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.lang.*;
import java.math.*;

public class quad {
	public void run() throws Exception {
		FastScanner sc = new FastScanner();
		
		int a = sc.nextInt();
		int b = sc.nextInt();
		int c = sc.nextInt();
		
		if (a == 0 && b == 0) {
			if (c == 0) System.out.println(-1);
			else System.out.println(0);
			return;
		}
		if (a == 0) {
			double root = -(double)c/b;
			System.out.println(1);
			System.out.println(root);
			return;
		}
		double x = (double)b*b-4.0*a*c;
		if (x<0) System.out.println(0);
		else if (x == 0) {
			double root = (-b+Math.sqrt(x))/2.0/a;
			System.out.println(1);
			System.out.println(root);
		}
		else {
			double r1 = (-b+Math.sqrt(x))/2.0/a;
			double r2 = (-b-Math.sqrt(x))/2.0/a;
			System.out.println(2);
			double root1 = Math.min(r1, r2);
			double root2 = Math.max(r1, r2);
			System.out.printf("%.10f",root1);
			System.out.println();
			System.out.printf("%.10f", root2);
		}
		
	}
	static class FastScanner {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public FastScanner() {
			reader = new BufferedReader(new InputStreamReader(System.in), 32768);
			tokenizer = null;
		}

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

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}

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