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>
#define NMAX 500000
#define SENTINEL 2000000000
using namespace std;

int c=0;

void merge(int a[],int n,int first,int mid,int last){
    int F[NMAX+1],L[NMAX+1];
    int nf=mid-first;
    int nl=last-mid;
    for(int i=0;i<nf;i++) F[i]=a[first+i];
    for(int i=0;i<nl;i++) L[i]=a[mid+i];
    F[nf]=L[nl]=SENTINEL;
    int i=0,j=0;
    for(int k=first;k<last;k++){
        if(F[i]<=L[j]) a[k]=F[i++];
        else a[k]=L[j++];
        c++;
    }
}

void mergeSort(int a[],int n,int first,int last){
    if(last-first>1){
        int mid=(first+last)/2;
        mergeSort(a,n,first,mid);
        mergeSort(a,n,mid,last);
        merge(a,n,first,mid,last);
    }
}

int main(){
    int n,a[NMAX];
    cin>>n;
    for(int i=0;i<n;i++) cin>>a[i];
    mergeSort(a,n,0,n);
    for(int i=0;i<n;i++){
        cout<<a[i]<<((i==n-1)?'\n':' ');
    }
    cout<<c<<endl;
}
