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:
/**
 * Created by ankeet on 7/5/16.
 */
import java.io.*;
import java.util.*;
import java.math.*;

public class B20 {

    public static BufferedReader read = null;
    public static PrintWriter out = null;
    public static StringTokenizer token = null;


    public static void solve()
    {
        long a = nlong(), b = nlong(), c = nlong();

        if(a==0 && b == 0 && c == 0)
        {
            out.println(-1);
        }
        else if(a == 0 )
        {
            if(b == 0 && c != 0)
            {
                out.println(0);
            }
            else
            {
                out.println(1);
                out.printf("%.5f", (-1.0*c)/b);
            }
        }
        else
        {
            if(b*b-4*a*c < 0)
            {
                out.println(0);
            }
            else if(b*b-4*a*c == 0)
            {
                out.println(1);
                out.printf("%.5f", (-1.0*b)/(2.0*a));
            }
            else
            {
                out.println(2);
                double r1 = (-b+Math.sqrt(b*b-4*a*c))/(2.0*a);
                double r2 = (-b-Math.sqrt(b*b-4*a*c))/(2.0*a);
                if(r1 > r2) out.printf("%.5f\n%.5f", r2,r1);
                else out.printf("%.5f\n%.5f", r1,r2);
            }
        }

    }

    public static void main(String[] args)
    {
        read = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.flush();
        out.close();

    }

    // i/o functions
    public static String next() // returns the next string
    {
        while(token == null || !token.hasMoreTokens())
        {
            try {
                token = new StringTokenizer(read.readLine());
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }
        return token.nextToken();
    }

    public static int nint()
    {
        return Integer.parseInt(next());
    }
    public static long nlong()
    {
        return Long.parseLong(next());
    }
    public static double ndouble()
    {
        return Double.parseDouble(next());
    }
    public static int[] narr(int n)
    {
        int[] a = new int[n];
        for(int i=0; i<n; i++) a[i] = nint();
        return a;
    }

    public static long[] nal(int n)
    {
        long[] a = new long[n];
        for(int i=0; i<n; i++) a[i] = nlong();
        return a;
    }


}