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;

const int INF=2000000000; 

int cnt;

void merge(int *A,int l,int mid,int r){
    int n1=mid-l;
    int n2=r-mid;
    int L[n1+1],R[n2+1];
    for(int i=0;i<n1;i++) L[i]=A[l+i];
    for(int i=0;i<n2;i++) R[i]=A[mid +i];
    L[n1]=INF;
    R[n2]=INF;
    int i=0,j=0;
    for(int k=l;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){
        int mid=(l+r)/2;
        mergesort(A,l,mid);
        mergesort(A,mid,r);
        merge(A,l,mid,r);
    }
}

int main(){
    int n;
    cin>>n;
    int a[n];
    for(int i=0;i<n;i++)scanf("%d",&a[i]);
    mergesort(a,0,n);
    for(int i=0;i<n;i++){
        cout<<a[i];
        if(i!=n-1)cout<<' ';
        else cout<<endl;
    }
    cout<<cnt<<endl;
}
