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.Arrays;
import java.util.StringTokenizer;

/**
 * Created by peacefrog on 11/24/15.
 * Time : 7:54 PM
 */

public class CF20B {
	final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
	PrintWriter out;
	long timeBegin, timeEnd;

	public void runIO() throws IOException {
		timeBegin = System.currentTimeMillis();

		InputStream inputStream;
		OutputStream outputStream;


		if (ONLINE_JUDGE) {
			inputStream = System.in;
			Reader.init(inputStream);
			outputStream = System.out;

			out = new PrintWriter(outputStream);

		} else {
			inputStream = new FileInputStream("/home/peacefrog/Dropbox/IdeaProjects/Problem Solving/input");
			Reader.init(inputStream);
			out = new PrintWriter(System.out);
		}

		solve();

		out.flush();
		out.close();
		timeEnd = System.currentTimeMillis();

		System.err.println("Time = " + (timeEnd - timeBegin));

	}

	/*
	 * Start Solution Here
	 */

	private void solve() throws IOException {
		double a = Reader.nextInt(); //This Variable default in Code Template
		double b = Reader.nextInt();
		double c  = Reader.nextInt();

		double inf = b* b - 4  * a* c ;
		if(a == 0.0D && b == 0.0D && c == 0 ) {
			out.println(-1);
			return;
		}
		if(a == 0.0D && b == 0.0D && c != 0 ) {
			out.println(0);
			return;
		}
		if (inf < 0.0D){
			out.println(0);
			return;
		}
		if (inf == 0.0D)
		{
			out.printf("1\n%.10f\n", (-b + Math.sqrt(inf))/(2.0 * a));
			return;
		}

		if (a == 0 )
		{
			out.printf("1\n%.10f\n", (-c/b) );
			return;
		}

		double ans[] = new double[2];

		ans[0] = (-b + Math.sqrt(inf))/(2.0 * a);
		ans[1] = (-b - Math.sqrt(inf))/(2.0 * a);
		Arrays.sort(ans);

		out.printf("2\n%.10f\n%.10f", ans[0] ,ans[1]);
	}

	public static void main(String[] args) throws IOException {

		new CF20B().runIO();
	}

	static class Reader {
		static BufferedReader reader;
		static StringTokenizer tokenizer;

		/**
		 * call this method to initialize reader for InputStream
		 */
		static void init(InputStream input) {
			reader = new BufferedReader(new InputStreamReader(input));
			tokenizer = new StringTokenizer("");
		}

		/**
		 * get next word
		 */
		static String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		static String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return "";
		}

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

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

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

		static long[] nextLongArray(int n) throws IOException {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}

			return arr;
		}

		static int[] nextIntArray(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}

			return arr;
		}
	}

}