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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class codeforces554 {

	int chests, keys;
	int[] chestsNumA, keysNumA;
	int x;
	
	public int maxChestsOpened() {
		int chestsOddCount = 0, chestsEvenCount = 0;
		int keysOddCount = 0, keysEvenCount = 0;
		for(int i:chestsNumA) {
			if(i%2 == 0)
				chestsEvenCount++;
			else
				chestsOddCount++;
		}
		
		for(int i:keysNumA) {
			if(i%2 == 0)
				keysEvenCount++;
			else
				keysOddCount++;
		}
		int ans = 0;
		ans+= Math.min(chestsEvenCount, keysOddCount);
		ans+= Math.min(keysEvenCount, chestsOddCount);
		return ans;
	}
	
	public void operations() {
		int posA[] = new int[41];
		int posIndex = 0;
		int ans = 0;
		while(!isAllOnes(x)) {
			int a =firstOnePos(x);
			// posA[posIndex++] = a;
			a++;
			posA[posIndex++] = a;
			x = (x^((1<<a) -1));
			// System.out.println("x is: " + x);
			ans++;
			if(x == 0 || isAllOnes(x)) 
				break;
			x = x+1;
			// System.out.println("x is: " + x);
			ans++;
		}
		System.out.println(ans);
		// System.out.println("x is: " + x);
		if(ans != 0)
		{
			for(int i = 0;i<posIndex;i++) {
				System.out.print(posA[i] + " ");
			}
		}
	}
	
	int firstOnePos(int n) {
		int count = 0;
		while(n!=0) {
			if(n!=1) {
				n = n/2;
				count++;
			}
			else {
				return count;
			}
		}
		return -1;
	}
	
	boolean isAllOnes(int n) {
		while(n!=0) {
			if((n&1) == 1)
				n = n/2;
			else
				return false;
		}
		return true;
	}
	
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		codeforces554 cf = new codeforces554();
		cf.read();
		 // System.out.println(cf.maxChestsOpened());
		cf.operations();
	}
	
	void read() {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer tokenizer = null;
		// x
		x = nextInt(tokenizer, br);
		
//		int[] ip1 = nextIntsSpace(tokenizer, br);
//		chests = ip1[0];
//		keys = ip1[1];
//		chestsNumA = nextIntsSpace(tokenizer, br);
//		keysNumA = nextIntsSpace(tokenizer, br);
		//chests keys
		// n chests m keys
		// o/p
		/*
		nums = nextIntsSpace(tokenizer, br);
		String input1 = next(tokenizer, br);
		int input2 = nextInt(tokenizer, br);
		String input3 = next(tokenizer, br);
		System.out.println("Input1: " + input1 + " input2: " + input2 + " input3: " + input3);
		*/
	}
	
	public String next(StringTokenizer tokenizer, BufferedReader br) {
		try {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				String line = br.readLine();
				if (line == null)
					throw new IOException();
				tokenizer = new StringTokenizer(line);
			}
		}
		catch(IOException e) {
			
		}
		return tokenizer.nextToken();
	}
	
	public String[] nextSpace(StringTokenizer tokenizer, BufferedReader br) {
		try {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				String line = br.readLine();
				if (line == null)
					throw new IOException();
				tokenizer = new StringTokenizer(line);
			}
		}
		catch(IOException e) {
			
		}
		String s[] = new String[tokenizer.countTokens()];
		int sCount = 0;
		while(tokenizer.hasMoreTokens()) {
			s[sCount++] = tokenizer.nextToken();
		}
		return s;
	}
	
	public int[] nextIntsSpace(StringTokenizer tokenizer, BufferedReader br) {
		try {
			String s[] = nextSpace(tokenizer, br);
			int n[] = new int[s.length];
			for(int i = 0;i < s.length; i++) {
				n[i] = Integer.parseInt(s[i]);
			}
			return n;
		}
		catch(Exception e) {
			e.printStackTrace();
			return new int[0];
		}
	}

	public int nextInt(StringTokenizer tokenizer, BufferedReader br) {
		try {
			
			return Integer.parseInt(next(tokenizer, br));
		}
		catch(Exception e) {
			return -1;
		}
	}

}