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.*;
import java.io.*;
import java.lang.*;
 
public class Main {
    static final int INF = 1000000000;         
    static int cmps = 0;
     
    public static void main(String[] args) throws Exception {                
        Scanner input = new Scanner(System.in);
        int n = input.nextInt();
        int[] s = new int[n];
        for (int i = 0; i < n; ++i) s[i] = input.nextInt();
        mergeSort(s, 0, n);
        System.out.print(s[0]);
        for (int i = 1; i < n; ++i) System.out.print(" " + s[i]);
        System.out.println("");
        System.out.println(cmps);
    }              
     
    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);
        }
    }
     
    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] = R[n2] = INF;
        int i, k;
        i = k = 0;
        for (int t = left; t < right; ++t) {
            if (L[i] < R[k]) {
                A[t] = L[i++];
                ++cmps;
            } else {
                A[t] = R[k++];
                ++cmps;
            }
        }
    }
}