Petya has n integers: 1, 2, 3, ..., n. He wants to split these integers in two non-empty groups in such a way that the absolute difference of sums of integers in each group is as small as possible. 

Help Petya to split the integers. Each of n integers should be exactly in one group.

Input

The first line contains a single integer n (2 ≤ n ≤ 60 000) — the number of integers Petya has.

Output

Print the smallest possible absolute difference in the first line.

In the second line print the size of the first group, followed by the integers in that group. You can print these integers in arbitrary order. If there are multiple answers, print any of them.

Examples

Input

4


Output

0
2 1 4 


Input

2


Output

1
1 1 

Note

In the first example you have to put integers 1 and 4 in the first group, and 2 and 3 in the second. This way the sum in each group is 5, and the absolute difference is 0.

In the second example there are only two integers, and since both groups should be non-empty, you have to put one integer in the first group and one in the second. This way the absolute difference of sums of integers in each group is 1.
//>>>BaZ<<<//
import java.util.*;
import java.io.*;
import static java.lang.Math.*;
public class Student
{  
    static int dx[] = {-1,1,0,0};
    static int dy[] = {0,0,1,-1};
    static long MOD = 1000000007;
    static int INF = Integer.MAX_VALUE/10;
    static PrintWriter pw;
    static InputReader scan;
    //static MyFileReader1 ss;
    //static MyFileReader scan;
    static int ni() throws IOException{return scan.nextInt();}
    static long nl() throws IOException{return scan.nextLong();}
    static double nd() throws IOException{return scan.nextDouble();}
    static String ne() throws IOException{return scan.next();}
    static void pl() throws IOException {pw.println();}
    static void pl(Object o) throws IOException {pw.println(o);}
    static void p(Object o) throws IOException {pw.print(o+" ");}
    static void psb(StringBuilder sb) throws IOException {pw.print(sb);}
    public static void main(String[] args) {
        new Thread(null,null,"BaZ",99999999)
        {
            public void run()
            {
                try
                {
                    solve();
                }
                catch(Exception e)
                {  
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }.start();
    }
    static void solve() throws IOException
    {  
        Calendar CAL1 = Calendar.getInstance();
        CAL1.setTime(new Date());
        scan = new InputReader(System.in);
        pw = new PrintWriter(System.out,true);
        //pw = new PrintWriter(new File("C://Users/Aman deep/Desktop/output.txt"));  
        //ss = new MyFileReader1();
        //scan = new MyFileReader();
        StringBuilder sb = new StringBuilder();
        int n = ni();
        if(n%4==0)
        {
            pl("0");
            p(n/2);
            int curr = 1;
            for(int i=0;i<n/4;++i)
            {
                p(curr);
                curr+=2;
            }
            curr = n;
            for(int i=0;i<n/4;++i)
            {
                p(curr);
                curr-=2;
            }
            pl();
        }
        else if(n%4==1)
        {
            pl(1);
            p(n/2);
            int curr = 2;
            for(int i=0;i<n/4;++i)
            {
                p(curr);
                curr+=2;
            }
            curr = n;
            for(int i=0;i<n/4;++i)
            {
                p(curr);
                curr-=2;
            }
            pl();
        }
        else if(n%4==2)
        {
            pl(1);
            p(2*(n/4)+1);
            int curr = 1;
            for(int i=0;i<n/4;++i)
            {
                p(curr);
                curr+=2;
            }
            curr = n;
            for(int i=0;i<n/4;++i)
            {
                p(curr);
                curr-=2;
            }
            p(n/2);
            pl();
        }
        else
        {
            pl(0);
            p((2*(n/4)+2));
            int curr = 2;
            for(int i=0;i<n/4;++i)
            {
                p(curr);
                curr+=2;
            }
            curr = n;
            for(int i=0;i<n/4;++i)
            {
                p(curr);
                curr-=2;
            }
            p((1+(n/2)));
            p(1);
            pl();
        }
        Calendar CAL2 = Calendar.getInstance();
        CAL2.setTime(new Date());
        double Execution_Time = (double)(CAL2.getTimeInMillis()-CAL1.getTimeInMillis())/1000.000;
        //System.out.println("Execution time : "+Execution_Time+" seconds");
        pw.flush();
        pw.close();
    }
    static class InputReader     //NoSuchElementException -> EOF
	{
		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 String nextLine()
		{
			BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
			String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
		}
		public int nextInt()
		{
			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 long nextLong() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			long 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 double nextDouble() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			double res = 0;
			while (!isSpaceChar(c) && c != '.') 
			{
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, nextInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			if (c == '.') 
			{
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) 
				{
					if (c == 'e' || c == 'E')
						return res * Math.pow(10, nextInt());
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}
		
		public String readString() 
		{
			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 readString();
		}
		
		public interface SpaceCharFilter 
		{
			public boolean isSpaceChar(int ch);
		}
	}
    static class MyFileReader                                          //File input template
    {
        StringTokenizer st;
        BufferedReader br;
        MyFileReader() throws IOException
        {
            br = new BufferedReader(new FileReader("C://Users/Aman deep/Desktop/input.txt"));
        }
        String nextLine() throws IOException
        {
            return br.readLine();
        }
        String next() throws IOException
        {
            if(st==null || !st.hasMoreTokens())
                st = new StringTokenizer(nextLine());
            return st.nextToken();
        }
        int nextInt() throws IOException
        {
            return Integer.parseInt(next());
        }
        long nextLong() throws IOException
        {
            return Long.parseLong(next());
        }
        double nextDouble() throws IOException
        {
            return Double.parseDouble(next());
        }
    }
    static class MyFileReader1                                          //File input template
    {
        StringTokenizer st;
        BufferedReader br;
        MyFileReader1() throws IOException
        {
            br = new BufferedReader(new FileReader("C://Users/Aman deep/Desktop/output.txt"));
        }
        String nextLine() throws IOException
        {
            return br.readLine();
        }
        String next() throws IOException
        {
            if(st==null || !st.hasMoreTokens())
                st = new StringTokenizer(nextLine());
            return st.nextToken();
        }
        int nextInt() throws IOException
        {
            return Integer.parseInt(next());
        }
        long nextLong() throws IOException
        {
            return Long.parseLong(next());
        }
        double nextDouble() throws IOException
        {
            return Double.parseDouble(next());
        }
    }
}
