Problem: You are given an equation: 

Ax2 + Bx + C = 0. 

Your task is to find the number of distinct roots of the equation and print all of them in ascending order.

Input

The first line contains three integer numbers A, B and C ( - 105 ≤ A, B, C ≤ 105). Any coefficient may be equal to 0.

Output

In case of infinite root count print the only integer -1. In case of no roots print the only integer 0. In other cases print the number of root on the first line and the roots on the following lines in the ascending order. Print roots with at least 5 digits after the decimal point.

Examples

Input

1 -5 6


Output

2
2.0000000000
3.0000000000

Solution (in JAVA):

Solution:
import java.util.*;
import java.text.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public*/
public class Equation
{
    static 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;
        }
    }
    
    static class Node {
        
        long pp;
        long a, b;
        
        Node(long x, long y) {
            a = x;
            b = y;
            pp = a * b;
        }
    }
    static class Comp implements Comparator<Node> {
        
        public int compare(Node o1, Node o2) {
            if (o1.pp > o2.pp) {
                return 1;
            } else {
                return -1;
            }
        }
    }
    public static void main(String[] args) {
        FastReader sc=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        DecimalFormat ft=new DecimalFormat("#.########");
        //your code starts here
        int a=sc.nextInt();
        int b=sc.nextInt();
        int c=sc.nextInt();
        int ans=-69; double roots[]=new double[2];
        if(a==0 && b==0 && c==0) ans=-1; //infinite roots
        else if(a==0 && b==0 && c!=0) ans=0; //no roots satisfy
        else if(a==0 && b!=0 && c==0) 
        {
            out.println("1 \n0.0000000000"); out.close();return;
        }
        else if(a==0 && b!=0 && c!=0){
            double res=(-1)*((double)c/(double)b); out.println("1 \n"+String.format("%.8f", res)); out.close(); return;
        }
        else{
            long D=(long)b*b-4*(long)a*c;
            if(D<0) ans=0;
            else{
                roots[0]=(-(double)b+Math.sqrt(D))/(2.0*(double)a);
                roots[1]=(-(double)b-Math.sqrt(D))/(2.0*(double)a);
                Arrays.sort(roots);
                if(D==0) //equal roots
                {
                    out.println("1 \n"+String.format("%.8f",roots[0])); out.close(); return;
                }
            }
        }
        if(ans==-69) //both roots present
        {
            out.println("2");
            out.println(String.format("%.8f",roots[0]));
            out.println(String.format("%.8f", roots[1]));
        }
        else out.println(ans);
        out.close();
    }
}