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;
int b[999999], n, c[999999];
int main() {
	cin >> n;
	for (int i = 0; i < n; i++) {
		scanf("%d",&c[i]);
	}
	b[1] = 0;
	for (int i = 2; i <= n; i++) {
		b[i] = b[i / 2] + b[(i + 1) / 2] + i;
	}
	sort(c, c + n);
	for (int i = 0; i < n; i++) {
		cout << c[i];
		if (i < n - 1) {
			cout << ' ';
		}
		else { cout << endl; }
	}
	cout << b[n] << endl;
	return 0;
}