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 MAXN 1000000+20 
using namespace std;
int n,a[MAXN],t[MAXN];
int tot;

void msort(int l,int r){
	if (l < r-1){
		int mid=l+(r-l)/2;
		int now=l;
		int p=l,q=mid;
		
		msort(l,mid);
		msort(mid,r);
		
		while (p < mid || q < r){
			tot++;
			if (p < mid && a[p] < a[q] || q == r) {
				t[now++]=a[p++];
			}
			else t[now++]=a[q++];
		}
		for (int i = l;i < now;++i)
			a[i]=t[i];
	}
}

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