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.Arrays;
import java.util.Scanner;

/**
 * マージソート
 * @author nobu
 * @see <a href="http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ALDS1_5_B&lang=ja">ALDS1_5_B</a>
 */
public class Main {

	private static int count = 0;
	private static int l[] = new int[1000000];
	private static int r[] = new int[1000000];

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int a[] = new int[n];

		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
		}

		Arrays.fill(l, Integer.MAX_VALUE);
		Arrays.fill(r, Integer.MAX_VALUE);

		mergeSort(a, n, 0, n);

		System.out.println(Arrays.toString(a).replace("[", "").replace("]", "").replace(",", ""));
		System.out.println(count);

		sc.close();

	}

	private static void mergeSort(int a[], int n, int left, int right) {
		if (left + 1 < right) {
			int mid = (left + right) / 2;
			mergeSort(a, n, left, mid);
			mergeSort(a, n, mid, right);
			merge(a, n, left, mid, right);
		}
	}

	private static void merge(int a[], int n, int left, int mid, int right) {
		for (int i = 0; i < mid - left; i++) l[i] = a[left + i];
		for (int i = 0; i < right - mid; i++) r[i] = a[mid + i];

		l[mid - left] = r[right - mid] = Integer.MAX_VALUE;

		int j = 0, k = 0;
		for (int i = left; i < right; i++) {
			count++;
			if (l[j] <= r[k]) {
				a[i] = l[j++];
			} else {
				a[i] = r[k++];
			}
		}
	}

}

