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;

int num=0;

void Merge(int A[],int left,int mid,int right);
void MergeSort(int A[],int left,int right);

int main()
{
    int A[500000],N;
	cin>>N;
	for(int i=0;i<N;i++){
		cin>>A[i];
	}
	MergeSort(A,0,N);
	cout<<A[0];
	for(int i=1;i<N;i++){
		cout<<" "<<A[i];
	}
	cout<<endl<<num<<endl;
}

void Merge(int A[],int left,int mid,int right)
{
	int n1=mid-left;
	int n2=right-mid;
	int dL[n1+1],dR[n2+1];
	for(int i=0;i<n1;i++){
		dL[i]=A[left + i];
	}
	for(int i=0;i<n2;i++){
		dR[i]=A[mid + i];
	}
	dL[n1]=1000000001;
	dR[n2]=1000000001;
	int i,j;
	for(i=left,j=0;i<right;i++){
		if(dL[i-left-j]<dR[j]){
			A[i]=dL[i-left-j];
		}else{
			A[i]=dR[j];
			j++;
		}
		num++;
	}
	
}
void MergeSort(int A[],int left,int right)
{
	if(left+1<right){
		int mid=(left+right)/2;
		MergeSort(A,left,mid);
		MergeSort(A,mid,right);
		Merge(A,left,mid,right);
	}
}