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>
#include<vector>

std::vector<int> tmp;

int merge_sort(std::vector<int> &S,int left,int right){
	if(left>=right) return 0;
	int cnt=0;
	int mid=(right+left)/2;
	cnt+=merge_sort(S,left,mid);
	cnt+=merge_sort(S,mid+1,right);
	for(int i=left;i<=mid;i++)
		tmp[i]=S[i];
	for(int i=mid+1;i<=right;i++)
		tmp[right+mid+1-i]=S[i];
	int i=left,j=right;
	for(int k=left;k<=right;k++){
		if(tmp[i]>tmp[j]){
			S[k]=tmp[j--];
		}else{
			S[k]=tmp[i++];
		}
		cnt++;
	}
	return cnt;
}

int main(void){
	int n;
	std::cin>>n;
	std::vector<int> S(n);
	tmp.resize(n);
	for(int i=0;i<n;i++)
		std::cin>>S[i];
	int cnt_cmp=merge_sort(S,0,S.size()-1);
	for(int i=0;i<S.size();i++)
		std::cout<<(i?" ":"")<<S[i];
	std::cout<<std::endl<<cnt_cmp<<std::endl;

	return 0;
}

