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 int long long

const int INF = 1e18;
int n,cnt;
int a[500010];
int L[300010],R[300010];

void merge(int l,int m,int r){
  int n1 = m-l;
  int n2 = r-m;
  for(int i = 0; i < n1; i++) L[i] = a[l+i];
  for(int i = 0; i < n2; i++) R[i] = a[m+i];
  L[n1] = R[n2] = INF;
  int i = 0,j = 0;
  for(int k = l; k < r; k++){
    if(L[i] <= R[j]) a[k] = L[i++];
    else {
      a[k] = R[j++];
    }
    cnt++;
  }
}

void mergesort(int l,int r){
  if(l+1 == r) return;
  int m = (l+r)/2;
  mergesort(l,m);
  mergesort(m,r);
  merge(l,m,r);
}

signed main(){

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

  mergesort(0,n);

  for(int i = 0; i < n; i++){
    if(i == n-1) cout << a[i] << endl;
    else cout << a[i] << " ";
  }
  cout << cnt << endl;

  return 0;
}

