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.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {
	public static int cnt = 0;
	public static void main(String[] args) throws NumberFormatException, IOException {
		//System.setIn(new FileInputStream("./input.txt"));
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		int[] s = Arrays.stream(br.readLine().split(" ")).mapToInt(Integer::parseInt).toArray();
		
		mergeSort(s, 0, n);
		
		StringBuilder sb = new StringBuilder();
		sb.append(s[0]);
		for(int i = 1; i < n; ++i) {
			sb.append(" " + s[i]);
		}
		System.out.println(sb);
		System.out.println(cnt);
	}
	public static void mergeSort(int[] s, int left, int right) {
		if(left + 1 < right) {
			int mid = (left + right) / 2;
			mergeSort(s, left, mid);
			mergeSort(s, mid, right);
			merge(s, left, mid, right);
		}
	}
	public static void merge(int[] s, int left, int mid, int right) {
		int[] s1 = Arrays.copyOfRange(s, left, mid + 1);
		int[] s2 = Arrays.copyOfRange(s, mid, right + 1);
		
		s1[mid - left] = Integer.MAX_VALUE;
		s2[right - mid] = Integer.MAX_VALUE;
		int i = 0;
		int j = 0;
		for(int k = left; k < right; ++k) {
			cnt += 1;
			if(s1[i] <= s2[j]){
				s[k] = s1[i];
				i += 1;
			}else{
				s[k] = s2[j];
				j += 1;
			}
		}
		
	}
	
}