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>
#define N 500010
#define INF (1e9)+1
using namespace std;
int cnt;

void merge(int A[],int l,int m,int r){
  int n1 = m - l;
  int n2 = r - m;
  int L[N],R[N];
  for(int i=0;i<n1;i++) L[i] = A[l+i];
  for(int i=0;i<n2;i++) R[i] = A[m+i];
  L[n1] = R[n2] = INF;

  for(int k = l,i=0,j=0; k<r;k++){
    cnt++;
    if(L[i]<=R[j]) A[k] = L[i++];
    else A[k] = R[j++];
  }
}

void mergeSort(int A[],int l,int r){
  if(l+1 >= r) return;
  
  int m = (l+r)/2;
  mergeSort(A,l,m);
  mergeSort(A,m,r);
  merge(A,l,m,r);
}


int A[N];

int main(){
  int n;
  cin>>n;
  for(int i=0;i<n;i++) scanf("%d",&A[i]);

  mergeSort(A,0,n);

  for(int i=0;i<n;i++){
    if(i)printf(" ");
    printf("%d",A[i]);
  }
  cout<<endl<<cnt<<endl;
  return 0;
}