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.io.*;

public class Main
{
  public static void main(String[] args) {
    try {
      BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
      int n = Integer.parseInt(br.readLine());
      String[] strArray = br.readLine().split(" ");
      int[] A = new int[n];
      for(int i=0; i<n; i++) {
        A[i] = Integer.parseInt(strArray[i]);
      }
      int totalCount = mergeSort(A, 0, n, 0);
      StringBuilder sb = new StringBuilder();
      for(int i=0; i<n-1; i++) {
        sb.append(A[i]).append(" ");
      }
      sb.append(A[n-1]);
      System.out.println(sb.toString());
      System.out.println(totalCount);
    } catch (IOException e) {
    }
  }

  public static int merge(int[] A, int left, int mid, int right, int count) {
    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] = Integer.MAX_VALUE;
    R[n2] = Integer.MAX_VALUE;

    int i = 0;
    int j = 0;

    for(int k = left; k<right; k++) {
      count += 1;
      if( L[i] <= R[j] ) {
        A[k] = L[i];
        i = i+1;
      } else {
        A[k] = R[j];
        j = j+1;
      }
    }

    return count;

  }

  public static int mergeSort(int[] A, int left, int right, int count) {
    int totalCount = count;
    if(left + 1 < right) {
      int mid = (left + right) / 2;
      totalCount += mergeSort(A, left, mid, count);
      totalCount += mergeSort(A, mid, right, count);
      totalCount += merge(A, left, mid, right, count);
    }
    return totalCount;
  }

}