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
import java.util.*;
import java.io.*;
class Main{
  static int count = 0;
  public static void main(String args[])throws Exception{
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    int n = Integer.parseInt(br.readLine());
    int array[] = new int[n];
    StringTokenizer token = new StringTokenizer(br.readLine());

    for(int i = 0; i<n; i++){
      array [i] = Integer.parseInt(token.nextToken());
    }

    merge_sort(array,n,0,n);
    for(int i = 0; i<n-1; i++){
      System.out.print(array[i]+" ");
    }
    System.out.println(array[n-1]);
    System.out.println(count);
  }

  static void merge(int A[], int left, int mid, int right){
    int n1 = mid - left;
    int n2 = right - mid;
    int L[] = new int[n1+1];
    int R[] = new int[n2+1];
    for(int i = 0; i<n1;i++){
      L[i] = A[left+i];
    }
    for(int i =0; i<n2; i++){
      R[i] = A[i+mid];
    }
    L[n1] = (int)Double.POSITIVE_INFINITY;
    R[n2] = (int)Double.POSITIVE_INFINITY;
    int i = 0;
    int j = 0;
    for(int k = left; k<right; k++){
      count++;
      if(L[i]<=R[j]){
        A[k] = L[i++];
      }else{
        A[k] = R[j++];
      }
    }
  }

  static void merge_sort(int A[], int n, int left, int right){
    if(left+1<right){
      int mid = (left+right)/2;
      merge_sort(A, n, left, mid);
      merge_sort(A, n, mid, right);
      merge(A, left, mid, right);
    }
  }
}
