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<bits/stdc++.h>
using namespace std;

#define INF 1000000001

long s[500000];
int cnt = 0;


void Merge(int left, int mid , int right){

  int n1 = mid-left;
  int n2 = right - mid;

  long L[250001],R[250001];

  for(int i=0; i<n1; i++)L[i] = s[left+i];

  for(int i=0; i<n2; i++)R[i] = s[mid+i];

  L[n1] = R[n2] = INF;
  
  int r,l=r=0;
  for(int i=left; i<right; i++){
    if(L[l] <= R[r]) s[i] = L[l++];
    else             s[i] = R[r++];
    cnt++;
  }

}

void MergeSort(int left, int right){
  if(left+1 < right){
    int mid = (left+right)/2;
    MergeSort(left , mid);
    MergeSort(mid , right);
    Merge(left , mid , right);
  }
}


int main(){
 
  int n;

  cin >> n;

  for(int i=0; i<n; i++)cin>>s[i];

  MergeSort(0 , n);

  cout << s[0];
  for(int i=1; i<n; i++)cout << ' ' <<s[i];
  cout << endl << cnt << endl;

  return 0;
}