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.math.BigInteger;
import java.util.*;

public class Main {

    public static void main(String[] args) throws IOException {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(in, out);
        out.close();
    }

    private static class TaskB {

        static final double eps = 0.000001;

        void solve(InputReader in, PrintWriter out) throws IOException {

            double a = in.nextDouble();
            double b = in.nextDouble();
            double c = in.nextDouble();

            double d = b * b - 4 * a * c;

            if (a == 0 && b == 0 && c == 0)
                System.out.println(-1);
            else if (a == 0 && b == 0)
                System.out.println(0);
            else if (a == 0) {
                System.out.println(1);
                System.out.printf("%.6f\n", (-c) / b);
            } else if (d < 0)
                System.out.println(0);
            else if (d == 0) {
                System.out.println(1);
                double x1 = (-b + Math.sqrt(d)) / (2 * a);
                System.out.printf("%.6f\n", x1);
            } else {
                System.out.println(2);
                double x1 = (-b + Math.sqrt(d)) / (2 * a);
                double x2 = (-b - Math.sqrt(d)) / (2 * a);
                if (x1 < x2)
                    System.out.printf("%.6f\n%.6f\n", x1, x2);
                else System.out.printf("%.6f\n%.6f\n", x2, x1);
            }


        }

        static double segment(double x1, double y1, double x2, double y2) {
            return Math.sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
        }

        static long gcd(long a, long b) {
            if (b == 0) return a;
            return gcd(b, a % b);
        }

        static long lcm(long a, long b) {
            return (a * b) / gcd(a, b);
        }

    }

    private static class InputReader {
        StringTokenizer st;
        BufferedReader br;

        public InputReader(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public InputReader(FileReader s) throws FileNotFoundException {
            br = new BufferedReader(s);
        }

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

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

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

        public String nextLine() {
            try {
                return br.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public boolean ready() {
            try {
                return br.ready();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
    }
}