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;

public class Main {
    
    static int count;

    public static void main(String[] args) {
        
        Scanner sc = new Scanner(System.in);
        
        int n = Integer.parseInt(sc.next());
        int[] s = new int[n];
        for(int i = 0; i < n; i++){
            s[i] = Integer.parseInt(sc.next());
        }
        count = 0;
        
        mergeSort(s, 0, n);
        
        StringBuilder sb = new StringBuilder();
        for(int i = 0; i < n; i++){
            sb.append(s[i]).append(" ");
        }
        sb.deleteCharAt(sb.length()-1);
        System.out.println(sb);
        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[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++){
            if(l[i] <= r[j]){
                a[k] = l[i];
                i++;
            }else{
                a[k] = r[j];
                j++;
            }
        }
        count += right - left;
    }
    
    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);
        }
    }
}
