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;
  static int SENTINEL = 1000000001;

  public static void main(String... args) {
    Scanner sc = new Scanner(System.in);
    int size = Integer.parseInt(sc.next());
    int[] elements = new int[size];
    for (int i = 0; i < size; i++) {
      elements[i] = Integer.parseInt(sc.next());
    }

    mergeSort(elements, 0, size);

    for (int i = 0 ; i < size - 1; i++) {
      System.out.print(elements[i] + " ");
    }

    System.out.println(elements[size - 1]);
    System.out.println(count);
  }

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

  public static void merge(int[] elements, 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] = elements[left + i];
    }
    for (int i = 0; i < n2; i++) {
      r[i] = elements[mid + i];
    }
    l[n1] = SENTINEL;
    r[n2] = SENTINEL;

    int i = 0 ;
    int j = 0;
    for (int k = left; k <= right; k++) {
      if (l[i] <= r[j] && l[i] != SENTINEL) {
        elements[k] = l[i];
        count++;
        i++;
      } else if (r[j] != SENTINEL) {
        elements[k] = r[j];
        count++;
        j++;
      }
    }
  }
}

