Crazy Dreamoon

Dreamoon likes algorithm competitions very much. But when he feels crazy because he cannot figure out any solution for any problem in a competition, he often draws many meaningless straight line segments on his calculation paper.

Dreamoon's calculation paper is special: it can be imagined as the plane with Cartesian coordinate system with range $\[0, 2000] \times \[0, 2000]$ for the coordinates. The grid lines are all lines of the form $x = c$ or $y = c$ for every integer $c$ between $0$ and $2000$, inclusive. So, the grid contains $2000 \times 2000$ squares.

Now, Dreamoon wonders how many grid squares are crossed by at least one of the lines he drew. Please help Dreamoon find the answer. Note that touching an edge of a grid square is not considered as crossing this square.

The first line of input contains an integer $N$ denoting the number of lines Dreamoon draw. The $i$-th line of following $N$ lines contains four integers $x\_{i1}, y\_{i1}, x\_{i2}, y\_{i2}$, denoting that the $i$-th segment Dreamoon drew is a straight line segment between points $(x\_{i1}, y\_{i1})$ and $(x\_{i2}, y\_{i2})$.

Output one integer on a single line: how many grid squares are crossed by at least one of the line segments which Dreamoon drew.

•  $1 \le N \le 2 \times 10^3$ 
•  $0 \le x\_{i1}, y\_{i1}, x\_{i2}, y\_{i2} \le 2 \times 10^3$ 
• the lengths of all line segments in input are non-zero