A quadratic equation $$ax^2+bx+c=0$$ with coefficients $$a, b, c \in \mathbb{R}$$ has

• no real roots if $$\Delta = b^2-4ac<0$$,

• one real root, namely $$x=-\frac{b}{2a}$$, if $$\Delta=0$$,

• two real roots, namely $$x=\frac{-b\pm\sqrt{\Delta}}{2a}$$, if $$\Delta>0$$.

Input

The coefficients of the quadratic equation $$a, b, c \in \mathbb{R}$$, in this order on three separate lines.

Output

The text on the first line of the output states the number of real roots the given quadratic equation has: "no roots", "one root" or "two roots". If there is one real root, write it out as the second line of the output. If there are two real roots, write them out as the second and third line of the output. The smallest outcome should be on the second line.

Example

Input:

1.0
-5.0
6.0

Output:

two roots
2.0
3.0

Example

Input:

1.0
0.0
2.0

Output:

no roots

Example

Input:

1.0
-1.0
0.25

Output:

one root
0.5

Example

Input:

1.0
-5.5
7.36

Output:

two roots
2.3
3.2