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.Scanner;

class Main {
	static int count = 0;
	public static void main (String[] args) {
		Scanner scan = new Scanner (System.in);
		int n = scan.nextInt();
		int[] data = new int[n];
		
		for (int i = 0; i < n; i++) {
			data[i] = scan.nextInt();
		}
		scan.close();
		
		Main obj = new Main();
		obj.MergeSort (data, 0, n);
		printArray (data);
		System.out.println(count);
	}
	
	void MergeSort (int[] data, int left, int right) {
		
		if (left + 1 < right) {
			int mid = (left + right) / 2;
			
			MergeSort(data, left, mid);
			MergeSort(data, mid, right);
			
			Merge(data, left, mid, right);
			
		}
	}
	
	void Merge (int[] data, int left, int mid, int right) {
		int n1 = mid - left;
		int n2 = right - mid;
		final int INFTY = 1000000000;
		
		int[] L = new int[n1 + 1];
		int[] R = new int[n2 + 1];
		
		for (int i = 0; i < n1; i++) {
			L[i] = data[left + i];
		}
		for (int i = 0; i < n2; i++) {
			R[i] = data[mid + i];
		}
		
		L[n1] = INFTY;
		R[n2] = INFTY;
		
		int i = 0, j = 0;
		int k = left;
		
		while (true) {
			
			if (i == n1 && j == n2) break;
			
			if (L[i] <= R[j]) {
				data[k] = L[i];
				i++;
			} else {
				data[k] = R[j];
				j++;
			}
			k++;
			count++;
		}
		
	}

	static void printArray (int[] data) {
		int n = data.length;
		for (int i = 0; i < n; i++) {
			if ( i != n - 1) System.out.print(data[i] + " "); 
			else System.out.println(data[i]);
		}
	}
}

