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<cstring>
#include<algorithm>
using namespace std;
#define MAXN 500000+2
int AA[MAXN],TT[MAXN];
int n,g=0;
void input(){
	cin>>n;
	for(int i=0;i<n;++i){
		cin>>AA[i];
	}
}
void syf(int *A,int x,int y,int *T){
	if(y-x>1){
		int m=(x+y)/2;
		int i=x,p=x,q=m;
		syf(A,x,m,T);
		syf(A,m,y,T);
		while(p<m||q<y){
			if(q>=y||(p<m&&A[p]<=A[q])) T[i++]=A[p++];
			else T[i++]=A[q++];
			g++;
		}
		for(int i=x;i<y;++i){
			A[i]=T[i];
			AA[i]=T[i];
		}
	}
}
int main(){
	input();
	syf(AA,0,n,TT);
	for(int i=0;i<n-1;++i){
		cout<<AA[i]<<" ";
	}
	cout<<AA[n-1]<<endl;
	cout<<g<<endl;
	return 0;
}