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;

#define MAX 2000000000

int n, S[500000];
int L[500000/2+1], R[500000/2+1];
int cnt;

void merge(int left, int mid, int right) {
	int n1 = mid - left, n2 = right - mid;
	for (int i = 0; i < n1; i++)
		L[i] = S[left + i];
	for (int i = 0; i < n2; i++)
		R[i] = S[mid + i];
	L[n1] = MAX;
	R[n2] = MAX;
	int i = 0, j = 0;
	for (int k = left; k < right; k++) {
		if (L[i] <= R[j]) {
			S[k] = L[i];
			i++;
		} else {
			S[k] = R[j];
			j++;
		}
		cnt++;
	}
}

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];
	cnt = 0;
	mergesort(0, n);
	for (int i = 0; i < n - 1; i++)
		cout << S[i] << " ";
	cout << S[n - 1] << endl;
	cout << cnt << endl;
	return 0;
}

