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 maxn=5e5+5;
const int sentinel=2e9+5;

int l[maxn/2+5],r[maxn/2+5],cnt;

void merge(int a[],int left,int mid,int right)
{
	int n1=mid-left;
	int n2=right-mid;
	for(int i=0;i<n1;i++){
		l[i]=a[left+i];
	}
	for(int i=0;i<n2;i++){
		r[i]=a[mid+i];
	}
	l[n1]=r[n2]=sentinel;
	int i=0,j=0;
	for(int k=left;k<right;k++){
        cnt++;
		if(l[i]<=r[j]){
			a[k]=l[i++];
		}else{
			a[k]=r[j++];
		}
	}
}

void mergesort(int a[],int left,int right)
{
	if(left+1<right){
		int mid=((right+left)>>1);
		mergesort(a,left,mid);
		mergesort(a,mid,right);
		merge(a,left,mid,right);
	}
}

int main()
{
	int a[maxn],n;
	cin>>n;
	for(int i=0;i<n;i++){
		cin>>a[i];
	}
	mergesort(a,0,n);
	for(int i=0;i<n;i++){
		if(i){
			cout<<" ";
		}
		cout<<a[i];
	}
	cout<<endl;
    cout<<cnt<<endl;
	return 0;
}
/*
10
8 5 9 2 6 3 7 1 10 4
*/

