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- ProjectEuler+
- Project Euler #210: Obtuse Angled Triangles

# Project Euler #210: Obtuse Angled Triangles

# Project Euler #210: Obtuse Angled Triangles

Contest ends in

_{This problem is a programming version of Problem 210 from projecteuler.net}

Consider the set of points with integer coordinates satisfying .

Consider three integers and let be the point and the point .

Let be the number of points in , so that the triangle has an obtuse angle, i.e. the largest angle satisfies .

Given , , and , what is ?

**Input Format**

The only line of the input contains exactly four space-separated integers: .

**Constraints**

- .
- .
- .
- .
- .
- .
- .

**Output Format**

Print one line containing the answer.

**Sample Input 0**

```
8 0 1 1
```

**Sample Output 0**

```
100
```

**Sample Input 1**

```
17 3 7 2
```

**Sample Output 1**

```
486
```

**Sample Input 2**

```
15 -13 10 1
```

**Sample Output 2**

```
364
```

**Sample Input 3**

```
17 -5 13 3
```

**Sample Output 3**

```
438
```