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<bits/stdc++.h>
#define max 500000
#define sentinel 2000000000
int count,L[max/2+2],R[max/2+2];
void merge(int *A,int l,int mid,int r);
void mergesort(int*A,int l,int r);
int main(void){
	int n,A[max];
	memset(A,0,sizeof(A));
	scanf("%d",&n);
	for(int i=0;i<n;i++)	scanf("%d",A+i);
	count=0;
	mergesort(A,0,n);
	for(int i=0;i<n;i++){
		printf("%s%d",i==0? "":" ",A[i]);
	}
	printf("\n%d\n",count);
	return 0; 
}
void mergesort(int*A,int l,int r){
	if(l+1<r){
		int mid=(l+r)/2;
		mergesort(A,l,mid);
		mergesort(A,mid,r);
		merge(A,l,mid,r);
	}
	
}
void merge(int *A,int l,int mid,int r){
	int lenl,lenr,i,j,k;
	lenl=mid-l,lenr=r-mid;
	for(i=0;i<lenl;i++) L[i]=A[l+i];
	for(i=0;i<lenr;i++) R[i]=A[mid+i];
	L[lenl]=R[lenr]=sentinel;
	i=0,j=0;		
	for(k=l;k<r;k++){
		count++;
		if(L[i]<=R[j]) A[k]=L[i++];
		else A[k]=R[j++];
	}	
}
