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.util.*;

public class Test {

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    public static void main(String args[]) {
        FastScanner in = new FastScanner();
        double a = in.nextDouble();
        double b = in.nextDouble();
        double c = in.nextDouble();

        if(a==0&&b==0&&c==0){
            System.out.println(-1);
            return;
        }
        if(a==0&&b==0){
            System.out.println(0);
            return;
        }
        if(a==0){
            System.out.println(1);
            System.out.println(-1*c/b);
            return;
        }
        double d = b*b-4*a*c;
        if(d<0){
            System.out.println(0);
            return;
        }
        if(d==0){
            System.out.println(1);
            System.out.println(-1*b/(2*a));
            return;
        }
        System.out.println(2);
        double root1 = (-b+Math.sqrt(d))/(2*a);
        double root2 = (-b-Math.sqrt(d))/(2*a);
        System.out.println(Math.min(root2,root1));
        System.out.println(Math.max(root1,root2));
    }
}