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.*;

public class equation {
	static BufferedReader br;
	static StringTokenizer st;
	static PrintWriter out;
	public static boolean isquadratic(int a, int b, int c)	{
		if (a != 0)
			return true;
		return false;
		}
	public static long determinant(int a, int b, int c)	{
		return (long)(b)*(long)(b)-4*(long)(a)*(long)(c);
		}
	public static boolean islinear(int a, int b, int c)	{
		if (a == 0 && b != 0)
			return true;
		return false;
		}
	public static void main(String[] args) throws IOException {
		InputStream input = System.in;
		//InputStream input = new FileInputStream("fileIn.in");
		OutputStream output = System.out;
		//OutputStream output = new FileOutputStream("fileOut.out");
		br = new BufferedReader(new InputStreamReader(input));
		out = new PrintWriter(output);
		StringTokenizer st = new StringTokenizer(br.readLine());
		int a = Integer.parseInt(st.nextToken());
		int b = Integer.parseInt(st.nextToken());
		int c = Integer.parseInt(st.nextToken());
		if (isquadratic(a,b,c))
			{
			if (determinant(a,b,c) > 0)
				{
				out.println(2);
				if (a > 0)
					{
					out.println((-b-Math.sqrt(determinant(a,b,c)))/(2*a));
					out.println((-b+Math.sqrt(determinant(a,b,c)))/(2*a));
					}
				if (a < 0)
					{
					out.println((-b+Math.sqrt(determinant(a,b,c)))/(2*a));
					out.println((-b-Math.sqrt(determinant(a,b,c)))/(2*a));
					}
				}
			if (determinant(a,b,c) == 0)
				{
				out.println(1);
				out.println((float)(-b)/(2*a));
				}
			if (determinant(a,b,c) < 0)
				out.println(0);
			}
		else if (islinear(a,b,c))
			{
			out.println(1);
			out.println((float)(-c)/b);
			}
		else
			{
			if (c == 0)
				out.println(-1);
			else
				out.println(0);
			}
		out.close();
	}
}