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<vector>
#define N 500000
#define INF 2000000000
using namespace std;
int c;

void merge(int *A,int l,int m,int r){
  vector<int> L,R;
  for(int i=l;i<m;i++)L.push_back(A[i]);
  for(int i=m;i<r;i++)R.push_back(A[i]);  
  int i=0,j=0;
  L.push_back(INF);
  R.push_back(INF);
   for(int k=l;k<r;k++){
     if(R[j]>L[i])A[k]=L[i++];
     else A[k]=R[j++];
     c++;
  }
}

void mergesort(int *A,int l,int r){
  if(l+1<r){
    int m=(l+r)/2;
    mergesort(A,l,m);
    mergesort(A,m,r);
    merge(A,l,m,r);
  }
}
 
 
int main(){
  int n,S[N];
  cin>>n;
  for(int i=0;i<n;i++)cin>>S[i];
  mergesort(S,0,n);
  for(int i=0;i<n-1;i++)cout<<S[i]<<" ";
  cout<<S[n-1]<<endl<<c<<endl;
  return 0;
}
