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.InputStreamReader;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.InputStream;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashSet;
import java.util.Objects;
import java.util.TreeSet;
/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Erasyl Abenov
 * 
 * 
 */
public class Main {
    public static void main(String[] args) throws IOException {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
            try (PrintWriter out = new PrintWriter(outputStream)) {
                TaskB solver = new TaskB();
                solver.solve(1, in, out);
            }
    }
}
class TaskB {
    public void solve(int testNumber, InputReader in, PrintWriter out) throws IOException{
        long a = in.nextLong();
        long b = in.nextLong();
        long c = in.nextLong();
        ArrayList<Double> list = new ArrayList<>();
        int count = 0;
        if(a == b && b == c && c != 0) list.add(0.0);
        else if(a == 0){
            if(b == 0){
                if(c == 0) count--;
                else list.add(0.0);
            }
            else{
                 count++;
                 list.add((-1.0*c)/b);
            }
        }
        else if(b == 0){
            if(c <= 0){
                count++;
                list.add(Math.sqrt((-1.0*c)/a));
            }
            else list.add(0.0);
        }
        else if(c == 0){
            count += 2;
            list.add(-0.0);
            list.add((-1.0*b)/a);
        }
        else{
            long D = b*b*1L - 1L*4*a*c;
            if(D < 0) count = -1;
            else if(D == 0){
                count++;
                list.add((-b*1.0)/(1L*2*a));
            }
            else{
                count = 2;
                list.add((-b + Math.sqrt(D))/(1L*2*a));
                list.add((-b - Math.sqrt(D))/(1L*2*a));
            }
        }
        if(count != 0) out.println(count);
        Collections.sort(list);
        for(double ans : list){
            out.printf("%.10f", ans);
            out.println();
        }
    }
}
 
     
class InputReader {
    private final BufferedReader reader;
    private StringTokenizer tokenizer;
    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream));
        tokenizer = null;
    }
      
    public String nextLine() {
        try {
            return reader.readLine();
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }
      
    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(nextLine());
        }
        return tokenizer.nextToken();
    }
      
    public int nextInt() {
        return Integer.parseInt(next());
    }
    public BigInteger nextBigInteger(){
        return new BigInteger(next());
    }
    public long nextLong() {
        return Long.parseLong(next());
    }
    public double nextDouble() {
        return Double.parseDouble(next());
    }
}