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:
/*
 * Author: SKYDOS
 * E-mail: ACSKYDOS@gmail.com
 * SKYPE: sky-dos
 */
import java.io.BufferedReader;
import java.io.PrintWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.FileInputStream;
import java.io.FileOutputStream;
import java.util.*;
import java.math.*;
import static java.lang.Math.*;
import java.awt.geom.*;
import static java.lang.Integer.*;
import static java.lang.Long.*;
import static java.lang.Double.*;

public class Main implements Runnable {
    void solve(){
        console(!false);

        long a=Long(), b=Long(), c=Long();

        if(a==0 && b==0 && c==0){
				out.println(-1);
			} else if(a==0 && b==0){
				out.print(0);
			} else if(a==0){
				double x=-(double)c/b;
				out.println(1);
				if (c==0) out.printf("%.10f", 0.0);
				else out.printf("%.10f", x);
			} else {
				long d=b*b-4*a*c;
				if(d<0){
					print(0);
				} else if(d==0){
					println(1);
					if (b==0) out.printf("%.10f", 0.0); else
					out.printf("%.10f", -(double)b/(2*(double)a));
				} else {
					double x1=(-(double)b-sqrt((double)d))/(2*(double)a);
					double x2=(-(double)b+sqrt((double)d))/(2*(double)a);
					println(2);
					out.printf("%.10f\n", min(x1, x2));
					out.printf("%.10f", max(x1, x2));
				}
			}
    }

    StringTokenizer st;
    PrintWriter out;
    BufferedReader br;
    boolean eof = false, in_out = false, std = false;

    public static void main(String[] args) {
        new Thread(new Main()).start();
    }

    void println(Object o){ out.println(o); }
    void print(Object o){ out.print(o); }

    String nextToken() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                eof = true;
                return "$";
            }
        }
        return st.nextToken();
    }

    String Line() {
        String ret = "";
        try {
            ret = br.readLine();
        } catch (Exception e) {
            ret = "";
        }
        if (ret == null) {
            eof = true;
            return "$";
        }
        return ret;
    }

    String String() {
        return nextToken();
    }

    int Int() {
        return Integer.parseInt(nextToken());
    }

    long Long() {
        return Long.parseLong(nextToken());
    }

    double Double() {
        return Double.parseDouble(nextToken());
    }

    void console(boolean f){
        if (f){
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(new OutputStreamWriter(System.out));
        } else {
            try{
                br = new BufferedReader(new InputStreamReader(new FileInputStream("input.txt"), "ISO-8859-1"));
                out = new PrintWriter(new OutputStreamWriter(new FileOutputStream("output.txt"), "ISO-8859-1"));
            } catch(Exception e){
                e.printStackTrace();
                System.exit(111);
            }
        }
    }

    public void run() {
        long time = System.currentTimeMillis();
        try{
            solve();
        } catch (Exception e){
            e.printStackTrace();
            System.exit(111);
        }
        System.err.println(System.currentTimeMillis() - time);
        out.close();
    }
}