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.IOException;
import java.io.InputStreamReader;

class Main {
	public static int sum = 0;
	
	public static void main(String args[]) {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int num = 0;
		String line = null;
		
		try {
			num = Integer.parseInt(br.readLine());
			line = br.readLine();
		} catch (NumberFormatException e) {
			// TODO 自動生成された catch ブロック
			e.printStackTrace();
		} catch (IOException e) {
			// TODO 自動生成された catch ブロック
			e.printStackTrace();
		}
		
		String[] str = line.split(" ");
		int array[] = new int[num];
		
		for(int i = 0; i < num; i ++ ){
			array[i] =Integer.parseInt(str[i]);
		}
		
		mergeSort(array, 0, num);
		
		
		output(array,num);
		
		System.out.println(sum);
		
	}
	
	public static void output(int[] sort, int num){
	//出力
	StringBuilder sb = new StringBuilder("");
	sb.append(sort[0]);
	for (int i = 1; i < num; i++) {
		sb.append(" ").append(sort[i]);
	}
	System.out.println(sb);
	}
	
	public static void mergeSort(int[] array, int left, int right){
		if(left + 1 < right){
			int middle = (left + right) / 2;
			mergeSort(array, left, middle);
			mergeSort(array, middle, right);
			merge(array, left, middle, right);
		}	
	}

	public static void merge(int[] array, int left, int middle, int right){
		int left_m = middle - left;
		int right_m = right - middle;
		int[] left_box = new int[left_m+1];
		int[] right_box = new int[right_m+1];
		for (int i=0; i<left_m; i++) {
			left_box[i] = array[left+i];
		}
		for (int i=0; i<right_m; i++) {
			right_box[i] = array[middle+i];
		}
		left_box[left_m] = Integer.MAX_VALUE;
		right_box[right_m] = Integer.MAX_VALUE;
		int i = 0;
		int j = 0;
		for (int k=left; k<right; k++) {
			sum ++;
			if (left_box[i] <= right_box[j]) {
				array[k] = left_box[i];
				i++;
			}else {
				array[k] = right_box[j];
				j++;
			}
		}
	}
}
