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],num=0;
int l[250005],r[250005];

void merg(int s,int e){
    int mid=(s+e)/2;
    int n1=mid-s+1,n2=e-mid;
    int i;
    for(i=0;i<n1;i++){
        l[i]=a[s+i];
    }
    for(i=0;i<n2;i++){
        r[i]=a[mid+i+1];
    }
    int m1=0,m2=0;
    for(i=0;i<e-s+1;i++){
        l[n1]=r[n2]=1000000005;
        if(l[m1]<=r[m2])a[s+i]=l[m1++];
        else a[s+i]=r[m2++];
    }
    num+=(e-s+1);
}

void mergesort(int s,int e){
    if(s==e)return;
    int mid=(s+e)/2;
    mergesort(s,mid);
    mergesort(mid+1,e);
    merg(s,e);
}

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