E. Drawing Circles is Fun
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 ≥ 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).

Input

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.

Output

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

Examples
Input
10-46 46 0 360 20 -24 48-50 50 -49 49-20 50 8 40-15 30 14 284 10 -4 56 15 8 10-20 50 -3 154 34 -16 3416 34 2 17
Output
2
Input
1030 30 -26 260 15 -36 36-28 28 -34 3410 10 0 4-8 20 40 509 45 12 306 15 7 3536 45 -8 20-16 34 -4 344 34 8 17
Output
4
Input
100 20 38 38-30 30 -13 13-11 11 16 1630 30 0 376 30 -4 106 15 12 15-4 5 -10 25-16 20 4 108 17 -2 1716 34 2 17
Output
10