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 (109 + 7).

输入描述:

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 ai, bi, ci, di(0 ≤ ai, ci ≤ 50; 1 ≤ bi, di ≤ 50; (ai, ci) ≠ (0, 0)). These integers represent a point .No two points coincide.

输出描述:

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