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 (P1,P2),(P3,P4),...,(P2k-1,P2k). We'll call the set good if and only if:
k \ge 2. All Pi are distinct, and each Pi is an element of S. For any two pairs (P2i-1,P2i) and (P2j-1,P2j), the circumcircles of triangles OP2i-1P2j-1 and OP2iP2j have a single common point, and the circumcircle of triangles OP2i-1P2j and OP2iP2j-1 have a single common point.
Calculate the number of good sets of pairs modulo 1000000007 (109+7).

The first line contains a single integer n (1 \le n \le 1000) - the number of points in S. Each of the next n lines contains four integers ai,bi,ci,di (0 \le |ai|,|ci| \le 50;1 \le bi,di \le 50;(ai,ci) \neq (0,0)). These integers represent a point .

No two points coincide.

Print a single integer - the answer to the problem modulo 1000000007 (109+7).