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.*;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		String[] s = br.readLine().split(" ");
		int[] S = new int[n];
		for (int i = 0; i < n; i++) {
			S[i] = Integer.parseInt(s[i]);
		}
		margeSort(S, 0, n);
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < n; i++) {
			sb.append(S[i]).append((i != n - 1) ? " " : "\n");
		}
		sb.append(count).append("\n");
		System.out.print(sb);
	}
	public static int count = 0;
	public static void marge(int[] A, int left, int middle, int right) {
		int n1 = middle - left;
		int n2 = right - middle;
		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[middle + i];
		}
		L[n1] = Integer.MAX_VALUE;
		R[n2] = Integer.MAX_VALUE;
		int i = 0;
		int j = 0;
		for (int k = left; k < right; k++) {
			if (L[i] <= R[j]) {
				A[k] = L[i];
				i++;
			} else {
				A[k] = R[j];
				j++;
			}
			count++;
		}
	}
	public static void margeSort(int[] A, int left, int right) {
		if ((left + 1) < right) {
			int middle = (left + right) / 2;
			margeSort(A, left, middle);
			margeSort(A, middle, right);
			marge(A, left, middle, right);
		}
	}
}