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

public class Equation {
    private void solve() throws IOException {

        double a = nextInt();
        double b = nextInt();
        double c = nextInt();

        if (a == 0) {
            double r = -c / b;
            if (Double.isNaN(r)) {
                System.out.println(-1);
                return;
            }
            if (Double.isInfinite(r)) {
                System.out.println(0);
                return;
            }
            System.out.println(1);
            System.out.printf("%.5f\n", Double.isNaN(r) ? -1 : r);
            return;
        }
        double momaiaz, root1, root2;

        momaiaz = (b * b) - (4 * a * c);

        if (Double.isNaN(momaiaz)) {
            System.out.println(0);
            return;
        }

        if (momaiaz > 0) {
            root1 = (-b + Math.sqrt(momaiaz)) / (2 * a);
            root2 = (-b - Math.sqrt(momaiaz)) / (2 * a);
            System.out.println(2);
            System.out.printf("%.5f\n", Math.min(root1, root2));
            System.out.printf("%.5f\n", Math.max(root1, root2));
            return;
        }

        if (momaiaz == 0) {
            root1 = (-b) / (2 * a);
            System.out.println(1);
            System.out.printf("%.5f\n", root1);
            return;
        }
        
        System.out.println(0);
    }

    public static void main(String[] args) {
        new Equation().run();
    }

    BufferedReader reader;
    StringTokenizer tokenizer;
    PrintWriter writer;

    public void run() {
        try {
            reader = new BufferedReader(new InputStreamReader(System.in));
            tokenizer = null;
            writer = new PrintWriter(System.out);
            solve();
            reader.close();
            writer.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    int[] readIntArray(int size) throws IOException {
        int[] res = new int[size];
        for (int i = 0; i < size; i++) {
            res[i] = nextInt();
        }
        return res;
    }

    long[] readLongArray(int size) throws IOException {
        long[] res = new long[size];
        for (int i = 0; i < size; i++) {
            res[i] = nextLong();
        }
        return res;
    }

    double[] readDoubleArray(int size) throws IOException {
        double[] res = new double[size];
        for (int i = 0; i < size; i++) {
            res[i] = nextDouble();
        }
        return res;
    }

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

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

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

    BigInteger nextBigInteger() throws IOException {
        return new BigInteger(nextToken());
    }

    String nextToken() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
}