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 {
    public static void main(String... args) {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();

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

        MergeSort m = new MergeSort(A);

        for(int i=0; i < A.length; ++i) {
            if(i != 0) {
                System.out.print(" ");
            }
            System.out.print(A[i]);
        }
        System.out.println();
        System.out.println(m.getComp());
        scan.close();
    }
}

class MergeSort {
    private int[] A;
    private int comp = 0;

    public MergeSort(int[] A) {
        this.A = A;
        mergesort(0, A.length);
    }

    private void merge(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;
        int j = 0;

        for(int k=left; k < right; ++k) {
            comp += 1;
            if(L[i] <= R[j]) {
                A[k] = L[i];
                i += 1;
            } else {
                A[k] = R[j];
                j += 1;
            }
        }
    }
    public void mergesort(int left, int right) {
        if(left+1 < right) {
            int mid = (left + right) / 2;
            mergesort(left, mid);
            mergesort(mid, right);
            merge(left, mid, right);
        }
    }

    public int getComp() {return comp;}
}
