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.regex.Pattern;

public class Main {
    static int count = 0;

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = ip(br);
        int[] list = createListInt(br);
        mergeSort(list, 0, n);
        String[] str = new String[n];
        int i = 0;
        for (int m : list) {
            str[i++] = String.valueOf(m);
        }
        System.out.println(String.join(" ", str));
        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];
         System.arraycopy(a, left, l, 0, n1);

         System.arraycopy(a, mid, r, 0, n2);
        l[n1] = Integer.MAX_VALUE;
        r[n2] = Integer.MAX_VALUE;

        for (int i = 0, j = 0, k = left; k < right; k++) {
            a[k] = l[i] <= r[j] ? l[i++] : r[j++];
            count++;
        }

    }

    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 boolean isNumber(String num) {
        return Pattern.compile("^\\-?[0-9]*\\.?[0-9]+$").matcher(num).find();
    }

    static int[] createListInt(BufferedReader br) throws IOException {
        String[] lines = br.readLine().split(" ");
        int n = lines.length;
        int[] list = new int[n];
        while (n-- > 0) {
            list[n] = Integer.parseInt(lines[n]);
        }
        return list;
    }

    static int ip(BufferedReader s) throws IOException {
        return Integer.parseInt(s.readLine());
    }
}