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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {
	public static int count = 0;

	public static void merge(List<Integer> numbers, int left, int mid, int right) {
		int num1 = mid - left;
		int num2 = right - mid;
		int[] leftArray = new int[num1+1];
		int[] rightArray = new int[num2+1];

		for(int i = 0; i < num1; i++) {
			leftArray[i] = numbers.get(left+i);
		}
		for(int i = 0; i < num2; i++) {
			rightArray[i] = numbers.get(mid+i);
		}
		leftArray[num1] = Integer.MAX_VALUE;
		rightArray[num2] = Integer.MAX_VALUE;

		int i = 0;
		int j = 0;
		for(int k = left; k < right; k++, count++) {
			if(leftArray[i] <= rightArray[j]) {
				numbers.set(k, leftArray[i]);
				i++;
			} else {
				numbers.set(k, rightArray[j]);
				j++;
			}

		}
	}

	public static void mergeSort(List<Integer> numbers, int left, int right) {
		if(left + 1 < right) {
			int mid = (left + right) / 2;
			mergeSort(numbers, left, mid);
			mergeSort(numbers, mid, right);
			merge(numbers, left, mid, right);
		}
	}

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		List<Integer> numbers = new ArrayList<>();

		// 入力を受け取る
		int num = scan.nextInt();
		for(int i = 0; i < num; i++) {
			numbers.add(scan.nextInt());
		}

		// マージソートを行う
		mergeSort(numbers, 0, num);


		// 結果を出力する
		for(int i = 0; i < num; i++) {
			if(i == 0) {
				System.out.print(numbers.get(i));
			} else {
				System.out.print(" " + numbers.get(i));
			}
		}
		System.out.println("");
		System.out.println(count);
	}
}

