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

public class Lygtis1 {
     static class InputReader {

		private InputStream stream;
		private byte[] buf = new byte[8192];
		private int curChar;
		private int snumChars;
		private SpaceCharFilter filter;

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

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

		public int nextInt() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}

			int res = 0;

			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));

			return res * sgn;
		}
		
		public long nextLong() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}

			long res = 0;

			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));

			return res * sgn;
		}
		
		public String readString() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}


    public long diskriminantas(long a, long b, long c)
    {
        return (b*b-4*a*c);
    }
    public double pirmasaknis(long a, long b, long c)
    {
        return (((-b+Math.sqrt(diskriminantas(a,b,c)))/(2*a)));
    }
    public double antrasaknis(long a, long b, long c)
    {
        return (((-b-Math.sqrt(diskriminantas(a,b,c)))/(2*a)));
    }
    
   
    public static void main(String[] args) {
        Lygtis1 g = new Lygtis1();
        InputReader in=new InputReader(System.in);
        PrintWriter pw=new PrintWriter(System.out);
  
        long a = in.nextLong();
        long b = in.nextLong();
        long c = in.nextLong();      
        if (a == 0 && b == 0 && c == 0)
        {
            pw.println(-1);
        }        
        else if (a == 0 && b == 0)
        {
            pw.println(0);
        }
        else if (a == 0)
        {
            pw.println(1);
            double x = -(double)c/(double)b;
            pw.println(x);
        }

        else if (g.diskriminantas(a, b, c) > 0)
        {       
            pw.println(2);
            if (g.antrasaknis(a, b, c) < g.pirmasaknis(a, b, c))
            {
                pw.println(g.antrasaknis(a, b, c));
                pw.println(g.pirmasaknis(a, b, c));
            }
            else
            {
                pw.println(g.pirmasaknis(a, b, c));
                pw.println(g.antrasaknis(a, b, c));
            }
            
        }
        else if (g.diskriminantas(a, b, c) == 0)
        {
            pw.println(1);
            pw.println(g.antrasaknis(a, b, c));
        }
        else if (g.diskriminantas(a, b, c) < 0)
        {
             pw.println(0);
        }  
        pw.close();
    }
    
}