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
//17D8101026B 横川　大貴
//Java

import java.util.Scanner;

class Main{
    private static int[] A;
    private static int count=0;
    private static int max = 1100000000;
    public static void main(String[] args){
	Scanner sc = new Scanner(System.in);
	int n = sc.nextInt();
	A = new int[n];
	for(int i=0;i<n;i++){
	    A[i] = sc.nextInt();
	}
       
	mergeSort(0,n);

	for(int i=0;i<n; i++){	
	    System.out.print(A[i]);
		if(i<n-1){
		    System.out.print(" ");
		}else{
		    System.out.println();
		}
	}
	System.out.println(count);
	
	
    }
    public static void merge(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] = A[left+i];
	}
	for(int i=0; i<n2; i++){
	    R[i] = A[mid+i];
	}
	L[n1]=max;
	R[n2]=max;
	int i=0;
	int j=0;
	for(int k=left;k<right;k++){	    
	    if(L[i] <= R[j]){
		A[k] = L[i];
		i++;
		count++;
	    }else{
		A[k] = R[j];
		j++;
		count++;
	    }
	}
    }
    public static void mergeSort(int left,int right){
	if(left+1<right){
	    int mid = (left+right)/2;
	    mergeSort(left, mid);
	    mergeSort(mid, right);
	    merge(left,mid, right);
	}
    }
}

