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.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.math.BigInteger;
import java.util.Arrays;

public class a{

    public static void main(String[] args)throws IOException{
    	br = new BufferedReader(new InputStreamReader(System.in));
    	PrintWriter out = new PrintWriter(System.out);
	int a = nextInt();
	int b = nextInt();
	int c = nextInt();
	double d = (double)b*b-4.0*a*c;
	if(a!=0){
	    if(d==0){
		out.println(1);
		double ans = (double)(b*-1)/(double)(2.0*a);
		out.printf("%.7f",ans);
	    }else if(d<0){
		out.println(0);
	    }else{
		out.println(2);
		d = Math.sqrt(d);
		double gl = b*-1.0;
		double ans1 = (gl-d)/(2.0*a);
		double ans2 = (gl+d)/(2.0*a);
		double a1 = Math.max(ans1,ans2);
		double b1 = Math.min(ans1,ans2);
		out.printf("%.7f\n",b1);
		out.printf("%.7f",a1);

	    }
	    
	}else if(b!=0){
	    out.println(1);
	    double ans = (double)c*-1.0/(double)b;
	    out.printf("%.7f\n",ans);
	}else if(c==0){
	    out.println(-1);
	}else{
	    out.println(0);
	}
	


	out.close();
    }
        
    static BufferedReader br;
    static StringTokenizer st = new StringTokenizer("");
    static String next()throws IOException{
    	while(!st.hasMoreTokens()){
    	    st = new StringTokenizer(br.readLine());
    	}
    	return st.nextToken();
    }
    static int nextInt()throws IOException{
    	return Integer.parseInt(next());
    }
    static long nextLong()throws IOException{
    	return Long.parseLong(next());
    }
}