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>

#define INFTY 1000000001

using namespace std;

int cnt=0;

void merge(int a[],int left,int mid,int right){
  int n1=mid-left;
  int n2=right-mid;
  int L[n1+1],R[n2+1];
  for(int i=0;i<n1;i++) L[i]=a[left+i];
  for(int i=0;i<n2;i++) R[i]=a[mid+i];
  L[n1]=INFTY; R[n2]=INFTY;
  int i=0,j=0;
  for(int k=left;k<right;k++){
    cnt++;
    if(L[i]<=R[j]){
      a[k]=L[i];
      i++;
    }else{
      a[k]=R[j];
      j++;
    }
  }
}

void mergeSort(int a[],int left,int right){
  if(left+1<right){
    int mid=(left+right)/2;
    mergeSort(a,left,mid);
    mergeSort(a,mid,right);
    merge(a,left,mid,right);
  }
}

int main(){
  int n; cin >> n;
  int a[n];
  for(int i=0;i<n;i++) cin >> a[i];
  mergeSort(a,0,n);
  for(int i=0;i<n;i++){
    if(i) cout << " " << a[i];
    else cout << a[i];
  }
  cout << endl << cnt << endl;
}