CF372E 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

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