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:
//package round20;


import java.io.BufferedOutputStream;
import java.io.PrintStream;
import java.io.PrintWriter;
import java.io.StringReader;
import java.util.Arrays;
import java.util.Scanner;

public class A {
	private Scanner in;
	private PrintWriter out;
	
	public void solve()
	{
		double a = ni();
		int ai = (int)a;
		double b = ni();
		int bi = (int)b;
		double c = ni();
		int ci = (int)c;
		if(a != 0){
			double d = b * b - 4 * a * c;
			int di = bi * bi - 4 * ai * ci;
			if(di > 0){
				out.println(2);
				if(ai > 0){
					out.printf("%1.6f\n", (-b - Math.sqrt(d)) / (2 * a));
					out.printf("%1.6f\n", (-b + Math.sqrt(d)) / (2 * a));
				}else{
					out.printf("%1.6f\n", (-b + Math.sqrt(d)) / (2 * a));
					out.printf("%1.6f\n", (-b - Math.sqrt(d)) / (2 * a));
				}
			}else if(di == 0){
				out.println(1);
				out.printf("%1.6f\n", -b / (2 * a));
			}else{
				out.println(0);
			}
		}else if(b != 0){
			out.println(1);
			out.printf("%1.6f\n", -c / b);
		}else if(c != 0){
			out.println(0);
		}else{
			out.println(-1);
		}
	}
	
	public void run() throws Exception
	{
//		in = new Scanner(new StringReader("1 -5 6"));
		in = new Scanner(System.in);
		System.setOut(new PrintStream(new BufferedOutputStream(System.out)));
		out = new PrintWriter(System.out);
		
//		int n = in.nextInt();
		int n = 1;
		for(int i = 1;i <= n;i++){
			long t = System.currentTimeMillis();
			solve();
			out.flush();
//			System.err.printf("%04d/%04d %7d%n", i, n, System.currentTimeMillis() - t);
		}
	}
	
	
	public static void main(String[] args) throws Exception
	{
		new A().run();
	}
	
	private int ni() { return Integer.parseInt(in.next()); }
	private static void tr(Object... o) { System.out.println(o.length == 1 ? o[0] : Arrays.toString(o)); }
	private void tra(int[] a) {System.out.println(Arrays.toString(a));}
	private void tra(int[][] a)
	{
		for(int[] e : a){
			System.out.println(Arrays.toString(e));
		}
	}
	
}