Covered Points

有$n$条线段，问它们覆盖了多少个整点 $1 \le n \le 1000$ 点的坐标范围是$[-10^6,10^6]$的整数 保证每条线段不会退化成点 一些解释: 1. 定位点$p(x,y)$为整点，当且仅当$x,y$为整数 2. 如果一个整点在某条给定的线段上，那它就被覆盖了 3. 没有两条线段在同一直线上

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.

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.

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

9
0 0 4 4
-1 5 4 0
4 0 4 4
5 2 11 2
6 1 6 7
5 6 11 6
10 1 10 7
7 0 9 8
10 -1 11 -1

42

4
-1 2 1 2
-1 0 1 0
-1 0 0 3
0 3 1 0

7

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: