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.Scanner;

class Main{
  static int count = 0;

  static void trace(int[] a){
    int i;
    for(i = 0; i < a.length - 1; i++)
      System.out.print(a[i] + " ");
    System.out.println(a[i]);
  }

  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[mid + i];

    L[n1] = 1000000001;
    R[n2] = 1000000001;

    int i = 0;
    int j = 0;

    for(int k = left; k < right; k++){
      if(L[i] <= R[j])
        a[k] = L[i++];
      else
        a[k] = R[j++];
      count++;
    }
  }

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

  public static void main(String[] args){
    Scanner stdIn = new Scanner(System.in);
    int n = stdIn.nextInt();
    int[] A = new int[n];

    for(int i = 0; i < n; i++)
      A[i] = stdIn.nextInt();

    mergeSort(A, 0, n);
    trace(A);
    System.out.println(count);
  }
}