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>

#define N 500000
#define MAX 2147483647

int s[N], count, i,n,left,right;

void Merge(int *s,int left,int mid,int right){
  int i,n1,n2,k,j;
  n1=mid-left;
  n2=right-mid;

  int L[n1+1],R[n2+1];

  for(i=0;i<n1;i++){
    L[i]=s[left+i];
  }
  for(i=0;i<n2;i++){
    R[i]=s[mid+i];
  }
  L[n1]=MAX;
  R[n2]=MAX;
  i=0;
  j=0;
  for(k=left;k<right;k++){
    if(L[i]<=R[j]){
      s[k]=L[i];
      i++;
    }
    else{
      s[k]=R[j];
      j++;
    }
    count++;
  }
}

void MergeSort(int *s,int left,int right){
  long mid;
  if(left+1<right){
    mid=(left+right)/2;
    MergeSort(s,left,mid);
    MergeSort(s,mid,right);
    Merge(s,left,mid,right);
  }
}


int main(){
  scanf("%d",&n);
  left=0;
  right=n;
  for(i=0;i<n;i++){
    scanf("%d",&s[i]);
  }
  MergeSort(s,left,right);
  for(i=0;i<n-1;i++) printf("%d ",s[i]);
  printf("%d\n%d\n",s[n-1],count);
  return 0;
}