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 {

	public static final int MAX = 500000;
	public static final int SENTINAL = 1000000001;
	public static int[] L = new int[MAX / 2 + 2];
	public static int[] R = new int[MAX / 2 + 2];
	public static int count = 0;

	public static void main(String[] args) throws Exception {

		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		String tmparray[] = br.readLine().split(" ");
		int s[] = new int[n];

		for(int i = 0 ; i < n ; i++){
			s[i] =Integer.parseInt(tmparray[i]);
		}

		mergeSort(s,0,n);
		StringBuffer sb = new StringBuffer();
		for(int i = 0 ; i < n ; i++){
			sb.append(s[i]);
			sb.append(" ");
		}

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

	}

	public static void mergeSort(int[] s,int left, int right){

		if(right - left == 1){
			return;
		}
		int mid = (right + left) / 2;
		mergeSort(s,left,mid);
		mergeSort(s,mid,right);
 		merge(s,left,mid,right);
	}


	private static void merge(int[] s,int left, int mid, int right){

		int li = 0;
		int ri = 0;
		for(int i = left ; i < mid ; i++) L[li++] = s[i];
		L[li] = SENTINAL;
		for(int i = mid ; i < right ; i++) R[ri++] = s[i];
		R[ri] = SENTINAL;

		li = ri = 0;

		for(int i = left ; i < right ; i++){
			count++;
			if(L[li] < R[ri]){
				s[i] = L[li++];
			}else{
				s[i] = R[ri++];
			}
		}
	}
}