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>
int a[6000000];
int n;
int sum=0;
void hebing(int a[],int q,int p,int l,int d){
  int i,j,k,b[n];
  i=q;
  j=l;
  k=q;
  while(i<=p&&j<=d){
    if(a[i]<a[j]){b[k++]=a[i++];sum++;}
    else {b[k++]=a[j++];sum++;}
  }
  while (i<=p){b[k++]=a[i++];sum++;}
  while (j<=d){b[k++]=a[j++];sum++;}
  for(int i=q;i<=d;i++){
    a[i]=b[i];
  }
}
void paixu(int a[],int m,int n){
    if(n>m){
int x=(n+m)/2;
paixu(a,m,x);
paixu(a,x+1,n);
hebing(a,m,x,x+1,n);
}
}
int main(){
scanf("%d",&n);
for(int i=0;i<n;i++){
    scanf("%d",&a[i]);
}
paixu(a,0,n-1);
printf("%d",a[0]);
for(int i=1;i<n;i++){
    printf(" %d",a[i]);
}
printf("\n%d\n",sum);
return 0;
}