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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.StringTokenizer;


public class B20{
	BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
	StringTokenizer st = null;
	
	private void solution() throws IOException {
		double a=nextInt();
		double b=nextInt();
		double c=nextInt();
		if(a==0 && b==0 && c==0){System.out.println(-1);System.exit(0);}
		if(a==0 && b==0){System.out.println(0);System.exit(0);}
		if(a==0){System.out.println(1);System.out.println(-c/b);System.exit(0);}
		double d=b*b-4*a*c;
		int k=0;
		if(d<0){k=0;}
		if(d==0){k=1;}
		if(d>0){k=2;}
		if(k==0){System.out.println(0);System.exit(0);}
		System.out.println(k);
		if(k==1){System.out.println((-b+Math.sqrt(d))/(2*a));}
		if(k==2){double ans =(-b-Math.sqrt(d))/(2*a);
		double ans1=(-b+Math.sqrt(d))/(2*a);
		if(ans>ans1){
			System.out.println(ans1);
			System.out.println(ans);
		}else{
			System.out.println(ans);
			System.out.println(ans1);
		}
		}
	}

	String nextToken() throws IOException {
		if (st == null || !st.hasMoreTokens()) {
			st = new StringTokenizer(bf.readLine());
		}
		return st.nextToken();
	}
	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

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

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

	public static void main(String args[]) throws IOException {
		new B20().solution();
	}
	
}