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>
#include <stack>
#include <cmath>
using namespace std;

int n, a[500000], cnt = 0;

void func(int l, int r){
  if(l + 1 >= r) return;
  int m = (l + r) / 2;
  func(l, m);
  int t1[m - l + 1], t2[r - m + 1];
  for(int i = l; i < m; i++){
    t1[i - l] = a[i];
  }
  t1[m - l] = 1000000001;
  func(m, r);
  for(int i = m; i < r; i++){
    t2[i - m] = a[i];
  }
  t2[r - m] = 1000000001;
  int t1i = 0, t2i = 0;
  for(int i = l; i < r; i++){
    if(t1[t1i] <= t2[t2i]) a[i] = t1[t1i++];
    else a[i] = t2[t2i++];
    cnt++;
  }
  /*for(int i = l; i < r; i++){
    cout << a[i]
  }*/
  return;
}

void solve(){
  cin >> n;
  for(int i = 0; i < n; i++) cin >> a[i];
  func(0, n);
  for(int i = 0; i < n - 1; i++) cout << a[i] << " "; cout << a[n - 1] << endl;
  cout << cnt << endl;
  return;
}

int main(){
  solve();
  return 0;
}

