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.BufferedWriter;
	import java.io.IOException;
	import java.io.InputStream;
	import java.io.OutputStream;
	import java.io.OutputStreamWriter;
	import java.io.PrintWriter;
	import java.io.Writer;
	import java.util.Arrays;
	import java.util.InputMismatchException;
	import java.util.*;
	import java.io.*;
	import java.math.*;
	public class Main7{

	static class Pair
		{ 
			int x; 
			int y;
			public Pair(int x, int y) 
			{	 
				this.x = x; 
				this.y = y;
				
			}	 
		} 
		static class Pair1
		{
			String x;
			int y;
			int z;
			
		}
		static class Compare
		{ 
			static void compare(Pair arr[], int n) 
			{ 
				// Comparator to sort the pair according to second element 
				Arrays.sort(arr, new Comparator<Pair>() { 
					@Override public int compare(Pair p1, Pair p2) 
					{ 
						if(p1.x>p2.x)
						{
							return 1;
						}
						else if(p1.x<p2.x)
						{
							return -1;
						}
						else
						{
							return 0;
						} 
					} 
				}); 
			} 
		}
		
		static class pqcomparator implements Comparator<Pair>
		{
		                // for Ascending order of cgpa 
            public int compare(Pair s1, Pair s2) { 
                if (s1.x > s2.x) 
                    return -1; 
                else if (s1.x < s2.x) 
                    return 1; 
                return 0; 
                } 
        } 
		
		
		public static long pow(long a, long b)
		{
			long result=1;
			while(b>0)
			{
				if (b % 2 != 0)
				{
					result=(result*a)%mod;
					b--;
				} 
				a=(a*a)%mod;
				b /= 2;
			}   
			return result;
		}
		public static long fact(long num)
		{
					long value=1;
					int i=0;
					for(i=2;i<num;i++)
					{
						value=((value%mod)*i%mod)%mod;
					}
					return value;
				}
				public static long gcd(long a, long b)
				{
					if (a == 0)
						return b;
					return gcd(b%a, a);
				}
				
				public static long lcm(int a,int b)
				{
					return a * (b / gcd(a, b));
				}
				public static long sum(int h)
				{
					return (h*(h+1)/2);
				}
				/*public static void dfs(int parent,boolean[] visited)
				{
					TreeSet<Integer> arr=new TreeSet<Integer>();
					arr=graph.get(parent);
					visited[parent]=true;
					if(a[parent]==1)
					{
						flag=1;
					}
					if(a[parent]==2)
					{
						flag1=1;
					}
					if(flag==1 && flag1==1)
					{
						return;
					}
					Iterator itr=arr.iterator();
					while(itr.hasNext())
					{
						int num=(int)itr.next();
						if(visited[num]==false)
						{
							dfs(num,visited);
						}
					}
					
				}*/
			//	static int flag1=0;
				static int[] dis;
				static long mod=64735492;
				static ArrayList<ArrayList<Integer>> graph;
				
			//	static int[] a;			  
				
				public static int[] sort(int[] a)
				{
					int n=a.length;
					ArrayList<Integer> ar=new ArrayList<>();
					for(int i=0;i<a.length;i++)
					{
						ar.add(a[i]);
					}
					Collections.sort(ar);
					for(int i=0;i<n;i++)
					{
						a[i]=ar.get(i);
					}
					return a;
				}
			//	static int flag=1;
				public static void main(String args[])throws IOException
				{
				//	InputReader in=new InputReader(System.in);
				//	OutputWriter out=new OutputWriter(System.out);
				//	long a=pow(26,1000000005);
				    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
					ArrayList<Long> ar=new ArrayList<>();
					ArrayList<Integer> ar4=new ArrayList<>();
				//	TreeSet<Long> ts=new TreeSet<>();
					TreeSet<Long> ts1=new TreeSet<>();
					HashMap<Long,Integer> hash=new HashMap<>();
					HashMap<Integer,Integer> odd=new HashMap<Integer,Integer>();
					HashMap<Long,Integer> hash2=new HashMap<Long,Integer>();
				/*	boolean[] prime=new boolean[5000001];
					for(int i=2;i*i<=5000000;i++)
					{
						if(prime[i]==false)
						{
							fact[i]=1;
							for(int j=2*i;j<=5000000;j+=i)
							{
								prime[j]=true;
							}
						}
					}*/
					int x=i();
					long num=x;
					long max=0;
					long count=0;
					TreeSet<Long> ts=new TreeSet<>();
					for(int i=0;i<63;i++)
					{
						ts.add((long)pow(2,i)-(long)1);
					}
					for(int i=0;i<40;i++)
					{
						if(ts.contains(num)==true)
						{
							break;
						}
						if(i%2==0)
						{
							long n=0;
							String s=Long.toBinaryString(num);
							long flag=0;
							for(int j=0;j<s.length();j++)
							{
								if(s.charAt(j)=='0')
								{
									flag=j;
									break;
								}
							}
							if(flag==s.length()-1)
							{
								n=0;
								ar.add((long)0);
							}
							else
							{
								n=s.length()-flag;
							}
							if(n!=0)
							{
								char[] ch=new char[(int)n];
								for(int j=0;j<n;j++)
								{
									ch[j]='1';
								}
								String s1=new String(ch);
								ar.add(n);
								num=num^(int)(Integer.parseInt(s1,2));
							}
						}
						else
						{
							num++;
						}
						count++;
					}
					pln(count+"");
					for(int i=0;i<ar.size();i++)
					{
						System.out.print(	ar.get(i)+" ");
					}
					pln("");
				}
				
				
				
				
				
				
				/**/
				static InputReader in=new InputReader(System.in);
					static OutputWriter out=new OutputWriter(System.out);
					public static long l()
					{
						String s=in.String();
						return Long.parseLong(s);
					}
					public static void pln(String value)
					{
						System.out.println(value);
					}
					public static int i()
					{
						return in.Int();
					}
					public static String s()
					{
						return in.String();
					}
		}
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			class InputReader {
				 
				private InputStream stream;
				private byte[] buf = new byte[1024];
				private int curChar;
				private int numChars;
				private SpaceCharFilter filter;
			 
				public InputReader(InputStream stream) {
					this.stream = stream;
				}
			 
				public int read() {
					if (numChars== -1)
						throw new InputMismatchException();
					if (curChar >= numChars) {
						curChar = 0;
						try {
							numChars = stream.read(buf);
						} catch (IOException e) {
							throw new InputMismatchException();
						}
						if (numChars <= 0)
							return -1;
					}
					return buf[curChar++];
				}
			 
				public int Int() {
					int c = read();
					while (isSpaceChar(c))
						c = read();
					int sgn = 1;
					if (c == '-') {
						sgn = -1;
						c = read();
					}
					int res = 0;
					do {
						if (c < '0' || c > '9')
							throw new InputMismatchException();
						res *= 10;
						res += c - '0';
						c = read();
					} while (!isSpaceChar(c));
					return res * sgn;
				}
			 
				public String String() {
					int c = read();
					while (isSpaceChar(c))
						c = read();
					StringBuilder res = new StringBuilder();
					do {
						res.appendCodePoint(c);
						c = read();
					} while (!isSpaceChar(c));
					return res.toString();
				}
			 
				public boolean isSpaceChar(int c) {
					if (filter != null)
						return filter.isSpaceChar(c);
					return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
				}
			 
				public String next() {
					return String();
				}
			 
				public interface SpaceCharFilter {
					public boolean isSpaceChar(int ch);
				}
			}
			 
			class OutputWriter {
				private final PrintWriter writer;
			 
				public OutputWriter(OutputStream outputStream) {
					writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
				}
			 
				public OutputWriter(Writer writer) {
					this.writer = new PrintWriter(writer);
				}
			 
				public void print(Object...objects) {
					for (int i = 0; i < objects.length; i++) {
						if (i != 0)
							writer.print(' ');
						writer.print(objects[i]);
					}
				}
			 
				public void printLine(Object...objects) {
					print(objects);
					writer.println();
				}
			 
				public void close() {
					writer.close();
				}
			 
				public void flush() {
					writer.flush();
				}
			 
				}
			 
				class IOUtils {
			 
				public static int[] readIntArray(InputReader in, int size) {
					int[] array = new int[size];
					for (int i = 0; i < size; i++)
						array[i] = in.Int();
					return array;
				}
			 
				}