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<climits>
#define INF INT_MAX;
void merge(int*, int, int, int);
void mergeSort(int*, int, int);
int cnt=0;
int main(){
  int n;
  std::cin >> n;
  int A[n];
  for(int i=0; i<n; i++) std::cin >> A[i];
  mergeSort(A, 0, n);
  for(int i=0; i<n;i ++) std::cout << A[i] << (i != n-1 ? " " : "\n");
  std::cout << cnt << "\n";
  return 0;
}
void merge(int *A, int l, int m, int r){
  int n1=m-l, n2=r-m, i, j, L[n1+1], R[n2+1];
  for(i=0; i<n1; i++) L[i] = A[l+i];
  for(i=0; i<n2; i++) R[i] = A[m+i];
  i = j = 0, L[n1] = R[n2] = INF;
  for(int k=l;k<r;k++){
    if(L[i] <= R[j]) A[k] = L[i], i++, cnt++;
    else A[k] = R[j], j++, cnt++;
  }
}
void mergeSort(int *A, int l, int r){
  int m;
  if(l+1 < r){
    m = (l + r) / 2;
    mergeSort(A, l, m);
    mergeSort(A, m, r);
    merge(A, l, m, r);
  }
}