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.*;

class Main{
	static int c=0;
	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);
		System.out.print(A[0]);
		for(int i=1; i<n; i++){
			System.out.print(" "+A[i]);
		}
		System.out.println();
		System.out.println(c);
	}
	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);
		}
	}
	static void merge(int A[], 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] = R[n2] = Integer.MAX_VALUE;
		int i, j;
		i = j = 0;
		for(int k=left; k<right; k++){
			c++;
			if(L[i] <= R[j]){
				A[k] = L[i++];
			} else{
				A[k] = R[j++];
			}
		}
	}
}