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), ..., (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 - 1P_2j - 1 and OP_2iP_2j have a single common point, and the circumcircle of triangles OP_2i - 1P_2j and OP_2iP_2j - 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 ≤ 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 (10⁹ + 7).