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;
const int SENTINEL=2000000000;
int cnt=0;
void merge(int A[],int n,int left,int mid,int right){
	int n1=mid-left;
	int n2=right-mid;
	int *L=new int[n1+1];
	int *R=new int[n2+1];
	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++];
    }
    delete L;
    delete R;

}
void mergeSort(int A[],int n,int left,int right){
   if(left+1<right){
   		int mid=(left+right)/2;
   		mergeSort(A,n,left,mid);
   		mergeSort(A,n,mid,right);
   		merge(A,n,left,mid,right);
   }
}
int main(){
	int n;
	cin>>n;
	int *A=new int[n];
	for(int i=0;i<n;++i)cin>>A[i];

	mergeSort(A,n,0,n);
	
	for(int i=0;i<n;++i){
		if(i>0)cout<<' ';
		cout<<A[i];
	}
	cout<<endl;

	cout<<cnt<<endl;
	delete A;
	return 0;
}
