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.util.Scanner;

/**
 *
 * @author Administrator
 */
public class Main {

    /**
     * @param args the command line arguments
     */
public static double sqrtt(double x)  
{  
    if(x<0) return -Math.sqrt(-x);  
    else return Math.sqrt(x);  
}  
    public static void main(String[] args) {
        // TODO code application logic here
        Scanner sc=new Scanner(System.in);
        double a=sc.nextDouble();
        double b=sc.nextDouble();
        double c=sc.nextDouble();
        int flag=0,count=0;
       if(a==0&&b==0) {  
            if(c==0) System.out.println("-1");
            else System.out.println("0"); 
        }  
        else if(a==0&&c==0) {  
            System.out.println("1");
            System.out.println("0");
        }  
        else if(b==0&&c==0) {  
           System.out.println("1");
           System.out.println("0"); 
        }  
        else if(a==0) {  
            System.out.println("1");
            System.out.format("%.6f\n",-c/b);  
        }  
        else {  
            double tem=b*b-4*a*c;  
            if(tem<0) System.out.println("0");  
            else if(tem==0) {  
                System.out.println("1");
                System.out.format("%.6f\n",(-b/(2*a)));  
            }  
            else {  
                System.out.println("2"); 
               double x1=(-b-sqrtt(tem))/(2*a);  
               double x2=(-b+sqrtt(tem))/(2*a);  
                if(x1>x2) {
                    double t=x1;
                    x1=x2;
                    x2=t;
                }  
                System.out.format("%.6f\n%.6f\n",x1,x2);  
            }  
       
    }
    }
}