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 A[500002];
int O[500002];
int n;
int c = 0;
void msort(int b, int e){
	if (e-b==1) return;
	
	if (e-b==2)
	{
		int & ab = A[b];
		int & ae = A[b+1];
		if (ab > ae)
		{
			int abb = ab;
			ab=ae;
			ae=abb;
		}
		c+=2;
		return;
	}
	
	int m=(b+e)/2;
	msort(b,m);
	msort(m,e);
	int j=0;
	for(int i=b;i<m;i++){
		O[j++]=A[i];
	}
	O[j++]=0x7fffffff;
	for(int i=m;i<e;i++){
		O[j++]=A[i];
	}
	O[j++]=0x7fffffff;
	int o1=0;
	int o2=m-b+1; /// <-- was the bug.
	for (int i=b;i<e;i++){
		if(O[o1]<O[o2]){
			A[i]=O[o1++];
		}else{
			A[i]=O[o2++];
		}
		c++;
	}
}
int main(){
	cin >> n;
	for(int i=0;i<n;i++)cin>>A[i];
	msort(0,n);
	for(int i=0;i<n;i++){
		if (i) cout <<' ';
		cout<<A[i];
	}
	cout << endl<<c<<endl;
}