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;

int x[500001];
int tmp[500001];
int cnt = 0;

void MergeSort(int left, int right){
  int mid, i, j, k;

  if(left >= right) return;

  mid = (left+right)/2;
  MergeSort(left, mid);
  MergeSort(mid+1, right);
  // x[left]~x[mid]???????\??????????
  for(i = left; i <= mid; i++) tmp[i] = x[i];
  // x[mid+1]~x[right]??????????????????
  for(i = mid+1, j = right; i <= right; i++, j--) tmp[i] = x[j];

  i = left;
  j = right;
  for(k = left; k <= right; k++){
    cnt++;
    if(tmp[i] <= tmp[j]){
      x[k] = tmp[i++];
    }else{
      x[k] = tmp[j--];
    }
  }
}

int main(){
  int n;
  cin >> n;
  for(int i = 0; i < n; i++) cin >> x[i];
  MergeSort(0, n-1);
  for(int i = 0; i < n; i++){
    cout << x[i] << (i != n-1 ? " " : "\n");
  }
  cout << cnt << endl;
  return 0;
}
