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 merge_sort(int a[],int left,int right){
    if(left+1<right)
    {   int mid=(left+right)/2;
        return merge_sort(a,left,mid)+merge_sort(a,mid,right)+right-left;}
    else return 0;
};
int main()
{   int n;
    cin>>n;int a[n];for(int i=0;i<n;i++) {cin>>a[i];}
    sort(a,a+n);
    for(int i=0;i<n;i++)
        if(i==n-1)cout<<a[i]<<endl; else cout<<a[i]<<' ';
    cout<<merge_sort(a,0,n)<<endl;
    return 0;
}
