cin>>arr[i];
	msort(0,N);
	for(int i=N-1;i>0;--i)
		cout<<arr[i]<<' ';cout<<arr[0]<<endl;
	cout<<T<<endl;
	return 0;
}