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 n,m;
long long g=0;
int jl[MAXN];
int t[MAXN];
void input(){
	cin>>n;
	for(int i=0;i<n;++i){
		cin>>jl[i];
	}
}
void gb(int* A,int x,int y,int* T){
    if(y-x>1){
    	int m=(x+y)/2;
    	int p=x,q=m,i=x;
    	gb(A,x,m,T);
    	gb(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(i=x;i<y;++i){
    	    A[i]=T[i];
	    }
    }
    return;
}
int main(){
	input();
	gb(jl,0,n,t);
	for(int i=0;i<n-1;++i){
		cout<<jl[i]<<" ";
	}
	cout<<jl[n-1]<<endl;
	cout<<g<<endl;
}