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

public class Main 
{
    public static void main ( String[] args ) throws IOException
    {
        Scanner in = new Scanner(System.in);
        BufferedReader Reader = new BufferedReader(new InputStreamReader(System.in));
        FastScanner sc = new FastScanner(Reader);
        double A = in.nextDouble(), B = in.nextDouble(), C = in.nextDouble();
        if (A != 0 && B != 0 && C != 0)
        {
            double D = B * B - 4 * A *C;
            if (D > 0)
            {
                double x1 = (-B - Math.sqrt(D)) / (2 * A), x2 = (-B + Math.sqrt(D)) / (2 * A);
                System.out.printf("2\n%.10f\n%.10f", Math.min(x1, x2), Math.max(x1,  x2));
            }
            if (D == 0)
                System.out.printf("1\n%.10f", -B / (2 * A));
            if (D < 0)
                System.out.print(0);
        }
        if (A == 0 && B != 0 && C != 0)
            System.out.printf("1\n%.10f", -C / B);
        if (A != 0 && B == 0 && C != 0)
            if (C <= 0)
                System.out.printf("2\n%.10f %.10f", -Math.sqrt(-C / A), Math.sqrt(-C / A));
            else
                System.out.print(0);
        if (A != 0 && B != 0 && C ==0)
        {
            double x1 = 0, x2 = -B / A;
            System.out.printf("2\n%.10f %.10f", Math.min(x1, x2), Math.max(x1,  x2));
        }
        if (A == 0 && B == 0 && C != 0)
            System.out.print(0);
        if (A == 0 && B != 0 && C == 0 || A != 0 && B ==0 && C == 0)
            System.out.printf("1\n0");
        if (A == 0 && B == 0 && C == 0)
            System.out.print(-1);
        System.out.close();
    }
}

class FastScanner
{
    private BufferedReader Reader;
    private StringTokenizer Tokenizer;
    public FastScanner (BufferedReader Reader)
    {
        this.Reader = Reader;
    }
    public String nextToken() throws IOException
    {
        while (Tokenizer == null || !Tokenizer.hasMoreTokens())
            Tokenizer = new StringTokenizer(Reader.readLine());
        return Tokenizer.nextToken();
    }
    public int nextInt() throws NumberFormatException, IOException
    {
        return Integer.parseInt(nextToken());
    }
    public long nextLong() throws NumberFormatException, IOException
    {
        return Long.parseLong(nextToken());
    }
    public double nextDouble() throws NumberFormatException, IOException
    {
        return Double.parseDouble(nextToken());
    }
}