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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

		int A = sc.nextInt(), B = sc.nextInt(), C = sc.nextInt();
		if(A == 0 && B == 0)
			out.println(C == 0 ? -1 : 0);
		else if(A == 0)
		{
			out.println(1);
			out.printf("%.5f\n", 1.0 * -C / B);
		}
		else
		{
			long dis = 1l * B * B - 4l * A * C;
			if(dis < 0)
				out.println(0);
			else if(dis == 0)
			{
				out.println(1);
				out.printf("%.5f\n", -B / (2.0 * A));
			}
			else
			{
				out.println(2);
				if(A > 0)
				{
					out.printf("%.5f\n", (-B - Math.sqrt(dis)) / (2.0 * A));
					out.printf("%.5f\n", (-B + Math.sqrt(dis)) / (2.0 * A));
				}
				else
				{
					out.printf("%.5f\n", (-B + Math.sqrt(dis)) / (2.0 * A));
					out.printf("%.5f\n", (-B - Math.sqrt(dis)) / (2.0 * A));
				}
			}
			
		}
		out.flush();
		out.close();
	}

	static class Scanner 
	{
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}

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

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

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

		public String nextLine() throws IOException {return br.readLine();}

		public double nextDouble() throws IOException { return Double.parseDouble(next()); }

		public boolean ready() throws IOException {return br.ready();} 
	}
}