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 <stdio.h>
#include <limits.h>
#include <algorithm>

using namespace std;

int cmp_count = 0;


void merge(int A[],int left,int mid, int right){
	int n1 = mid - left;
	int n2 = right - mid;
	int L[n1+1],R[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] =  INT_MAX;

	int i = 0, j = 0;
	for(int k = left;k < right; k++){
		if(L[i] <= R[j]){
			A[k] = L[i++];
			cmp_count++;
		}else{
			A[k] = R[j++];
			cmp_count++;
		}
	}
}

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);
	}
}

int main(){
	int n;
	scanf("%d",&n);
	int S[n];
	for(int i = 0; i < n; i++) scanf("%d",&S[i]);

	mergeSort(S,0,n);

	for(int i = 0; i < n-1; i++) printf("%d ",S[i]);
	printf("%d\n",S[n-1]);
	printf("%d\n",cmp_count);

}

