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<bits/stdc++.h>
using namespace std;
#define int long long
const int INF=1LL<<55LL; 
int cnt;
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]=INF;
  R[n2]=INF;
  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 *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);
  }
}
signed main(){
  cin.tie(0);
  ios::sync_with_stdio(0);
  int n;
  cin>>n;
  int S[n];
  for(int i=0;i<n;i++) cin>>S[i];
  cnt=0;
  mergeSort(S,0,n);
  for(int i=0;i<n;i++) cout<<S[i]<<" \n"[i==n-1];
  cout<<cnt<<endl;
  return 0;
}