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.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {

	private static final int max = 500000;
	private static int count = 0;
	private static int[] l = new int[max/2+1];
	private static int[] r = new int[max/2+1];
	private static int sentinel = 1000000001;

	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n  = Integer.parseInt(br.readLine());
		String[] AStr = br.readLine().split(" ");
		int[] A = new int[n];
		for(int i = 0; i < n ; i++){
			A[i] = Integer.parseInt(AStr[i]);
		}

		mergeSort(A,0,n);

		StringBuilder sb = new StringBuilder();

		for(int i = 0 ; i < n ; i++){
			sb.append(A[i] + " ");
		}

		System.out.println(sb.toString().trim());
		System.out.println(count);

	}

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

	private static void merge(int[] A,int left,int mid,int right){
		for(int i = 0 ; i < mid - left ; i++) l[i] = A[left + i];
		for(int i = 0 ; i < right - mid ; i++) r[i] = A[mid + i];
		l[mid - left] = r[right - mid] = sentinel;

		int x = 0;
		int y = 0;

		for(int i = left ; i < right; i++ ){
			if(l[x] <= r[y]){
				A[i] = l[x++];
			}else{
				A[i] = r[y++];
			}
			count++;
		}
	}
}