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

     //--------------->>>>IF YOU ARE HERE FOR QUICKSORT HACK THEN SORRY NO HACK FOR YOU<<<-------------------

public class a{ 
     static int[] count,count1,count2;
     static Node[] nodes;
     static int[] arr;
     static int[] dp;
     static char[] ch,ch1;
     static long[] darr,farr;
     static char[][] mat,mat1;
     static long x,h;
     static long maxl;
     static double dec;
     static long mx = (long)1e9;
     static String s;
     static long minl;
     static int start_row;
     static int start_col;     
     static int end_row;     
     static int end_col;     
     static long mod = 998244353;
     // static int minl = -1;
     // static long n;
     static int n,n1,n2,q;
     static long a;
     static long b;
     static long c;
     static long d;
     static long y,z;
     static int m;
     static long k;
     static FastScanner sc;
     static String[] str,str1;
     static Set<Long> set,set1,set2;
     static SortedSet<Long> ss;
     static List<Integer> list,list1,list2,list3;
     static PriorityQueue<Long> pq,pq1;
     static LinkedList<Integer> ll;
     static Map<String,Integer> map,map1;
     static StringBuilder sb,sb1,sb2;
     static int index;
     static int[] dx = {0,-1,0,1,-1,1,-1,1};
     static int[] dy = {-1,0,1,0,-1,-1,1,1};

     // public static void solve(){

     //    FastScanner sc = new FastScanner();
     //    // int t = sc.nextInt();
     //    int t = 1;
     //    for(int tt = 0 ; tt < t ; tt++){
     //        int n = sc.nextInt();
     //        int m = sc.nextInt();
     //        int prev = 0;

     //        for(int i = 0 ; i < n ; i++){
     //           int s = sc.nextInt();
     //           int e = sc.nextInt();
     //           if(s > prev){
     //                System.out.println("NO");
     //                return;
     //           }
     //            prev = Math.max(prev,e);
     //        }
     //        if(prev == m)
     //            System.out.println("YES");
     //        else
     //            System.out.println("NO");

     //        // System.out.println(sb);
     //    }
        
        
     // }

     //--------------->>>>IF YOU ARE HERE FOR QUICKSORT HACK THEN SORRY NO HACK FOR YOU<<<-------------------

     public static void solve(){


        long a = 1;
        long b = d;
        long count = 0;
        sb = new StringBuilder();
        sb1 = new StringBuilder();
        sb1.append("1 2 ");
        if(d == 3){
            System.out.println(0);
            System.out.println("2 1 2");
            return;
        }
        long diff = 0;

        while((b-a+1)%2 == 0 && (b-a+1) > 0){
            if((b-a+1) >= 4){
                sb.append(a +" " + (b) +" ");
                a += 2;
                b -= 2;
                count += 2;
            }
            else{
                sb.append(a);
                a += 1;
                b -= 1;
                diff = 1;
                count += 1;
            }
            if((b-a+1) <= 0){
                 System.out.println(diff);
                System.out.println(count +" " +sb);
                return;
            }
        }

        a = 4;
        count = 2;
        while((b-a+1) > 0){
            if((b-a+1) >= 4){
                sb1.append(a +" " + (b) +" ");
                a += 2;
                b -= 2;
                count += 2;
            }
            else{
                sb1.append(a);
                a += 1;
                b -= 1;
                diff = 1;
                count += 1;
            }
            if((b-a+1) <= 0){
                 System.out.println(diff);
                System.out.println(count +" " +sb1);
                return;
            }
        }

     }

     public static void main(String[] args) {

            sc = new FastScanner();
            // Scanner sc = new Scanner(System.in);
            // int t = sc.nextInt();
            int t = 1;
            // int l = 1;
            while(t > 0){
                
                // n = sc.nextInt();
                // n = sc.nextLong();
                // a = sc.nextLong();
                // b = sc.nextLong();
                // c = sc.nextLong();
                d = sc.nextLong();

                // x = sc.nextLong();
                // y = sc.nextLong();
                
                // n = sc.nextLong();
                // n = sc.nextInt();
                // n1 = sc.nextInt();

                // m = sc.nextInt();
                // q = sc.nextInt();

                // k = sc.nextLong();
                // s = sc.next();

                // ch = sc.next().toCharArray();
                // ch1 = sc.next().toCharArray();

                // arr = new int[n];
                // for(int i = 0 ; i < n ; i++){
                //     arr[i] = sc.nextInt();
                // }
                // ch = sc.next().toCharArray();
                // m = n;
                // darr = new long[m];
                // for(int i = 0 ; i < m ; i++){
                //     darr[i] = sc.nextLong();
                // }

                // farr = new int[n];
                // for(int i = 0; i < n ; i++){
                //     farr[i] = sc.nextInt();
                // }

                // mat = new int[n][n];
                // for(int i = 0 ; i < n ; i++){
                //     for(int j = 0 ;  j < n ; j++){
                //         mat[i][j] = sc.nextInt();
                //     }
                // }

                // mat = new char[n][m];
                // for(int i = 0 ; i < n ; i++){
                //     String s = sc.next();
                //     for(int j = 0 ; j < m ; j++){
                //         mat[i][j] = s.charAt(j);
                //     }
                // }

                // str = new String[n];
                // for(int i = 0 ; i < n ; i++)
                //     str[i] = sc.next();

                // nodes = new Node[n];
                // for(int i = 0 ; i < n ;i++)
                //     nodes[i] = new Node(sc.nextInt(),sc.nextInt());

                // System.out.println(solve()?"YES":"NO");
                 solve();       
                 // System.out.println(solve());
                 t -= 1;
            }

     }

    public static int log(long n,long base){

         if(n == 0 || n == 1)
             return 0;

         if(n == base)
             return 1;

         double num = Math.log(n);
         double den = Math.log(base);

         if(den == 0)
             return 0;

         return (int)(num/den);
     }

    public static boolean isPrime(long n) { 
    // Corner cases 
        if (n <= 1)  
            return false; 

        if (n <= 3)  
            return true; 
      
        // This is checked so that we can skip  
        // middle five numbers in below loop 
        if (n%2 == 0 || n%3 == 0) 
            return false; 
      
        for (int i=5; i*i<=n; i=i+6) 
            if (n%i == 0 || n%(i+2) == 0) 
               return false; 
      
        return true; 
    } 

     public static long gcd(long a,long b){

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

     }

     // public static void swap(int i,int j){
     //     long temp = arr[j];
     //     arr[j] = arr[i];
     //     arr[i] = temp;
     // } 

    static final Random random=new Random();
    
    static void ruffleSort(long[] a) {
        int n=a.length;//shuffle, then sort 
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n);
            long temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }

    static class Node{
        Integer first;
        Integer second;
        Node(Integer f,Integer s){
            this.first = f;
            this.second = s;
        }
    }

     static class FastScanner {

                BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
                StringTokenizer st=new StringTokenizer("");
                String next() {
                        while (!st.hasMoreTokens())
                                try {
                                        st=new StringTokenizer(br.readLine());
                                } catch (IOException e) {
                                        e.printStackTrace();
                                }
                        return st.nextToken();
                }
                
                int nextInt() {
                        return Integer.parseInt(next());
                }
                int[] readArray(int n) {
                        int[] a=new int[n];
                        for (int i=0; i<n; i++) a[i]=nextInt();
                        return a;
                }
                long nextLong() {
                        return Long.parseLong(next());
                }
        }

}