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 {
	public static int merge(int left, int mid, int right, int[] arr) {
		int n1 = mid - left;
		int n2 = right - mid;
		int[] l = new int[n1 + 1];
		for (int i = 0; i < l.length - 1; i++) {
			l[i] = arr[left + i];
		}
		int[] r = new int[n2 + 1];
		for (int i = 0; i < r.length - 1; i++) {
			r[i] = arr[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++) {
			if(l[i] > r[j]) {
				arr[k] = r[j];
				j++;
			} else {
				arr[k] = l[i];
				i++;
			}
		}
		return n1 + n2;
	}
	public static int mergeSort(int left, int right, int[] arr) {
		int count = 0;
		if (left + 1 < right) {
			int mid = (left + right) / 2;
			count += mergeSort(left, mid, arr);
			count += mergeSort(mid, right, arr);
			count += merge(left, mid, right, arr);
		}
		return count;
	}
	public static void main(String[] args) throws IOException {
		BufferedReader br =
			new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		int[] arr = new int[n];
		String[] str = br.readLine().split(" ");
		for (int i = 0; i < str.length; i++) {
			arr[i] = Integer.parseInt(str[i]);
		}
		int count = mergeSort(0, n, arr);
		for (int i = 0; i < arr.length; i++) {
			if (i == arr.length - 1) {
				System.out.println(arr[i]);
			} else {
				System.out.print(arr[i] + " ");
			}
		}
		System.out.println(count);
	}
}
