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.util.*;
import java.io.*;

public class B0020 {

    public static void main(String args[]) throws Exception {
        new B0020();
    }

    B0020() throws Exception {
        PandaScanner sc = null;
        PrintWriter out = null;
        try {
            sc = new PandaScanner(System.in);
            out = new PrintWriter(System.out);
        } catch (Exception ignored) {
        }

        long a = sc.nextInt();
        long b = sc.nextInt();
        long c = sc.nextInt();

        //Quadratic case
        if (a != 0) {
            long determinent = b * b - 4 * a * c;
            if (determinent < 0) {
                out.println(0);
            }
            else if (determinent == 0) {
                out.println(1);
                out.println(-b / (2.0 * a));
            }
            else {
                double d = Math.sqrt(determinent);
                double[] ans = new double[] {(-b - d) / (2.0 * a), (-b + d) / (2.0 * a)};
                Arrays.sort(ans);

                out.println(2);
                out.println(ans[0]);
                out.println(ans[1]);
            }
        }
        //Non-horizontal linear case
        else if (b != 0) {
            out.println(1);
            out.println((-1.0 * c) / (double) (b));
        }
        //Horizontal linear case
        else {
            if (c == 0) {
                out.println(-1);
            }
            else {
                out.println(0);
            }
        }

        out.close();
        System.exit(0);
    }


    //The PandaScanner class, for Panda fast scanning!
    public class PandaScanner {
        BufferedReader br;
        StringTokenizer st;
        InputStream in;

        PandaScanner(InputStream in) throws Exception {
            br = new BufferedReader(new InputStreamReader(this.in = in));
        }

        public String next() throws Exception {
            if (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(br.readLine().trim());
                return next();
            }
            return st.nextToken();
        }

        public boolean hasNext() throws Exception {
            return (st != null && st.hasMoreTokens()) || in.available() > 0;
        }

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

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