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.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.lang.management.ManagementFactory;
import java.lang.management.ThreadMXBean;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;
import java.util.PriorityQueue;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) throws IOException {

		Scanner scan = new Scanner(System.in);
		// Scanner scan = new Scanner(new
		// File("D:\\UserArea\\J0124567\\Downloads\\ALDS1_3_C-in10.txt"));
		// while (scan.hasNext()) {

		int n = scan.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = scan.nextInt();

		msort(a, 0, n);

		System.out.print(a[0]);
		for (int i = 1; i < n; i++)
			System.out.print(" " + a[i]);
		System.out.print("\n" + cnt + "\n");

		scan.close();
		System.exit(0);
	}

	static int cnt;

	private static void msort(int[] a, int st, int max) {
		if (max - st < 2)
			return;
		int mid = (max + st) / 2;
		msort(a, st, mid);
		msort(a, mid, max);
		marge(a, st, mid, max);
	}

	private static void marge(int[] a, int st, int mid, int max) {
		int[] m1 = new int[mid - st + 1];
		int[] m2 = new int[max - mid + 1];

		for (int p = st, i = 0; p < mid; p++, i++)
			m1[i] = a[p];
		m1[m1.length - 1] = Integer.MAX_VALUE;

		for (int p = mid, i = 0; p < max; p++, i++)
			m2[i] = a[p];
		m2[m2.length - 1] = Integer.MAX_VALUE;

		int p1 = 0, p2 = 0;
		for (int i = st; i < max; i++)
			if (m1[p1] > m2[p2])
				a[i] = m2[p2++];
			else
				a[i] = m1[p1++];
		cnt += (max - st);
	}

}