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 static java.util.Arrays.*;
import static java.lang.Math.*;
import static java.math.BigInteger.*;
import java.util.*;
import java.math.*;
import java.io.*;

public class B implements Runnable
{
    String file = "input";
    
    void init() throws IOException
    {
        //input = new BufferedReader(new FileReader(file + ".in"));
        input = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(new BufferedWriter(new FileWriter(file + ".out")));
    }
    double EPS = 1e-9;
    void solve() throws IOException
    {
        long A = nextInt(), B = nextInt(), C = nextInt();
        if(A == 0)
        {
            if(B == 0)
            {
                if(C == 0) System.out.println(-1);
                else System.out.println(0);
            }
            else
            {
                System.out.println(1);
                System.out.printf("%.5f", -1. * C / B);
            }
        }
        else
        {
            long delta = B * B - 4 * A * C;
            if(delta >= 0)
            {
                if(delta == 0)
                {
                    double x = - B / 2. / A;
                    System.out.println(1);
                    System.out.printf("%.5f", x);
                }
                else
                {
                    double x1 = (- B - sqrt(delta)) / 2. / A;
                    double x2 = (- B + sqrt(delta)) / 2. / A;
                    System.out.println(2);
                    if(A < 0)
                    {
                        double t = x1;
                        x1 = x2;
                        x2 = t;
                    }
                    System.out.printf("%.5f\n%.5f", x1, x2);
                }
            }
            else
                System.out.println(0);
        }
    }
    
    String next() throws IOException
    {
        if(st == null || !st.hasMoreTokens()) st = new StringTokenizer(input.readLine());
        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());
    }
    
    void print(Object... o)
    {
        System.out.println(deepToString(o));
    }
    
    void gcj(Object o)
    {
        String s = String.valueOf(o);
        out.println("Case #" + test + ": " + s);
        System.out.println("Case #" + test + ": " + s);
    }
    
    BufferedReader input;
    PrintWriter out;
    StringTokenizer st;
    int test;
    
    public static void main(String[] args) throws IOException
    {
        new Thread(null, new B(), "", 1 << 20).start();
    }
    
    public void run()
    {
        try
        {
            init();
            solve();
            out.close();        
        }
        catch(Exception e)
        {
            e.printStackTrace();
            System.exit(1);
        }
    }
}