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 Practice1;

    import java.util.Scanner;

    public class CF020B {
        public static void main(String[] args) {
            Scanner s = new Scanner(System.in);
            int A = s.nextInt();
            int B = s.nextInt();
            int C = s.nextInt();
            if(!((A == 0) && (B == 0) && (C == 0))) {
                if (A == 0) {
                    if (B != 0 && C != 0) {
                        double ans = (C * -1.0) / B;
                        System.out.println(1);
                        System.out.println(ans);
                    } else if (B != 0) {
                        System.out.println(1);
                        System.out.println(0);
                    } else  {
                        System.out.println(0);
                    }
                } else if (B == 0) {
                    if (C <= 0) {
                        System.out.println(1);
                        double ans = (C * -1.0) / A;
                        if(ans == 0){
                            ans = 0;
                        }
                        ans = Math.sqrt(ans);
    //                System.out.println(a/ns);
                        System.out.println(ans);
                    } else {
                        System.out.println(0);
                    }
                } else if (C == 0) {
                    System.out.println(2);
                    double ans = (B * -1.0) / A;
                    if (ans > 0) {
                        System.out.println(0);
                        System.out.println(ans);
                    } else {
                        System.out.println(ans);
                        System.out.println(0);
                    }
                } else {
                    double a = A, b = B, c = C;
                    double root1, root2;

                    double determinant = (b * b) - (4 * a * c);

                    // condition for real and different roots
                    if(determinant > 0) {
                        root1 = (-b + Math.sqrt(determinant)) / (2 * a);
                        root2 = (-b - Math.sqrt(determinant)) / (2 * a);

                        System.out.println(2);
                        if(root1 < root2) {
                            System.out.println(root1);
                            System.out.println(root2);
                        }else{
                            System.out.println(root2);
                            System.out.println(root1);
                        }
                    }
                    // Condition for real and equal roots
                    else if(determinant == 0) {
                        root1 = root2 = -b / (2 * a);
                        System.out.println(1);
                        System.out.println(root1);
                    }
                    // If roots are not real
                    else {
    //                double realPart = -b / (2 *a);
    //                double imaginaryPart = Math.sqrt(-determinant) / (2 * a);
    //
                        System.out.println(0);
    //                System.out.format("root1 = %.2f+%.2fi and root2 = %.2f-%.2fi", realPart, imaginaryPart, realPart, imaginaryPart);
                    }
                }
            } else {
                System.out.println(-1);
            }

        }
    }