Migrated from Lutece 329 Equation

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Description

You are given an equation:

$Ax^2 + Bx + C = 0$

Your task is to find the number of distinct roots of the equation and print all of them in ascending order.

Input

There are multi-cases. The first line of each case contains three integer numbers $A$, $B$ and $C$ ($-10^5 \leq  A, B, C \leq 10^5$). 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 $6$ digits after the decimal point. Make sure that your program does not print $-0.000000$ for the answer, otherwise you will get Wrong Answer.

Samples

1 -5 6

2
2.000000
3.000000

Resources

2011寒假训练（一）(Not Original)