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>

const int SENTINENTAL=1e9+7;

using namespace std;

int cnt=0;
int n;
int A[500009];

void merge(int left, int mid, int right){
  int n1 = mid - left;
  int n2 = right - mid;
  vector<int>L, R;
  for(int i=0;i<n1;i++)L.push_back(A[left+i]);
  for(int i=0;i<n2;i++)R.push_back(A[mid+i]);
  L.push_back(SENTINENTAL);
  R.push_back(SENTINENTAL);
  int i=0, j=0;
  for(int k=left;k<right;k++){
    cnt++;
    if(L[i]<=R[j])A[k]=L[i++];
    else A[k]=R[j++];
  }
}

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(){
  cin >> n;
  int tmp;
  for(int i=0;i<n;i++){
    cin >> A[i];
  }
  mergeSort(0, n);
  for(int i=0;i<n;i++)cout << A[i] << (i<n-1?' ': '\n');
  cout << cnt << endl;
}
