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 n;
    static int[] A;

    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        n = s.nextInt();
        A = new int [n];
        for (int i = 0; i < n; i++) {
            A[i] = s.nextInt();
        }
        int cmp = mergeSort(A, 0, n);

        for (int i = 0; i < n; i++) {
            if (i != 0) {
                System.out.print(" ");
            }
            System.out.print(A[i]);
        }
        System.out.println();
        System.out.println(cmp);
    }

    static int merge(int[] B, int left, int middle, int right) {
        int [] L, R;
        L = new int [middle - left + 1];
        R = new int [right - middle + 1];

        for (int k = 0; k < middle - left; k++) {
            L[k] = A[left + k];
        }

        for (int k = 0; k < right - middle; k++) {
            R[k] = A[middle + k];
        }

        L[middle - left] = Integer.MAX_VALUE;
        R[right - middle]  = Integer.MAX_VALUE;

        int i = 0, j = 0, k = 0;
        while (i < middle - left || j < right - middle) {
            if (L[i] < R[j]) {
                A[left + k] = L[i];
                i++;
            } else {
                A[left + k] = R[j];
                j++;
            }
            k++;
        }
        return k;
    }

    static int mergeSort(int []B, int left, int right) {
        if (left + 1 == right) {
            return 0;
        }
        int middle = (left + right) / 2;

        int s = mergeSort(B, left, middle);
        int t = mergeSort(B, middle, right);
        int cmp = merge(B, left, middle, right);
        return cmp + s + t;
    }
}

