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;

public class Main {

	public static final int SENTINEL = 2000000000;
	static int[] MERGETMPA;
	static int[] MERGETMPB;
	static int[] S;
	static int count = 0;

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

		MERGETMPA = new int[n / 2 + 2];
		MERGETMPB = new int[n / 2 + 2];
		S = new int[n];
		for(int i = 0 ; i < n ; i++) S[i] = input.nextInt();
		mergeSort(0,n);
		input.close();
		StringBuilder sb = new StringBuilder();
		for(int i = 0; i < S.length ; i++){
			sb.append(String.valueOf(S[i]));
			sb.append(" ");
		}
		System.out.println(sb.toString().trim());
		System.out.println(count);
	}


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

	public static void merge(int left,int mid,int right){
		int i = 0;
		int s = left;
		for(i = 0 ; i < mid - left ; i++) MERGETMPA[i] = S[s++];
		MERGETMPA[i] = SENTINEL;
		s = mid;
		for(i = 0 ; i < right - mid ; i++) MERGETMPB[i] = S[s++];
		MERGETMPB[i] = SENTINEL;

		int x = 0;
		int y = 0;
		for(i = left ; i < right; i++){
			count++;
			if(MERGETMPA[x] <= MERGETMPB[y]){
				S[i] = MERGETMPA[x];
				x++;
			}else{
				S[i] = MERGETMPB[y];
				y++;
			}
		}

	}

}