- All Contests
- ProjectEuler+
- Project Euler #246: Tangents to an ellipse

# Project Euler #246: Tangents to an ellipse

# Project Euler #246: Tangents to an ellipse

_{This problem is a programming version of Problem 246 from projecteuler.net}

A definition for an ellipse is:

Given a circle with centre and radius and a point such that , the locus of the points that are equidistant from and form an ellipse.

The construction of the points of the ellipse is shown below.

Given are the points and .

Given is also the circle with centre and radius .

The locus of the points that are equidistant from and form an ellipse .

From a point outside the two tangents and to the ellipse are drawn.

Let the points where and touch the ellipse be and .

For how many lattice points is angle greater than degrees?

**Input Format**

First line of each test file contains three integers separated by single spaces: , and .

Second line of each test file contains a single integer .

Third line of each test file contains two integers and separated by a single space which represent the angle in such a way that .

**Constraints**

- is even
- is acute

**Output Format**

Print exactly one number which is the answer to the problem.

**Sample Input 0**

```
64817 64819 11420
3
30 1
```

**Sample Output 0**

```
4
```

**Explanation 0**

These points are , , and .

**Sample Input 1**

```
-13896 -13894 43360
3
1 1
```

**Sample Output 1**

```
32
```