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geometry

number theory

*2400

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E. Covered Points

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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.

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.

Examples

Input

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

Output

42

Input

4

-1 2 1 2

-1 0 1 0

-1 0 0 3

0 3 1 0

Output

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:

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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