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<algorithm>
using namespace std;
int n,num[600001];
int s[600001];
int tot=0;
void hb(int s1,int e1,int s2,int e2){
	int w=s1,t=s1;
	while(s1<=e1&&s2<=e2){
		if(num[s1]<num[s2]) s[w++]=num[s1++];
		else s[w++]=num[s2++];
		tot++;
	}
	if(s1<=e1){
		for(s1;s1<=e1;s1++){
			s[w++]=num[s1];
			tot++;
		}
	}
	else{
		for(s2;s2<=e2;s2++){
			s[w++]=num[s2];
			tot++;
		}
	}
	for(int i=t;i<=e2;i++){
		num[i]=s[i];
		s[i]=0;
	}
}
void gb(int l,int r){
	if(l==r) return;
	int mid=(l+r)/2;
	gb(l,mid);
	gb(mid+1,r);
	hb(l,mid,mid+1,r);
}
int main(){
	cin>>n;
	for(int i=0;i<n;i++) cin>>num[i];
	gb(0,n-1);
	for(int i=0;i<n-1;i++) cout<<num[i]<<" ";
	cout<<num[n-1]<<"\n";
	cout<<tot<<"\n";
	return 0;
}