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.
import java.io.*;
	import java.math.BigInteger;
	import java.math.RoundingMode;
	import java.text.DecimalFormat;
	import java.util.*;
	
/**
 * @author Aayush Agrawal
 *
 */
public class some {
		
	
		static double eps=(double)1e-6;
		static long mod=(int)1e9+6;
		
		public static void main(String args[]) throws IOException{
			InputReader sc = new InputReader(System.in);
			OutputStream outputStream = System.out;
			PrintWriter out = new PrintWriter(outputStream);
			//-------------------------------------
			
			cal3(sc, out);
			
			//-------------------------------------
			out.close();
		}
		
		static void cal3(InputReader sc, PrintWriter out)
		{
			long n = sc.nextLong();
			long sum = 0;
			
			sum = (n*(n+1))/2;
			
			long diff = sum%2;
			
			long part = sum/2 + sum%2;
			
			LinkedList<Long> list = new LinkedList<Long>();
			
			for(long i = n; i>=1; i--)
			{
				if(part<=i)
				{
					list.add(part);
					break;
				}
				
				list.add(i);
				part-=i;
			}
			out.println(diff);
			out.print(list.size() + " ");
			for(int i=0; i<list.size(); i++)
				out.print(list.get(i) + " ");
		}
		
		static void cal2(InputReader sc, PrintWriter out)
		{
			int n = sc.nextInt();
			long[] arr = new long[n+1];
			
			//presum
			for(int i=1; i<=n; i++)
				arr[i]=arr[i-1]+sc.nextInt();
			
			//If last value divisible by 3, then only possible
			if(arr[n]%3!=0)
				out.println(0);
			else
			{
				//If last value is 0, (special case)
				if(arr[n]==0)
				{
					long count0=0;
					for(int i=1; i<=n; i++)
					{
						if(arr[i]==0)
							count0++;
					}
					if(count0<3)
						out.println(0);
					else
					{
						//allocate 1 zero to each group, then distribute the remaining zeros in 3 groups
						count0-=1;
						out.println((count0*(count0-1))/2);
					}
				}
				else
				{	
					long count1n3=0, count2n3=0, ans=0;
					for(int i=0; i<arr.length; i++)
					{
						if(arr[i]==arr[n]/3)
							count1n3+=1;
						else if(arr[i]==(2*arr[n])/3)
							ans+=count1n3;	
					}
					out.println(ans);
				}
			}
		}
	
		static class Pair implements Comparable<Pair> {
			int a, b;

			Pair(int a, int b) {
				this.a = a;
				this.b = b;
			}

			public int compareTo(Pair o) {
				// TODO Auto-generated method stub
				if (this.a != o.a)
					return Integer.compare(this.a, o.a);
				else
					return Integer.compare(this.b, o.b);
				//return 0;
			}

			public boolean equals(Object o) {
				if (o instanceof Pair) {
					Pair p = (Pair) o;
					return p.a == a && p.b == b;
				}
				return false;
			}

			public int hashCode() {
				return new Integer(a).hashCode() * 31 + new Integer(b).hashCode();
			}

			public String toString() {
				return a + " " + b;
			}
		}
		
		static int[] sieve(int n,int[] arr)
		{
			for(int i=2;i*i<=n;i++)
			{
				if(arr[i]==0)
				{
					for(int j=i*2;j<=n;j+=i)
						arr[j]=1;
				}
			}
			return arr;
		}
		
		static boolean isPal(String s)
		{
			for(int i=0, j=s.length()-1;i<=j;i++,j--)
			{
				if(s.charAt(i)!=s.charAt(j)) return false;
			}
			return true;
		}
		public static String rev(String s)
		{
			StringBuilder sb=new StringBuilder(s);
			sb.reverse();
			return sb.toString();
		}
		    
		static long lcm(long a, long b)
		{
		    return a * (b / gcd(a, b));
		}
		
		static long gcd(long a, long b)
		{
		    while (b > 0)
		    {
		        long temp = b;
		        b = a % b; // % is remainder
		        a = temp;
		    }
		    return a;
		}
		static long modulo(long a,long b,long c) {
			long x=1;
			long y=a;
			while(b > 0){
				if(b%2 == 1){
					x=(x*y)%c;
				}
				y = (y*y)%c; // squaring the base
				b /= 2;
			}
			return  x%c;
		}
		public static void debug(Object... o) {
			System.out.println(Arrays.deepToString(o));
		}
		
		static long sort(int a[]) {
			int n = a.length;
			int b[] = new int[n];
			return mergeSort(a, b, 0, n - 1);
		}

		static long mergeSort(int a[], int b[], long left, long right) {
			long c = 0;
			if (left < right) {
				long mid = left + (right - left) / 2;
				c = mergeSort(a, b, left, mid);
				c += mergeSort(a, b, mid + 1, right);
				c += merge(a, b, left, mid + 1, right);
			}
			return c;
		}

		static long merge(int a[], int b[], long left, long mid, long right) {
			long c = 0;
			int i = (int) left;
			int j = (int) mid;
			int k = (int) left;
			while (i <= (int) mid - 1 && j <= (int) right) {
				if (a[i] <= a[j]) {
					b[k++] = a[i++];
				} else {
					b[k++] = a[j++];
					c += mid - i;
				}
			}
			while (i <= (int) mid - 1)
				b[k++] = a[i++];
			while (j <= (int) right)
				b[k++] = a[j++];
			for (i = (int) left; i <= (int) right; i++)
				a[i] = b[i];
			return c;
		}  
		
	
		static class InputReader {
    		public BufferedReader reader;
    		public StringTokenizer tokenizer;
     
    		public InputReader(InputStream inputstream) {
    			reader = new BufferedReader(new InputStreamReader(inputstream));
    			tokenizer = null;
    		}
     
    		public String nextLine(){
    			String fullLine=null;
    			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
    				try {
    					fullLine=reader.readLine();
    				} catch (IOException e) {
    					throw new RuntimeException(e);
    				}
    				return fullLine;
    			}
    			return fullLine;
    		}
    		public String next() {
    			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
    				try {
    					tokenizer = new StringTokenizer(reader.readLine());
    				} catch (IOException e) {
    					throw new RuntimeException(e);
    				}
    			}
    			return tokenizer.nextToken();
    		}
    		public long nextLong() {
    			return Long.parseLong(next());
    		}
    		public int nextInt() {
    			return Integer.parseInt(next());
    		}
    	}
    	
    }