A quadratic equation is any equation that can be rearranged in standard form as

\[ax^2 + bx + c = 0\,,\]

where \(a, b, c \in \mathbb{R}\) and \(a \neq 0\).

The expression

\[\Delta = b^2 - 4ac\]

is called the discriminant of the quadratic equation. The sign of \(\Delta\) determines the number of real-valued solutions:

• if \(\Delta > 0\), then there are two distinct real-valued solutions (\(x_1 \neq x_2\))

• als \(\Delta = 0\), then both real-valued solutions are the same (\(x_1 = x_2\))

• als \(\Delta < 0\), then there are no real-valued solutions

The real-valued solutions can be determined as:

\[x_{1} = \frac{-b - \sqrt{\Delta}}{2a}\ \ \ \text{en}\ \ \ x_{2} = \frac{-b + \sqrt{\Delta}}{2a}\]

Input

The three parameters \(a\), \(b\) and \(c\) of a quadratic equation, each on a separate line.

Output

A line that indicates the number of different real-valued solutions of the quadratic equation. The solutions themselves must also be mentioned (if they exist). When \(a \neq 0\) solve the equation as a quadratic equation. If \(a = 0\), \(b \neq 0\) and \(c \neq 0\) then solve the equation as a linear equation with the solution \(-c/b\). If a and b = 0 then you return the string “Invalid equation”.

Example

Input:

1
4
-5

Output:

Er zijn 2 reële oplossingen: -5.0 en 1.0

Example

Input:

1
-12
36

Output:

Er is 1 reële oplossing: 6.0

Example

Input:

4
2
7

Output:

Er zijn geen reële oplossingen

Example

Input:

0
0
3

Output:

Ongeldige vergelijking