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<cstdio>
int i,j,k,o,n,c,s[500000];
void g(int l,int m,int r){
  int L[m-l+1],R[r-m+1];
  for(i=0;i<m-l;++i)L[i]=s[i+l];
  for(i=0;i<r-m;++i)R[i]=s[i+m];
  L[m-l]=R[r-m]=1e9,i=o=0;
  for(k=l;k<r;++c)s[k++]=L[i]>R[o]?R[o++]:L[i++];
}
void e(int l,int r){
  int m=(l+r)/2;
  if(l+1<r)e(l,m),e(m,r),g(l,m,r);
}
int main(){
  for(scanf("%d",&n);i<n;scanf("%d",&s[i++]));
  e(0,n);
  for(;j<n;)printf(j-n?"%d ":"%d\n",s[j++]);
  printf("%d\n",c);
}