CF1036E.Covered Points

You are given $n$ segments on a Cartesian plane. Each segment's endpoints have integer coordinates. Segments can intersect with each other. No two segments lie on the same line.

Count the number of distinct points with integer coordinates, which are covered by at least one segment.

给你 $n$ 条位于笛卡尔平面上的线段。每条线段的端点坐标均为整数。线段之间可以相交。任意两条线段都不共线。

请计算被至少一条线段覆盖的、具有整数坐标的不同点的个数。

The first line contains a single integer $n$ ($1 \le n \le 1000$) — the number of segments.

Each of the next $n$ lines contains four integers $Ax_i, Ay_i, Bx_i, By_i$ ($-10^6 \le Ax_i, Ay_i, Bx_i, By_i \le 10^6$) — the coordinates of the endpoints $A$, $B$ ($A \ne B$) of the $i$-th segment.

It is guaranteed that no two segments lie on the same line.

第一行包含一个整数 $n$（$1 \le n \le 1000$）—— 表示线段的数量。

接下来的 $n$ 行，每行包含四个整数 $Ax_i, Ay_i, Bx_i, By_i$（$-10^6 \le Ax_i, Ay_i, Bx_i, By_i \le 10^6$）—— 分别表示第 $i$ 条线段两个端点 $A$ 和 $B$（其中 $A \ne B$）的坐标。

保证任意两条线段不共线。

Print a single integer — the number of distinct points with integer coordinates, which are covered by at least one segment.

输出一个整数——被至少一个线段覆盖的、具有整数坐标的互异点的个数。

The image for the first example:

Several key points are marked blue, the answer contains some non-marked points as well.

The image for the second example:

第一个示例的图像：

若干关键点被标为蓝色，答案中还包含一些未标记的点。

第二个示例的图像：