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.util.*;
import java.io.*;



public class Main{
    static long m=998244353l;                   //line 156 modInverse
    static boolean[] vis;                       //line 74 and 91 hasElement ans pth_fnd
    static int MOD=1000000007;
    public static void main(String[] args) throws IOException{
        // long sttm=System.currentTimeMillis();
        FastReader sc=new FastReader();
        OutputStream out=new BufferedOutputStream(System.out);
        int n=sc.nextInt();
        int i=n;
        ArrayList<Integer> arrl=new ArrayList<Integer>();
        while(i>=4){
            arrl.add(i);arrl.add(i-3);i-=4;
        }
        if(i==1){
            out.write(("1\n"+arrl.size()+" ").getBytes());
        }
        else if(i==2){
            out.write(("1\n"+(arrl.size()+1)+" 1 ").getBytes());
        }
        else if(i==3){
            out.write(("0\n"+(arrl.size()+1)+" 3 ").getBytes());
        }
        else{
            out.write(("0\n"+arrl.size()+" ").getBytes());
        }
        for(int x:arrl){
            out.write((x+" ").getBytes());
        }
        out.flush();
        return;
    }

    public static long pow(long n,long k){                 //n-pow(k)
        if(k==1){
            return n%MOD;
        }
        if(k==0){
            return 1;
        }
        long val=pow(n,k/2)%MOD;
        if(k%2==0)return ((val%MOD)*(val%MOD))%MOD;
        else return (((val*val)%MOD)*n)%MOD;
    }


    public static long cnt_sum_k_subar(long[] a,int n,int k){
        HashMap<Long,Long> map=new HashMap<Long,Long>();
        long ret=0;
        long cur_sum=0;
        for(int i=0;i<n;i++){
            cur_sum+=a[i];
            if(cur_sum==k){
                ret++;
            }
            if(map.containsKey(cur_sum-k)){
                ret+=map.get(cur_sum-k);
            }
            if(map.containsKey(cur_sum)){
                map.put(cur_sum, map.get(cur_sum)+1);
            }
            else{
                map.put(cur_sum, (long)1);
            }
        }
        return ret;
    }



    public static ArrayList<Integer> lcm(int num){
        ArrayList<Integer> arrl=new ArrayList<Integer>();
        while(num%2==0){
            arrl.add(2);
            num/=2;
        }
        for(int i=3;i*i<=num;i+=2){
            while(num%i==0){
                arrl.add(i);
                num/=i;
            }
        }
        if(num>2){
            arrl.add(num);
        }
        return arrl;
    }


    static long modInverse(long a,long m) 
    { 
        long m0 = m; 
        long y = 0l, x = 1l; 
  
        if (m == 1) 
            return 0l; 
  
        while (a > 1) 
        { 
  
            long q = a / m; 
  
            long t = m; 
  
            m = a % m; 
            a = t; 
            t = y; 
  
            y = x - q * y; 
            x = t; 
        } 
        if (x < 0) 
            x += m0; 
  
        return x; 
    } 


    public static TreeSet<Long> arr_fact(long num){
        TreeSet<Long> arr=new TreeSet<Long>();
        int cnt=0;
        for(long i=1;i*i<=num;i++){
            if(num%i==0){
                if(i*i==num){
                    cnt+=1;
                    arr.add(i);
                }
                else{
                    arr.add(i);arr.add(num/i);
                    cnt+=2;
                }
            }
        }
        return arr;
    }



    public static int num_fact(int num){
        ArrayList<Integer> arr=new ArrayList<Integer>();
        int cnt=0;
        for(int i=1;i*i<=num;i++){
            if(num%i==0){
                if(i*i==num){
                    cnt+=1;
                }
                else{
                    cnt+=2;
                }
            }
        }
        return cnt;
    }


    public static long cal(int k,int x){
        long val=1;

        for(int i=0;i<k;i++){
            val*=2;
            if(val>x){
                break;
            }
        }
        return val;
    }

    public static void sort_inc(int[][] arr,int col){        //change dimention if req
        Arrays.sort(arr, new Comparator<int[]>() {
            public int compare(final int[] entry1,final int[] entry2) { 
                if (entry1[col] > entry2[col])              //this is for inc
                    return 1; 
                else if(entry1[col]==entry2[col])
                    return 0;
                else
                    return -1; 
            }
        });
    }


    public static boolean prime(int n){
        for(int i=2;i*i<=n;i++){
            if(n%i==0){
                return false;
            }
        }
        return true;
    }


    static long gcd(long a, long b) 
	{ 
	if (b == 0) 
		return a; 
	return gcd(b, a % b); 
	} 
}


class FastReader{ 
    BufferedReader br; 
    StringTokenizer st; 

    public FastReader(){ 
        br = new BufferedReader(new
                 InputStreamReader(System.in)); 
    } 
  
    String next(){ 
        while (st == null || !st.hasMoreElements()){ 
            try{ 
                st = new StringTokenizer(br.readLine()); 
            } 
            catch (IOException  e){ 
                e.printStackTrace(); 
            } 
        } 
        return st.nextToken(); 
    } 
  
    int nextInt(){ 
        return Integer.parseInt(next()); 
    } 
  
    long nextLong(){ 
        return Long.parseLong(next()); 
    }
  
    double nextDouble(){ 
        return Double.parseDouble(next()); 
    }
  
    String nextLine(){ 
        String str = ""; 
        try{ 
            str = br.readLine(); 
        }
        catch (IOException e){ 
            e.printStackTrace(); 
        }
        return str; 
    }
}