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.BufferedReader;
import java.io.Closeable;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.text.DecimalFormat;
import java.text.NumberFormat;
import java.util.StringTokenizer;

public class Equation implements Closeable {

    private InputReader in = new InputReader(System.in);
    private PrintWriter out = new PrintWriter(System.out);
    
    void format(double d) {
        out.println(String.format("%.12f", d));
    }
    
    public void solve() {
        long a = in.nl(), b = in.nl(), c = in.nl();
        if (a == 0) {
            if (b == 0) {
                if (c == 0) {
                    out.println(-1);
                } else {
                    out.println(0);
                }
            } else {
                out.println(1);
                format((double) -c / b);
            }
        } else {
            if (b == 0) {
                if (c > 0) {
                    out.println(0);
                } else if (c == 0) {
                    out.println(1);
                    format(0);
                } else {
                    out.println(2);
                    double root = Math.sqrt((double) c / a);
                    format(root);
                    format(-root);
                }
            } else {
                long d = b * b - 4 * a * c;
                if (d < 0) {
                    out.println(0);   
                } else if (d == 0) {
                    out.println(1);
                    format((double) -b / (2 * a));
                } else {
                    double sqrt = Math.sqrt(d);
                    double first = (-b - sqrt) / (2 * a);
                    double second = (-b + sqrt) / (2 * a);
                    out.println(2);
                    format(Math.min(first, second));
                    format(Math.max(first, second));
                }
            }
        }
    }

    @Override
    public void close() throws IOException {
        in.close();
        out.close();
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int ni() {
            return Integer.parseInt(next());
        }

        public long nl() {
            return Long.parseLong(next());
        }

        public void close() throws IOException {
            reader.close();
        }
    }

    public static void main(String[] args) throws IOException {
        try (Equation instance = new Equation()) {
            instance.solve();
        }
    }
}