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.*;
import java.io.*;

class Main {

	static int count = 0;

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		int n = Integer.parseInt(br.readLine());
		String line = br.readLine();
		String[] str = line.split(" ");
		int[] a = new int[n];

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

		margeSort(a,0,n);

		StringBuilder sb = new StringBuilder();
		sb.append(a[0]);
		for (int i=1; i<n; i++) {
			sb.append(" ").append(a[i]);
		}
		System.out.println(sb);
		System.out.println(count);

		br.close();
	}

	static void marge(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] = Integer.MAX_VALUE;
		R[n2] = Integer.MAX_VALUE;
		int i = 0;
		int j = 0;
		for (int k=left; k<right; k++) {
			count++;
			if (L[i] <= R[j]) {
				a[k] = L[i];
				i++;
			}else {
				a[k] = R[j];
				j++;
			}
		}
	}

	static void margeSort(int[] a,int left,int right){
		if (left+1 < right) {
			int mid = (left+right)/2;
			margeSort(a,left,mid);
			margeSort(a,mid,right);
			marge(a,left,mid,right);
		}
	}
}