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>

using namespace std;

#define MAX 500000
#define N 2000000000

int L[MAX/2+2],R[MAX/2+2];
int tmp;

void marge(int A[],int n,int l,int mid,int r){
  int n1=mid-l;
  int n2=r-mid;

  for(int i=0;i<n1;i++) L[i]=A[l+i];
  for(int i=0;i<n2;i++) R[i]=A[mid+i];

  L[n1]=R[n2]=N;
  int i=0,j=0;

  for(int k=l;k<r;k++){
    tmp++;
    if(L[i]<=R[j]){
      A[k]=L[i++];
    }else{
      A[k]=R[j++];
    }
  }
}

void sort(int A[],int n,int l,int r) {
  if(l+1<r){
    int mid=(l+r)/2;
    sort(A,n,l,mid);
    sort(A,n,mid,r);
    marge(A,n,l,mid,r);
  }
}

int  main() {
int A[MAX],n,i;
tmp=0;

cin >>n;

for( i=0;i<n;i++) cin >> A[i];

sort(A,n,0,n);

for (i=0;i<n;i++) {
 if(i) cout << " ";
 cout << A[i];
}
cout << endl;

cout << tmp << endl;
  return 0;
}

