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.*;

/**
 * @author Tran Anh Tai
 * @template for CP codes
 * What a trick prob!
 */
public class ProbA {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }
    // main solver
    static class Task{
        public void solve(InputReader in, PrintWriter out) {
            int a = in.nextInt();
            int b = in.nextInt();
            int c = in.nextInt();
            long delta = (long)b * b - (long)4 * a * c;
            if (delta < 0){
                out.println(0);
            }
            else if (a == 0 || delta == 0) {
                if (a == 0){
                    if (b == 0) {
                        out.println((c == 0) ? -1 : 0);
                    }
                    else {
                        out.println(1);
                        out.println((double)(-c) / b);
                    }
                }
                else{
                    out.println(1);
                    double x = (double)(-b) / (a << 1);
                    out.println(x);
                }
            }
            else{
                double x1 = (-b - Math.sqrt(delta)) / (a << 1);
                double x2 = (-b + Math.sqrt(delta)) / (a << 1);
                out.println(2);
                out.println(Math.min(x1, x2));
                out.println(Math.max(x1, x2));
            }
        }
    }
    // fast input reader class;
    static class InputReader {
        BufferedReader br;
        StringTokenizer st;

        public InputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream));
        }

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

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }
        public double nextDouble(){
            return Double.parseDouble(nextToken());
        }
        public long nextLong(){
            return Long.parseLong(nextToken());
        }
    }
}