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;
import java.util.Arrays;
class Main{
    public static int count = 0;
    //番兵
    
    public static void main(String[] args){
	
	Scanner sc = new Scanner(System.in);
	int N = sc.nextInt();
	int[] A = new int[N];
	for(int i = 0;i < N;i++){
	    A[i] = sc.nextInt();
	}
	mergeSort(A,0,N);
			
	for (int i = 0; i < N - 1; i ++) {
	    System.out.print(A[i] + " ");
	}
	System.out.println(A[N - 1]);
	System.out.println(count);
		
    }

    static void merge(int[] A,int left,int mid,int right){
	//分割
	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] = A[left + i];
	for(int i = 0;i < n2;i++)R[i] = A[mid + i];
	L[n1] = R[n2] = Integer.MAX_VALUE;
	int i = 0,j = 0;
	for(int k = left;k < right;k++){
	    count++;
	    /*配列L,Rに入ってる要素の小さい方から先に入れ、インクリメントを行う*/
	    if(L[i] <= R[j]){
		A[k] = L[i++];
	    }else{
		A[k] = R[j++];
	    }
	}
	

    }
        static void  mergeSort(int[] A,int left,int right){
    	if(left+1 < right){
    	    int mid = (left + right)/2;
    	    mergeSort(A, left, mid);
    	    mergeSort(A, mid, right);
    	    merge(A, left, mid, right);
    	}

    }
}

