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.*;
import java.util.*;

public class Main {

    static int cnt = 0;

    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        PrintWriter pw = new PrintWriter(System.out);

        int n = sc.nextInt();
        int[] A = new int[n];
        for (int i = 0; i < n; i++) {
            A[i] = sc.nextInt();
        }

        mergeSort(A, 0, n);
        for (int i = 0; i < n-1; i++) {
            pw.print(A[i] + " ");
        }
        pw.println(A[n-1]);
        pw.println(cnt);
        pw.flush();
    }

    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, j = 0;
        for (int k = left; k < right; k++) {
            if (L[i] <= R[j])
                A[k] = L[i++];
            else
                A[k] = R[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);
        }
    }

    static class MyScanner {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in), 1 << 15);
        StringTokenizer tokenizer;

        String next() {
            try {
                while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                    tokenizer = new StringTokenizer(reader.readLine());
                }
            } catch (IOException ignored) {
            }
            return tokenizer.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }
}
