A9363 | Drawing Circles is Fun

There are a set of points $S$ on the plane. This set doesn't contain the origin $O(0,0)$ , and for each two distinct points in the set $A$ and $B$ , the triangle $OAB$ has strictly positive area.

Consider a set of pairs of points $(P_{1},P_{2}),(P_{3},P_{4}),...,(P_{2k-1},P_{2k})$ . We'll call the set good if and only if:

- $k>=2$ .
- All $P_{i}$ are distinct, and each $P_{i}$ is an element of $S$ .
- For any two pairs $(P_{2i-1},P_{2i})$ and $(P_{2j-1},P_{2j})$ , the circumcircles of triangles $OP_{2i-1}P_{2j-1}$ and $OP_{2i}P_{2j}$ have a single common point, and the circumcircle of triangles $OP_{2i-1}P_{2j}$ and $OP_{2i}P_{2j-1}$ have a single common point.

Calculate the number of good sets of pairs modulo $1000000007$ $(10^{9}+7)$ .

The first line contains a single integer $n$ $(1<=n<=1000)$ — the number of points in $S$ . Each of the next $n$ lines contains four integers $a_{i},b_{i},c_{i},d_{i}$ $(0<=|a_{i}|,|c_{i}|<=50; 1<=b_{i},d_{i}<=50; (a_{i},c_{i})≠(0,0))$ . These integers represent a point .

No two points coincide.

Print a single integer — the answer to the problem modulo $1000000007$ $(10^{9}+7)$ .