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.*;
import java.util.*;
import java.math.*;

public class P20B {

  public void run() throws Exception {
    double a = nextDouble();
    double b = nextDouble();
    double c = nextDouble();

    if (a == 0) {
      if (b == 0) {
        if (c == 0) {
          println(-1);
          return;
        } else {                                                                                               
          println(0);
          return;
        }
      } else {
        println(1);
        println(-c / b);
        return;
      }
    }

    double d = b * b - 4 * a * c;

    if (d < 0) {
      println(0);
      return;
    }

    double x1 = (-b + Math.sqrt(d)) / (2 * a);
    double x2 = (-b - Math.sqrt(d)) / (2 * a);

    if (d == 0) {
      println(1);
      println(x1);
    } else {
      println(2);
      println(Math.min(x1, x2));
      println(Math.max(x1, x2));
    }
  }

  public static void main(String... args) throws Exception {
    br = new BufferedReader(new InputStreamReader(System.in));
    pw = new PrintWriter(new BufferedOutputStream(System.out));
    new P20B().run();
    br.close();
    pw.close();
  }

  static BufferedReader br;
  static PrintWriter pw;                                                                                                          
  StringTokenizer stok;

  String nextToken() throws IOException {
    while (stok == null || !stok.hasMoreTokens()) {
      String s = br.readLine();
      if (s == null) {
        return null;
      }
      stok = new StringTokenizer(s);
    }
    return stok.nextToken();
  }

  void print(byte b) {
    print("" + b);
  }

  void print(int i) {
    print("" + i);
  }

  void print(long l) {
    print("" + l);
  }

  void print(double d) {
    print("" + d);
  }

  void print(char c) {
    print("" + c);
  }

  void print(StringBuffer sb) {
    print("" + sb);
  }

  void print(String s) {
    pw.print(s);
  }

  void println(byte b) {
    println("" + b);
  }

  void println(int i) {
    println("" + i);
  }

  void println(long l) {
    println("" + l);
  }

  void println(double d) {
    println("" + d);
  }

  void println(char c) {
    println("" + c);
  }

  void println(StringBuffer sb) {
    println("" + sb);
  }

  void println(String s) {
    pw.println(s);
  }

  int nextInt() throws IOException {
    return Integer.parseInt(nextToken());
  }

  long nextLong() throws IOException {
    return Long.parseLong(nextToken());
  }

  double nextDouble() throws IOException {
    return Double.parseDouble(nextToken());
  }

  char nextChar() throws IOException {
    return (char) (br.read());
  }

  String next() throws IOException {
    return br.readLine();
  }

}