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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.stream.Collectors;

public class Main {
    static int cnt = 0;

    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];
        System.arraycopy(A, left, L, 0, n1);
        System.arraycopy(A, mid, R, 0, n2);
        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++;
            }
            cnt++;
        }
    }

    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);
        }
    }

    public static void main(String[] args) {
        try (BufferedReader in = new BufferedReader(new InputStreamReader(System.in))) {
            cnt = 0;
            int n = Integer.parseInt(in.readLine());
            int[] A = Arrays.stream(in.readLine().split(" ")).mapToInt(Integer::parseInt).toArray();
            mergeSort(A, 0, n);

            System.out.println(Arrays.stream(A).mapToObj(String::valueOf).collect(Collectors.joining(" ")));
            System.out.println(cnt);
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
}

