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<cstdio>
#include<cmath>
#include<string>
#include<cstdlib>
#include<utility>
using namespace std;

int A[500500];
int L[500500];
int R[500500];
int cnt;

void merge(int l, int m, int r){
	int n1 = m-l;
	int n2 = r-m;
	for(int i=0; i<n1; i++){
		L[i] = A[l+i];
	}
	for(int i=0; i<n2; i++){
		R[i] = A[m+i];
	}
	L[n1] = 1001001001;
	R[n2] = 1001001001;
	int i = 0;
	int j = 0;
	for(int k=l; k<r; k++){
		if(L[i]<R[j]){
			A[k] = L[i];
			i++;
		}else{
			A[k] = R[j];
			j++;
		}
		cnt++;
	}
}

void merge_sort(int l, int r){
	if(l+1<r){
		int m = (l+r)/2;
		merge_sort(l, m);
		merge_sort(m, r);
		merge(l, m, r);
	}
}

int main(){
	int n;
	cin >> n;
	for(int i=0; i<n; i++){
		cin >> A[i];
	}
	cnt = 0;
	merge_sort(0, n);

	for(int i=0; i<n; i++){
		cout << A[i];
		if(i==n-1) cout << endl;
		else cout << " ";
	}
	cout << cnt << endl;
	return 0;
}