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;
int a[500000],cnt,l[250005],r[250005];
void merge(int left,int mid,int right){
  int x=mid-left,y=right-mid;
  for(int i=0;i<x;++i) l[i]=a[left+i];
  for(int i=0;i<y;++i) r[i]=a[mid+i];
  l[x]=r[y]=1000000001;
  x=y=0;
  for(int i=left;i<right;++i){
    ++cnt;
    if(l[x]<=r[y]) a[i]=l[x++];
    else a[i]=r[y++];
  }
}

void mergesort(int left,int right){
  if(left+1<right){
    int mid=(right+left)/2;
    mergesort(left,mid);
    mergesort(mid,right);
    merge(left,mid,right);
  }
}

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

