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 java.lang.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;
public final class Main{//CF //B.Equation.
	static long mod = (long)(10e9+7);
	static BufferedReader br;
	static PrintWriter pw;
	static StringBuilder OUTPUT;
	public static void main(String[] args)throws Exception{
		OUTPUT = new StringBuilder("");
		br = new BufferedReader(new InputStreamReader(System.in));
		pw = new PrintWriter(System.out,true);//auto flush enabled....
		new Main().timer();
		br.close();
		pw.close();
	}
	public static void timer()throws Exception{
		long S = System.currentTimeMillis();
		solve();
		long E = System.currentTimeMillis();
		//pw.println("Time elapsed : "+(E-S)+" ms.");
	}
	public static void solve()throws Exception{
		String[] s;
		int t = 1;
		//int t = Integer.parseInt(br.readLine());
		for(int I=0;I<t;I++){
			//code from here....
			s = br.readLine().split("\\s+");
			double a = Integer.parseInt(s[0]);
			double b = Integer.parseInt(s[1]);
			double c = Integer.parseInt(s[2]);
			
			//checking for roots...
			if(a==0 && b==0 && c==0){
				pw.println("-1");
				return;
			}else if(a==0 && b==0){
				pw.println(0);
				return;
			}else if(a==0){
				pw.println("1");
				pw.println(-c/b);
				return;
			}
			double del = (b*b - 4f*a*c);
			
			if(del<0){
				pw.println(0);
				return;
			}else{
				double r1 = (-b+Math.sqrt(b*b-4f*a*c))/(2f*a);
				double r2 = (-b-Math.sqrt(b*b-4f*a*c))/(2f*a);
				
				if(r1==r2){
					pw.println(1);
					pw.println(r1);
				}else{
					pw.println(2);
					pw.println(Math.min(r1,r2));
					pw.println(Math.max(r1,r2));
				}
			}
		}
	}
}