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>

using namespace std;
int a[500000];
int b[500000];
int c =0;
void merge_sort(int l,int r){
    if (r-l==1)return;
    int mid = (l+r)/2;
    merge_sort(l,mid);
    merge_sort(mid,r);


    int lp=l,rp=mid;
    for(int i=l;i<r;i++){
        if (lp==mid){
            b[i]=a[rp];
            rp++;
        }
        else if(rp==r){
            b[i]=a[lp];
            lp++;
        }
        else if(a[lp]>a[rp]){
            b[i]=a[rp];
            rp++;
        }
        else{
            b[i]=a[lp];
            lp++;
        }
        c++;
    }
    for(int i=l;i<r;i++){
        a[i]=b[i];
    }
}

int main(){
    int n;
    cin>>n;
    for(int i=0;i<n;i++){
        cin>>a[i];
    }
    merge_sort(0,n);
    for (int i = 0;i < n;i++){
        cout << a[i];
        if(i<n-1){
            cout<<" ";
        }
    }
    cout<<endl;
    cout<<c<<endl;
}
