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.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */
/**
 *
 * @author pttrung
 */
public class B {

    public static void main(String[] args) {
        Scanner in = new Scanner();
        PrintWriter out = new PrintWriter(System.out);
        double A = in.nextInt();
        double B = in.nextInt();
        double C = in.nextInt();
        if (A != 0) {
            double delta = B * B - (4 * A * C);
            if (delta < 0) {
                out.println(0);
            } else {
                double first = (-B + Math.sqrt(delta)) / (2 * A);
                double second = (-B - Math.sqrt(delta)) / (2 * A);
                if (first == second) {
                    out.println(1);
                    out.println(first);
                } else {
                    out.println(2);
                    out.printf("%.5f\n", first > second ? second : first);

                    out.printf("%.5f", first > second ? first : second);
                }
            }
        } else if (B != 0) {
            out.println(1);
            out.printf("%.5f", (double) -C / B);
        } else {
            if (C != 0) {
                out.println(0);
            }else {
                out.println(-1);
            }
        }
        out.close();
    }

    public static int countTwo(int val) {
        int result = 0;
        while (val > 0 && val % 2 == 0) {
            val /= 2;
            result++;
        }
        return result;
    }

    public static int countFive(int val) {
        int result = 0;
        while (val > 0 && val % 5 == 0) {
            val /= 5;
            result++;
        }
        return result;
    }

    public static long count(long two, long five) {
        return Math.min(two, five);
    }

    public double pow(double a, int b) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        double val = pow(a, b / 2);
        if (b % 2 == 0) {
            return val * val;
        } else {
            return val * val * a;
        }
    }

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

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

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public String next() {

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

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

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

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

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}