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.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Solution implements Runnable {
  BufferedReader in;
  PrintWriter out;
  StringTokenizer tok = new StringTokenizer("");
  
  @Override
  public void run() {
    try {
      init();
    } catch (FileNotFoundException e) {
      e.printStackTrace();
    }
    long time = System.currentTimeMillis();
    try {
      solve();
    } catch (Exception e) {
      e.printStackTrace();
    }
    out.close();
    //System.err.println(System.currentTimeMillis() - time);
  }
  
  private void init() throws FileNotFoundException {
    String file = "";
    if (!file.equals("")) {
      in = new BufferedReader(new FileReader("input.txt"));
      out = new PrintWriter("output.txt");
    } else {
      in = new BufferedReader(new InputStreamReader(System.in));
      out = new PrintWriter(System.out);
    }
  }
  
  public static void main(String[] args) {
    new Thread(new Solution()).start();
  }
  
  private String readString() {
    while (!tok.hasMoreTokens()) {
      try {
        tok = new StringTokenizer(in.readLine());
      } catch (IOException e) {
        e.printStackTrace();
      }
    }
    return tok.nextToken();
  }
  
  private int readInt() {
    return Integer.parseInt(readString());
  }
  
  int[] counts = new int[1000];
  
  private long readLong() {
    return Long.parseLong(readString());
  }
  
  private void solve() {
    double a = readInt();
    double b = readInt();
    double c = readInt();
    double d = b*b-4*a*c;
    if(a==0 && b==0 && c!=0) {
      out.print(0);
      return;
    }
    if(a==0 && b==0 && c==0) {
      out.print(-1);
      return;
    }
    if(a==0) {
      out.println(1);
      out.print(-c/b);
      return;
    }
    if(d<0) {
      out.print(0);
    } else if(d==0) {
      out.println(1);
      out.print(-b/(2*a));
    } else {
      out.println(2);
      double x1 = (-b+Math.sqrt(d))/(2*a);
      double x2 = (-b-Math.sqrt(d))/(2*a);
      if(x1<x2) {
        out.println(x1);
        out.print(x2);
      } else {
        out.println(x2);
        out.print(x1);
      }
    }
  }
  
  
}