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.lang.*;
import java.util.*;
import java.io.*;

public class CodeforcesB {

    public void solve()throws IOException{
        FastScanner in = new FastScanner();
        StringBuilder ans = new StringBuilder("");
        double x1,x2,e;
        long a,b,c;
        a=in.nextLong();
        b=in.nextLong();
        c=in.nextLong();
        e=Math.pow(b,2)-4*a*c;
        if(a==0)
        {
            if(b!=0) {System.out.println(1);System.out.format("%.10f",1.0*(-c)/b);}
            else if(b==0&&c!=0)System.out.print(0);
            else if(b==0&&c==0)System.out.print(-1);
        }
        else
        {if(e<0)System.out.println(0);
        else if(e>0)
        {
            x1=(-b-Math.sqrt(e))/(2*a);x2=(-b+Math.sqrt(e))/(2*a);
            System.out.println(2);
            System.out.format("%.10f\n%.10f",x1<x2?x1:x2,x1>x2?x1:x2);
        }
        else if(e==0)
        {
            System.out.println(1);
            System.out.format("%.10f",-b*1.0/(2*a));
        }
        }
    }
    public static void main(String[]args)throws IOException{
       try {
           new CodeforcesB().solve();
       }catch (Exception e){
           e.printStackTrace();

       }
    }
    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
        int[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }
}