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.*;

public class Main {
    public static void main(String[] args) throws IOException {
        InputStream inputStream = System.in;
//        InputStream inputStream = new FileInputStream("sum.in");
        OutputStream outputStream = System.out;
//        OutputStream outputStream = new FileOutputStream("sum.out");


//        Path path = Paths.get(URI.create("file:///foo/bar/Main.java"));
//        System.out.print(path.getName(200));

//        Path p = Paths.get("/foo/bar/Main.java");
//        for (Path e : p) {
//            System.out.println(e);
//        }

        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Answer solver = new Answer();
        solver.solve(in, out);
        out.close();
    }
}

class Answer {
    private final int INF = (int) (1e9 + 7);
    private final int MOD = (int) (1e9 + 7);
    private final int MOD1 = (int) (1e6 + 3);
    private final long INF_LONG = (long) (1e18 + 1);
    private final double EPS = 1e-9;


    public void solve(InputReader in, PrintWriter out) throws IOException {
        int a = in.nextInt();
        int b = in.nextInt();
        int c = in.nextInt();

        if (a == 0 && b == 0 && c == 0) {
            out.print("-1");
            return;
        }

        int k = 0;
        double x1 = Double.MAX_VALUE;
        double x2 = Double.MAX_VALUE;

        if (a == 0) {
            if (b != 0) {
                k = 1;
                x1 = (-1d * c) / b;
            }
        } else {
            double d = 1L * b * b - 4L * a * c;
            if (1L * b * b - 4L * a * c == 0) {
                k = 1;
                x1 = (-1d * b) / (2 * a);
            } else if (1L * b * b - 4L * a * c > 0) {
                k = 2;
                x1 = (-b + Math.sqrt(d)) / (2 * a);
                x2 = (-b - Math.sqrt(d)) / (2 * a);
                double min = Math.min(x1, x2);
                double max = Math.max(x1, x2);

                x1 = min;
                x2 = max;
            }
        }

        out.println(k);
        if (k == 1) {
            out.println(x1);
        } else if (k == 2) {
            out.println(x1);
            out.println(x2);
        }

    }
}

class InputReader {
    private BufferedReader reader;
    private StringTokenizer tokenizer;

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

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

    public int[] nextArrayInt(int count) {
        int[] a = new int[count];
        for (int i = 0; i < count; i++) {
            a[i] = nextInt();
        }
        return a;
    }

    public long[] nextArrayLong(int count) {
        long[] a = new long[count];
        for (int i = 0; i < count; i++) {
            a[i] = nextLong();
        }
        return a;
    }
}