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;

typedef vector<int> vec;

int cnt=0;

void Merge_Sort(vec& A)
{
	int n=A.size();
	if(n==1) return;
	cnt+=A.size();
	vec A1,A2;
	for(int i=0;i<n;i++)
		if(i<(n>>1))
			A1.push_back(A[i]);
		else
			A2.push_back(A[i]);
	Merge_Sort(A1);Merge_Sort(A2);
	int t=0,t1=0,t2=0,n1=A1.size(),n2=A2.size();
	while(t1<n1&&t2<n2)
	{
		if(A1[t1]<A2[t2])
			A[t++]=A1[t1++];
		else
			A[t++]=A2[t2++];
	}
	while(t1<n1) A[t++]=A1[t1++];
	while(t2<n2) A[t++]=A2[t2++];
}

int main()
{
	int n;
	vec A;
	scanf("%d",&n);
	for(int i=0;i<n;i++)
	{
		int t;
		scanf("%d",&t);
		A.push_back(t);
	}
	Merge_Sort(A);
	for(int i=0;i<n;i++)
		printf("%d%c",A[i],i+1==n?'\n':' ');
	printf("%d\n",cnt);
}