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.awt.geom.Point2D;
import java.text.*;
import java.math.*;
import java.util.*;

public class Main implements Runnable {

    final String filename = "";

    public void solve() throws Exception {
        DecimalFormat df = new DecimalFormat("0.00000000");
        long A = iread(), B = iread(), C = iread();
        if (A == 0) {
            if (B == 0) {
                if (C == 0) {
                    out.write("-1\n");
                    return;
                } else {
                    out.write("0\n");
                    return;
                }
            } else {
                double ans = -C * 1.0 / B;
                out.write("1\n");
                out.write(df.format(ans) + "\n");
                return;
            }
        } else {
            long D = B * B - 4 * A * C;
            if (D < 0) {
                out.write("0\n");
                return;
            } else if (D == 0) {
                double ans = -B * 0.5 / A;
                out.write("1\n");
                out.write(df.format(ans) + "\n");
                return;
            } else {
                double ans1 = (-B - Math.sqrt(D*1.0)) * 0.5 / A;
                double ans2 = (-B + Math.sqrt(D*1.0)) * 0.5 / A;
                if (ans1 > ans2) {
                    double t = ans1;
                    ans1 = ans2;
                    ans2 = t;
                }
                out.write("2\n");
                out.write(df.format(ans1)+"\n");
                out.write(df.format(ans2)+"\n");
            }
        }
    }

    public void run() {
        try {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new BufferedWriter(new OutputStreamWriter(System.out));
            // in = new BufferedReader(new FileReader(filename+".in"));
            // out = new BufferedWriter(new FileWriter(filename+".out"));
            solve();
            out.flush();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    public int iread() throws Exception {
        return Integer.parseInt(readword());
    }

    public double dread() throws Exception {
        return Double.parseDouble(readword());
    }

    public long lread() throws Exception {
        return Long.parseLong(readword());
    }

    BufferedReader in;

    BufferedWriter out;

    public String readword() throws IOException {
        StringBuilder b = new StringBuilder();
        int c;
        c = in.read();
        while (c >= 0 && c <= ' ')
            c = in.read();
        if (c < 0)
            return "";
        while (c > ' ') {
            b.append((char) c);
            c = in.read();
        }
        return b.toString();
    }

    public static void main(String[] args) {
        try {
            Locale.setDefault(Locale.US);
        } catch (Exception e) {

        }
        new Thread(new Main()).start();
        // new Thread(null, new Main(), "1", 1<<25).start();
    }
}