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.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Locale;
import java.util.StringTokenizer;

public class Main {

    public static void main(String[] args) throws Exception {
        //System.setIn(new FileInputStream("1"));
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);

        solve();

        in.close();
        out.close();
    }

    private static void solve() throws Exception {
        double A = nextDouble(), B = nextDouble(), C = nextDouble();
        if (eq(A, 0.0)) {
            if (eq(B, 0.0)) {
                if (eq(C, 0.0)) {
                    out.println("-1");
                } else {
                    out.println("0");
                }
                return;
            } else {
                double x = -C / B;
                out.println("1");
                out.format(Locale.US, "%.10f", x);
                return;
            }
        } else {
            double D = B * B - 4.0 * A * C;
            if (eq(D, 0.0)) {
                out.println("1");
                double x = -B / (2.0 * A);
                out.format(Locale.US, "%.10f", x);
                return;
            } else if (D > 0.0) {
                out.println("2");
                double x1 = (-B + Math.sqrt(D)) / (2.0 * A);
                double x2 = (-B - Math.sqrt(D)) / (2.0 * A);
                out.format(Locale.US, "%.10f\n%.10f", Math.min(x1, x2), Math.max(x1, x2));
                return;
            } else {
                out.println("0");
            }
        }
    }

    private static boolean eq(double a, double d) {
        return Math.abs(a - d) < 1.0E-8;
    }

    static StringTokenizer st;
    static BufferedReader in;
    static PrintWriter out;

    static int nextInt() throws IOException {
        return Integer.parseInt(nextString());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(nextString());
    }

    static String nextString() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }
}