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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.DataInputStream;
import java.io.IOException;
import java.util.InputMismatchException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author xwchen
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            double a = in.nextDouble();
            double b = in.nextDouble();
            double c = in.nextDouble();

            double sq = b * b - 4 * a * c;
            if (eq(a, 0) && eq(b, 0)) {
                if (eq(c, 0)) {
                    out.println(-1);
                } else {
                    out.println(0);
                }
            } else if (eq(a, 0)) {
                out.println(1);
                double y = -c / b;
                out.println(y);
            } else if (sq < -1e-9) {
                out.println(0);
            } else if (Math.abs(sq) < 1e-9) {
                out.println(1);
                double y = -b / 2 / a;
                out.println(y);
            } else {
                sq = Math.sqrt(sq);
                double y1 = (-b - sq) / 2 / a;
                double y2 = (-b + sq) / 2 / a;
                if (y1 > y2) {
                    double t = y1;
                    y1 = y2;
                    y2 = t;
                }
                out.println(2);
                out.println(y1);
                out.println(y2);
            }
        }

        boolean eq(double a, double b) {
            return Math.abs(a - b) < 1e-9;
        }

    }

    static class InputReader {
        final private int BUFFER_SIZE = 1 << 10;
        private DataInputStream in;
        private byte[] buffer;
        private int bufferPointer;
        private int bytesRead;

        public InputReader(InputStream inputStream) {
            this.in = new DataInputStream(inputStream);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public double nextDouble() {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }
            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() {
            try {
                bytesRead = in.read(buffer, bufferPointer = 0, BUFFER_SIZE);
                if (bytesRead == -1)
                    buffer[0] = -1;
            } catch (IOException e) {
                throw new InputMismatchException();
            }
        }

        private byte read() {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

    }
}