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.*;

public class Main {
  public static int merge(List<Integer> list, int left, int mid, int right, int count) {
    int n1 = mid - left;
    int n2 = right - mid;
    int[] arrL = new int[n1 + 1];
    int[] arrR = new int[n2 + 1];
    for(int i = 0; i < n1; i++) {
      arrL[i] = list.get(left + i);
    }
    arrL[n1] = Integer.MAX_VALUE;
    for(int i = 0; i < n2; i++) {
      arrR[i] = list.get(mid + i);
    }
    arrR[n2] = Integer.MAX_VALUE;
    int i = 0;
    int j = 0;
    for(int k = left; k < right; k++) {
      if(arrL[i] <= arrR[j]) {
        list.set(k, arrL[i]);
        i++;
      } else {
        list.set(k, arrR[j]);
        j++;
      }
    }
    count += right - left;
    return count;
  }
  public static int mergeSort(List<Integer> list, int left, int right) {
    if(left + 1 < right) {
      int mid = (left + right) / 2;
      int count1 = mergeSort(list, left, mid);
      int count2 = mergeSort(list, mid, right);
      int count = merge(list, left, mid, right, count1 + count2);
      return count;
    } else {
      return 0;
    }
  }
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    List<Integer> arr = new ArrayList<>();
    for(int i = 0; i < n; i++) {
      arr.add(sc.nextInt());
    }
    int count = mergeSort(arr, 0, n);
    for(int i = 0; i < n; i++) {
      if(i == n - 1) {
        System.out.println(arr.get(i));
      } else {
        System.out.print(arr.get(i) + " ");
      }
    }
    System.out.println(count);
  }
}

