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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.InputMismatchException;

/**
 * @author Egor Kulikov (egor@egork.net)
 *         Created on 14.03.2010
 */
public class TaskB implements Runnable {
	private InputReader in;
	private PrintWriter out;

	public static void main(String[] args) {
		new Thread(new TaskB()).start();
//		new Template().run();
	}

	public TaskB() {
		String id = getClass().getName().toLowerCase();
//		try {
//			System.setIn(new FileInputStream(id + ".in"));
//			System.setOut(new PrintStream(new FileOutputStream(id + ".out")));
//			System.setIn(new FileInputStream("input.txt"));
//			System.setOut(new PrintStream(new FileOutputStream("output.txt")));
//		} catch (FileNotFoundException e) {
//			throw new RuntimeException();
//		}
		in = new InputReader(System.in);
		out = new PrintWriter(System.out);
	}

	public void run() {
//        int numTests = in.readInt();
//        for (int testNumber = 0; testNumber < numTests; testNumber++) {
//			out.print("Case #" + (testNumber + 1) + ": ");
//        }
		long a = in.readInt();
		long b = in.readInt();
		long c = in.readInt();
		if (a == 0) {
			if (b == 0) {
				if (c == 0)
					out.println(-1);
				else
					out.println(0);
			} else {
				double x = ((double) -c) / b;
				out.println(1);
				out.printf("%.6f\n", x);
			}
		} else {
			long d = b * b - 4 * a * c;
			if (d < 0) {
				out.println(0);
			} else {
				if (d == 0) {
					double x = ((double) - b) / (2 * a);
					out.println(1);
					out.printf("%.6f\n", x);
				} else {
					double x1 = (-b - Math.sqrt(d)) / (2 * a);
					double x2 = (-b + Math.sqrt(d)) / (2 * a);
					out.println(2);
					out.printf("%.6f\n", Math.min(x1, x2));
					out.printf("%.6f\n", Math.max(x1, x2));
				}
			}
		}
		out.close();
	}

	private static class InputReader {
		private InputStream stream;
		private byte[] buf = new byte[1000];
		private int curChar, numChars;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		private int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int readInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public long readLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public String readString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuffer res = new StringBuffer();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private String readLine0() {
			StringBuffer buf = new StringBuffer();
			int c = read();
			while (c != '\n' && c != -1) {
				buf.appendCodePoint(c);
				c = read();
			}
			return buf.toString();
		}

		public String readLine() {
			String s = readLine0();
			while (s.trim().length() == 0)
				s = readLine0();
			return s;
		}

		public String readLine(boolean ignoreEmptyLines) {
			if (ignoreEmptyLines)
				return readLine();
			else
				return readLine0();
		}

		public BigInteger readBigInteger() {
			try {
				return new BigInteger(readString());
			} catch (NumberFormatException e) {
				throw new InputMismatchException();
			}
		}

		public char readCharacter() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			return (char) c;
		}

		public double readDouble() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			double res = 0;
			while (!isSpaceChar(c) && c != '.') {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			if (c == '.') {
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) {
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}
	}
}