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<stack>
#include<string>
#include<stdio.h>
#include<algorithm>
using namespace std;
int merges(int start,int end) {
	int middle;
	if (start + 1 < end) {

		middle = (start + end) / 2;
		return (merges(start, middle) + merges(middle , end)-start+end);
	}
	else { return 0; }
}

int main()
{
	int n, dat[500000]; cin >> n;
	for (int i = 0; i < n; i++)
	{
		cin >> dat[i];
	}
	sort(dat, dat + n);
	for (int i = 0; i <n; i++)
	{
		if (i != 0) {
			cout << " ";
		}
		cout << dat[i];
	}
	
	cout << endl << merges(0, n) << endl;
	return 0;
}