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:
Calculate the number of good sets of pairs modulo 1000000007 (10^{9} + 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 (10^{9} + 7).
10
-46 46 0 36
0 20 -24 48
-50 50 -49 49
-20 50 8 40
-15 30 14 28
4 10 -4 5
6 15 8 10
-20 50 -3 15
4 34 -16 34
16 34 2 17
2
10
30 30 -26 26
0 15 -36 36
-28 28 -34 34
10 10 0 4
-8 20 40 50
9 45 12 30
6 15 7 35
36 45 -8 20
-16 34 -4 34
4 34 8 17
4
10
0 20 38 38
-30 30 -13 13
-11 11 16 16
30 30 0 37
6 30 -4 10
6 15 12 15
-4 5 -10 25
-16 20 4 10
8 17 -2 17
16 34 2 17
10
Name |
---|