#P1036E. Covered Points

    ID: 4377 Type: RemoteJudge 2000ms 256MiB Tried: 0 Accepted: 0 Difficulty: (None) Uploaded By: Tags>fftgeometrynumber theory*2400

Covered Points

No submission language available for this problem.

Description

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.

Input

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.

Output

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

Samples

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

Note

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: