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>
#define MAX 500000
#define INF 2000000000
using namespace std;

int L[MAX/2+2],R[MAX/2+2];
int cnt = 0;

void Merge(int a[], int n, int left, int mid, int right){
	for(int i = 0; i < mid-left; i++)	L[i] = a[left+i];
	for(int i = 0; i < right-mid; i++)	R[i] = a[mid+i];
	L[mid-left] = R[right-mid] = INF;
	int i = 0, j = 0;
	for(int k = left; k < right; k++){
		cnt++;
		if(L[i] <= R[j])	a[k] = L[i++];
		else	a[k] = R[j++];
	} 
}

void Merge_sort(int a[], int n, int left, int right){
	if(left+1 < right){
		int mid = (right+left)/2;
		Merge_sort(a, n, left, mid);
		Merge_sort(a, n, mid, right);
		Merge(a, n, left, mid, right);
	}
}

int main(){
	int a[MAX], n;
	cin>>n;
	for(int i = 0; i < n; i++)
		cin>>a[i];
	Merge_sort(a, n, 0, n);
	for(int i = 0; i < n; i++){
		if(i)	cout<<" ";
		cout<<a[i];
	}
	cout<<endl<<cnt<<endl;
	return 0 ;
}

