Problem: Cat Furrier Transform is a popular algorithm among cat programmers to create longcats. As one of the greatest cat programmers ever exist, Neko wants to utilize this algorithm to create the perfect longcat.

Assume that we have a cat with a number x. A perfect longcat is a cat with a number equal 2^m - 1 for some non-negative integer m. For example, the numbers 0, 1, 3, 7, 15 and so on are suitable for the perfect longcats.

In the Cat Furrier Transform, the following operations can be performed on x:

  * (Operation A): you select any non-negative integer n and replace x with x ⊕ (2^n - 1), with ⊕ being a [bitwise XOR operator](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
  * (Operation B): replace x with x + 1. 



The first applied operation must be of type A, the second of type B, the third of type A again, and so on. Formally, if we number operations from one in the order they are executed, then odd-numbered operations must be of type A and the even-numbered operations must be of type B.

Neko wants to produce perfect longcats at industrial scale, thus for each cat Neko only wants to perform at most 40 operations. Can you help Neko writing a transformation plan?

Note that it is not required to minimize the number of operations. You just need to use no more than 40 operations.

Input

The only line contains a single integer x (1 ≤ x ≤ 10^6).

Output

The first line should contain a single integer t (0 ≤ t ≤ 40) — the number of operations to apply.

Then for each odd-numbered operation print the corresponding number n_i in it. That is, print ⌈ t/2 ⌉ integers n_i (0 ≤ n_i ≤ 30), denoting the replacement x with x ⊕ (2^{n_i} - 1) in the corresponding step.

If there are multiple possible answers, you can print any of them. It is possible to show, that there is at least one answer in the constraints of this problem.

Examples

Input


39


Output


4
5 3 

Input


1


Output


0


Input


7


Output


0

Note

In the first test, one of the transforms might be as follows: 39 → 56 → 57 → 62 → 63. Or more precisely:

  1. Pick n = 5. x is transformed into 39 ⊕ 31, or 56. 
  2. Increase x by 1, changing its value to 57. 
  3. Pick n = 3. x is transformed into 57 ⊕ 7, or 62. 
  4. Increase x by 1, changing its value to 63 = 2^6 - 1. 



In the second and third test, the number already satisfies the goal requirement.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.util.regex.*;
import java.math.BigInteger;

public class Codeforces{

	static class MyScanner{
		BufferedReader br;
		StringTokenizer st;

		MyScanner(FileReader fileReader){
			br = new BufferedReader(fileReader);
		}

		MyScanner(){
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String nn(){
			while(st == null || !st.hasMoreElements()){
				try{
					st = new StringTokenizer(br.readLine());
				}catch(IOException e){
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		char nc(){
			return nn().charAt(0);
		}

		int ni(){
			return Integer.parseInt(nn());
		}

		long nl(){
			return Long.parseLong(nn());
		}

		double nd(){
			return Double.parseDouble(nn());
		}

		int[] niArr0(int n){
			int[] ar = new int[n];
			for(int i = 0; i < n; i++) ar[i] = ni();
			return ar;
		}

		int[] niArr1(int n){
			int[] ar = new int[n + 1];
			for(int i = 1; i <= n; i++) ar[i] = ni();
			return ar;
		}

		long[] nlArr0(int n){
			long[] ar = new long[n];
			for(int i = 0; i < n; i++) ar[i] = nl();
			return ar;
		}
	}

	public static <T> void mprintln(T ... ar){
		for(T i: ar) out.print(i + " ");
		out.println();
	}

	private static PrintWriter out;

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

		// Input from file
		// File inputFile = new File("JavaFile.txt");
		// File outputFile = new File("JavaOutputFile.txt");
		// FileReader fileReader = new FileReader(inputFile);
		// Here it ends

		MyScanner sc = new MyScanner();
		// MyScanner sc = new MyScanner(fileReader);

		out = new PrintWriter(new BufferedOutputStream(System.out)); // Output to console
		// out = new PrintWriter(new PrintStream(outputFile)); // Output to file

		getAns(sc);

		out.close();
	}

	private static void getAns(MyScanner sc){
		int n = sc.ni();
		
		ArrayList<Integer> ans = new ArrayList();
		
		while(n > 1){
			int cur = allSetBit(n);
			ans.add((int)(Math.log(cur) / Math.log(2)));
			n ^= cur - 1;
			if(n == 1 || n == allSetBit(n) - 1){
				out.println(2 * ans.size() - 1);
				ans.forEach(i -> out.print(i + " "));
				return;
			}
			n++;
		}
		
		out.println(2 * ans.size());
		ans.forEach(i -> out.print(i + " "));
	}
	
	private static int allSetBit(int n){
		n |= n >> 1;
		n |= n >> 2;
		n |= n >> 4;
		n |= n >> 8;
		n |= n >> 16;
		n |= n >> 32;
		
		return n + 1;
	}
}