18930번 - Lands of Infinistan 다국어

문제

The country of Infinistan can be represented as an infinite plane. In the country there are $n$ straight walls and a river which has the form of a quadratic curve (an ellipse, a parabola or a hyperbola). The walls and the river divide the country into some lands of non-zero area. Your task is, given all the equations, to count the number of those lands.

입력

The first line contains a single integer $n$ --- the number of straight walls (1ドル \le n \le 20$).

The second line contains six integers $q_0,ドル $q_1,ドル $q_2,ドル $q_3,ドル $q_4$ and $q_5$ --- coefficients of the river that is a quadratic curve $q_0\cdot x^2 + q_1 \cdot xy + q_2 \cdot y^2 + q_3 \cdot x + q_4 \cdot y + q_5 = 0$.

Each of the following $n$ lines contains three integers $a_i,ドル $b_i$ and $c_i$ --- coefficients of the straight line $a_i \cdot x + b_i \cdot y + c_i = 0$.

All $q_i,ドル $a_i,ドル $b_i$ and $c_i$ do not exceed 100 by absolute value. The straight lines may coincide. You may assume that the quadratic curve is not degenerate, and that for any $i$ either $a_i \ne 0$ or $b_i \ne 0$.

출력

Print one integer --- the number of lands.

제한

힌트