## Square on the Inside

### Problem 504

Let `ABCD` be a quadrilateral whose vertices are lattice points lying on the coordinate axes as follows:

`A`(`a`, 0), `B`(0, `b`), `C`(`−c`, 0), `D`(0, `−d`), where 1 ≤ `a`, `b`, `c`, `d` ≤ `m` and `a`, `b`, `c`, `d`, `m` are integers.

It can be shown that for `m` = 4 there are exactly 256 valid ways to construct `ABCD`. Of these 256 quadrilaterals, 42 of them __strictly__ contain a square number of lattice points.

How many quadrilaterals `ABCD` strictly contain a square number of lattice points for `m` = 100?