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[500009],t[500009],r=0;
void mergesort(int lo,int hi){
if(lo==hi) return;
int mid =(lo+hi)/2;
    mergesort(lo,mid);
    mergesort(mid+1,hi);

    int i,j,k;
    i=lo;
    j=mid+1;
    for(k=lo;k<=hi;k++){

        if(i==mid+1) t[k]=a[j++];
        else if(j==hi+1)  t[k]=a[i++];
        else if(a[i]<a[j]) t[k]=a[i++];
        else t[k]=a[j++];
        r++;
    }

     for(k=lo;k<=hi;k++){
     a[k]=t[k];
    }
}
int main()
{

  int m,n,i,j,s=0,t=0,te;
    cin>>n;
    for(i=0;i<n;i++) cin>>a[i];

mergesort(0,n-1);
for(i=0;i<n-1;i++) cout<<a[i]<<" ";
cout<<a[n-1]<<endl;
            cout<<r;
        cout<<endl;

    return 0;
}