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.*;

public class Main {
	int count = 0;
	public static void main(String[] args) {
		new Main().runSort();
	}
	
	public void runSort() {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] l = new int[n];
		for (int i = 0; i < n; i++) {
			l[i] = sc.nextInt();
		}
		sorting(l, 0, n);
		System.out.print(l[0]);
		for (int i = 1; i < n; i++) {
			System.out.print(" " +l[i]);
		}
		System.out.println();
		System.out.println(count);
	}

	public void sorting(int[] l, int nl, int nr) {
		if (nl + 1 < nr) {
			int nm = (nl + nr) / 2;
			sorting(l, nl, nm);
			sorting(l, nm, nr);
			merging(l, nl, nm, nr);
		}
	}

	public void merging(int[] list, int nl, int nm, int nr) {
		int n1 = nm - nl;
		int n2 = nr - nm;
		int[] l = new int[n1 + 1];
		int[] r = new int[n2 + 1];
		for (int i = 0; i < n1; i++) {
			l[i] = list[nl + i];
		}
		for (int i = 0; i < n2; i++) {
			r[i] = list[nm + i];
		}
		l[n1] = Integer.MAX_VALUE;
		r[n2] = Integer.MAX_VALUE;

		int LEFT = 0;
		int RIGHT = 0;
		for (int i = nl; i < nr; i++) {
			if (l[LEFT] <= r[RIGHT]) {
				list[i] = l[LEFT++];
			} else {
				list[i] = r[RIGHT++];
			}
			count++;
		}
	}

}
