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>
#define INF 1000000001
#define MAX 500000
using namespace std;
int N, S[MAX], res;

void Out() {
	cout << S[0];
	for (int i = 1; i < N; i++)
		cout << ' ' << S[i];
	cout << endl;
}

void Merge(int left, int mid, int right) {
	int n1 = mid - left, n2 = right - mid;
	vector<int> L(n1 + 1, INF), R(n2 + 1, INF);
	for (int i = 0; i < n1; i++)
		L[i] = S[left + i];
	for (int i = 0; i < n2; i++)
		R[i] = S[mid + i];
	for (int i = 0, j = 0, k = left; k < right; k++) {
		if (L[i] <= R[j]) {
			S[k] = L[i];
			i++;
		}
		else {
			S[k] = R[j];
			j++;
		}
		res++;
	}
}

void MergeSort(int left, int right) {
	if (left + 1 < right) {
		int mid = (left + right) / 2;
		MergeSort(left, mid);
		MergeSort(mid, right);
		Merge(left, mid, right);
	}
}

int main()
{
	cin >> N;
	for (int i = 0; i < N; i++)
		cin >> S[i];
	MergeSort(0, N);
	Out();
	cout << res << endl;
	return 0;
}