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;
typedef long long ll;
const int MOD = 1e9+7,MAX = 1e5;

int arr[500001];
int ans = 0;

void marge_sort(int l,int r)
{
	if(r-l==1)return;
	int mid = (l+r)/2;
	marge_sort(l,mid);
	marge_sort(mid,r);
	vector<int> v;
	int i = l;
	int j = mid;
	while(1)
	{
		
		if(i==mid||j==r)break;
		ans++;
		if(arr[i]<arr[j])
		{
			
			v.push_back(arr[i]);
			i++;
		}
		else
	 	{
			 v.push_back(arr[j]);
			 j++;
		}
	}
	
	for(;i<mid;i++)v.push_back(arr[i]),ans++;
	for(;j<r;j++)v.push_back(arr[j]),ans++;
	for(int k = l;k<r;k++)
	{
		arr[k] = v[k-l];
	}
}

int main()
{
	int n;
	cin >> n;
	for(int i =0;i<n;i++)
	{
		cin >> arr[i];
	}
	marge_sort(0,n);
	for(int i = 0;i<n;i++)
	{
		if(i)cout<<' ';
		cout<<arr[i];
	}
	cout<<endl;
	cout<<ans<<endl;
	return 0;
}
