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>

using namespace std;

int n;
int x = 0;

void merge_sort(int a[], int left, int right);
int main(){

  cin >> n;

  int a[n];

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

  merge_sort(a, 0, n-1);

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

  cout << "\n";

  cout << x << '\n';

  return 0;
}
void merge_sort (int a[], int left, int right) {

  int i, j, k, mid;
  int tmp[n];
  if(left < right){
    mid = (left + right) / 2;
    merge_sort(a, left, mid);
    merge_sort(a, mid+1, right);
    for(i = mid; i >= left; i--){
      tmp[i] = a[i];
    }
    for(j = mid + 1; j <= right; j++){
      tmp[right-(j-(mid+1))] = a[j];
    }
    i = left; j = right;
    for(k = left; k <= right; k++) {
      x++;
      if(tmp[i] < tmp[j]){
        a[k] = tmp[i++];
      }
      else{
        a[k] = tmp[j--];
      }
    }
  }
}

