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;

public class Main {
	private int count;
	private int[] a;
	
	public static void main(String[] args) {
		new Main();
	}
	
	public Main() {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		
		try {
			int nico = Integer.parseInt(in.readLine());
			String[] se = in.readLine().split(" ");
			
			a = new int[nico];
			for (int i = 0; i < nico; i++) {
				a[i] = Integer.parseInt(se[i]);
			}
			
			mergeSort(0, nico);
			
			System.out.print(a[0]);
			for (int i = 1; i < nico; i++) {
				System.out.print(" " + a[i]);
			}
			System.out.println();
			System.out.println(count);
		} catch (NumberFormatException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		} catch (IOException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		}
	}
	
	public void merge(int left, int mid, int right) {
		int n1 = mid - left;
		int n2 = right - mid;
		
		int[] l = new int[n1];
		int[] r = new int[n2];

		for (int i = 0; i < n1; i++) {
			l[i] = a[left + i];
		}
		
		for (int i = 0; i < n2; i++) {
			r[i] = a[mid + i];
		}
		
		int i = 0;
		int j = 0;
		for (int k = left; k < right; k++) {
			count++;

			if (i == n1) {
				a[k] = r[j];
				j++;
				continue;
			}
			if (j == n2) {
				a[k] = l[i];
				i++;
				continue;
			}
			
			if (l[i] <= r[j]) {
				a[k] = l[i];
				i++;
			} else {
				a[k] = r[j];
				j++;
			}
		}
	}
	
	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);
		}
	}
}