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.*;
import static java.lang.Math.*;

public class AlphaRound20_B implements Runnable {

	final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
	BufferedReader in;
	PrintWriter out;
	StringTokenizer tok = new StringTokenizer("");

	void init() throws IOException {
		if (ONLINE_JUDGE) {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
		} else {
			in = new BufferedReader(new FileReader("input.txt"));
			out = new PrintWriter("output.txt");
		}
	}

	String readString() throws IOException {
		while (!tok.hasMoreTokens()) {
			tok = new StringTokenizer(in.readLine());
		}
		return tok.nextToken();
	}

	int readInt() throws IOException {
		return Integer.parseInt(readString());
	}

	@Override
	public void run() {
		try {
			long t1 = System.currentTimeMillis();
			init();
			solve();
			out.close();
			long t2 = System.currentTimeMillis();
			System.err.println("Time = " + (t2 - t1));
		} catch (Exception e) {
			e.printStackTrace(System.err);
			System.exit(-1);
		}
	}

	public static void main(String[] args) {
		new Thread(new AlphaRound20_B()).start();
	}

	void solve() throws IOException {
		Locale.setDefault(Locale.US);
		double a = readInt();
		double b = readInt();
		double c = readInt();
		if (a == 0 && b == 0 && c == 0) {
			out.print(-1);
			return;
		}
		if (a == 0 && b == 0 && c != 0) {
			out.print(0);
			return;
		}
		if (a == 0) {
			double ans = -c / b;
			out.printf("1\n%.12f", ans);
		} else {
			double d = b*b - 4*a*c;
			if (d < 0) {
				out.print(0);
				return;
			}
			if (d == 0) {
				double ans = -b / (2*a);
				out.printf("1\n%.12f", ans);
				return;
			}
			double ans1 = (-b - sqrt(d)) / (2*a);
			double ans2 = (-b + sqrt(d)) / (2*a);
			if (ans1 > ans2) {
				double t = ans1;
				ans1 = ans2;
				ans2 = t;
			}
			out.printf("2\n%.12f\n%.12f", ans1, ans2);
		}
	}
	
}