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 Main implements Runnable {

	public void _main() throws IOException {
		double a = nextDouble();
		double b = nextDouble();
		double c = nextDouble();
		Locale.setDefault(Locale.UK);
		if (a == 0) {
			if (b == 0) {
				if (c == 0)
					out.print(-1);
				else
					out.print(0);
				return;
			}
			out.println(1);
			out.printf("%.5f", -c / b);
			return;
		}
		double d = b * b - 4 * a * c;
		if (d < 0) {
			out.println(0);
			return;
		}				
		double x1 = (-b - Math.sqrt(d)) / (2 * a);
		double x2 = (-b + Math.sqrt(d)) / (2 * a);
		if (Math.abs(x1 - x2) < 1e-9) {
			out.println(1);
			out.printf("%.5f", x1);
		}
		else {
			out.println(2);
			out.printf("%.5f\n", Math.min(x1, x2));
			out.printf("%.5f\n", Math.max(x1, x2));
		}
	}

	private BufferedReader in;
	private PrintWriter out;
	private StringTokenizer st;

	private String next() throws IOException {
		while (st == null || !st.hasMoreTokens()) {
			String rl = in.readLine();
			if (rl == null)
				return null;
			st = new StringTokenizer(rl);
		}
		return st.nextToken();
	}

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

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

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

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

	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);

			_main();

			out.close();
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(202);
		}
	}

}