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 {
	//???????????????????????§???????????????????????°????????????????????°
	private static int count;

	public static void main (String[]args){
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		int[] numList = new int[n];
		for(int i = 0; i< n; i++){ 
			numList[i] = scanner.nextInt();
		}
		//?????????????????????????????????????????°???????±???????(numList)????????????????°????????´???????(0)?????????????????§???????´???????(n)?????????
		mergeSort(numList, 0, n);
		
		System.out.print(numList[0]);
		for(int i = 1; i < n; i++){
			System.out.print(" " + numList[i]);
		}
		System.out.println();
		System.out.println(count);
	}
	
	//???????????????(mid)???????????????L??¨R????????????????´?????????? L??¨R????????????????´???°???????????¨?????????
	static void merge(int[] numList, int left, int mid, int right){
		int n1 = mid - left;
		int n2 = right - mid;
		int[] L = new int[n1 + 1];
		int[] R = new int[n2 + 1];

		for(int i = 0; i < n1; i++){
			L[i] = numList[left + i];
		}
		
		for(int i = 0; i < n2; i++){
			R[i] = numList[mid + i];
		}
		
		L[n1] = Integer.MAX_VALUE;
		R[n2] = Integer.MAX_VALUE;
		int i = 0;
		int j = 0;
		//L??¨R??????????????????????°????????????????numList???????´??????????
		//?°?????????????????????????????????????????¬??????????????????????????????????????´????????????????????????°?????????+1?????????
		for(int k = left; k < right; k++){
			count++;
			if(L[i] <= R[j]){
				numList[k] = L[i];
				i = i + 1;
			} else {
				numList[k] = R[j];
				j = j + 1;
			}
		}
	}
	
	//????¨????merge???????????????????±??????????????°?????´???????(left)??¨?????§????´???????(right)?????????-1??????????????§??°????????????
	static void mergeSort(int[] numList, int left, int right){
		if((left + 1) < right){
			int mid = (left + right) / 2;
			
		mergeSort(numList, left, mid);
		//System.out.println("???");
		mergeSort(numList, mid, right);
		//System.out.println("???");
		merge(numList, left, mid, right);
		}
	}
}