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- Project Euler #177: Integer angled Quadrilaterals.

# Project Euler #177: Integer angled Quadrilaterals.

# Project Euler #177: Integer angled Quadrilaterals.

_{This problem is a programming version of Problem 177 from projecteuler.net}

Let be a convex quadrilateral, with diagonals and . At each vertex the diagonal makes an angle with each of the two sides, creating eight corner angles.

For example, at vertex , the two angles are , .

We call such a quadrilateral for which all eight corner angles have integer values when measured in degrees an *integer angled quadrilateral*. An example of an integer angled quadrilateral is a square, where all eight corner angles are . Another example is given by , , , , , , , .

Consider to be sorted sequence of quadrilateral angles. What is the number of non-similar integer angled quadrilaterals such that ?

Note: In your calculations you may assume that a calculated angle is integral if it is within a tolerance of of an integer value.

**Input Format**

The input contains eight numbers .

**Constraints**

**Output Format**

Print the only integer which is the answer to the problem.

**Sample Input 0**

```
1 1 1 1 1 1 177 177
```

**Sample Output 0**

```
1
```

**Explanation 0**

There is exactly one such quadrilateral.