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 INF 1e9
using namespace std;
int cnt;

void merge(int A[],int L,int M,int R){
  int n1=M-L;
  int n2=R-M;
  int a[500000],b[500000];
  for(int i=0;i<n1;i++)a[i]=A[L+i];
  for(int i=0;i<n2;i++)b[i]=A[M+i];
  a[n1]=INF,b[n2]=INF;
  int i=0,j=0;

  for(int k=L;k<R;k++){
    cnt++;
    if(a[i]<=b[j]) A[k]=a[i++];
    else A[k]=b[j++];
  }
}

void mergeSort(int A[],int L,int R){
  if(L+1<R){
    int M=(L+R)/2;
    mergeSort(A,L,M);
    mergeSort(A,M,R);
    merge(A,L,M,R);
  }
}

int main(){
  int n, a[500000];
  cin>>n;
  for(int i=0;i<n;i++)cin>>a[i];
  mergeSort(a,0,n);
 
  for(int i=0;i<n-1;i++)cout <<a[i]<<" ";
  cout <<a[n-1]<<endl;
  cout <<cnt<<endl;
  return 0;
}