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 {

	private static int count = 0;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		sc.useDelimiter(System.getProperty("line.separator"));
		int n = sc.nextInt();
        String aStr = sc.next();
        int[] s = toIntAry(aStr, n);

        int[] ret = mergeSort(s,0,n);

        for (int i = 0; i < ret.length; i++) {
        	if(i==ret.length-1){
        		System.out.println(ret[i]);
        	}else{
        		System.out.print(ret[i] + " ");
        	}

		}
        System.out.println(count);

	}




	private static int[] 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);
		}

		return A;

	}




	private static void merge(int[] a, int left, int mid, int right) {
		final int MAX = 2147483647;
		int n1 = mid - left;
		int n2 = right -mid;
		int[] l1 = new int[n1+1];
		int[] r1 = new int[n2+1];
		for(int i=0; i<n1; i++){
			l1[i] = a[left+i];
		}
		for(int i=0; i<n2; i++){
			r1[i] = a[mid+i];
		}
		l1[n1] = MAX;
		r1[n2] = MAX;
		int i=0;
		int j=0;
		for(int k=left; k<right; k++){
			if(l1[i] <= r1[j]){
				a[k] = l1[i];
				i++;
				count++;
			}else{
				a[k] = r1[j];
				j++;
				count++;
			}
		}
	}




	private static int[] toIntAry(String str, int n) {
        String[] tmp = str.split(" ");
        int[] A = new int[n];
        for (int i = 0; i < n; i++) {
			A[i] = Integer.parseInt(tmp[i]);
		}
        return A;
	}


}