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.util.Arrays;
import java.util.Collections;
import java.util.InputMismatchException;
import java.util.PriorityQueue;


public class B {
	public static void main(String[] args) {
		MScanner sc = new MScanner();
		PrintWriter out = new PrintWriter(System.out);
		double A = sc.nextDouble();
		double B = sc.nextDouble();
		double C = sc.nextDouble();
		if(A==0&&B==0&C==0)out.println("-1");
		else if(A==0&&B==0)out.println("0");
		else if(A==0)out.printf("1\n%.9f",-C/B);
		else {
			double D = B*B - 4*A*C;
			if(D<0)out.println("0");
			else if(D==0)out.printf("1\n%.9f", -B/(2*A));
			else{
				double N = (-B-Math.sqrt(D))/(2*A);
				double P = (-B+Math.sqrt(D))/(2*A);
				out.printf("2\n%.9f\n%.9f",Math.min(N,P),Math.max(P, N));
			}
		}
		out.close();
	}



	static class MScanner{
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		
		public MScanner(){
			stream = System.in;
			//stream = new FileInputStream(new File("dec.in"));

		}
		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++];
		}
		
		boolean isSpaceChar(int c){
			return c==' '||c=='\n'||c=='\r'||c=='\t'||c==-1;
		}
		boolean isEndline(int c){
			return c=='\n'||c=='\r'||c==-1;
		}
		int nextInt(){
			return Integer.parseInt(next());
		}
		int[] nextIntArray(int N){
			int[] ret = new int[N];
			for(int a=0;a<N;a++)
				ret[a] = nextInt();
			return ret;
		}
		long nextLong(){
			return Long.parseLong(next());
		}
		long[] nextLongArray(int N){
			long[] ret = new long[N];
			for(int a=0;a<N;a++)
				ret[a] = nextLong();
			return ret;
		}
		double nextDouble(){
			return Double.parseDouble(next());
		}
		double[] nextDoubleArray(int N){
			double[] ret = new double[N];
			for(int a=0;a<N;a++)
				ret[a] = nextDouble();
			return ret;
		}
		String next(){
			int c = read();
			while(isSpaceChar(c))
				c=read();
			StringBuilder res = new StringBuilder();
			do{
				res.appendCodePoint(c);
				c=read();
			} while(!isSpaceChar(c));
			return res.toString();
		}
		String[] nextArray(int N){
			String[] ret = new String[N];
			for(int a=0;a<N;a++)
				ret[a] = next();
			return ret;
		}
		String nextLine(){
			int c = read();
			while(isEndline(c))
				c=read();
			StringBuilder res = new StringBuilder();
			do{
				res.appendCodePoint(c);
				c = read();
			}while(!isEndline(c));
			return res.toString();
		}
		
	}
}