When talking about points on the Cartesian plane, most people tend to deal only with points with integer coordinates (i.e. points whose `x`- and `y`-coordinates are integers). Given a line segment with integer coordinates, you are curious about how many points on the line segment (other than the endpoints) have integer coordinates.

The input file **DATA1.txt** will contain 5 lines, where each line has 4 integers −1000 ≤ `A`, `B`, `X`, `Y` ≤ 1000, such that (`A`, `B`) and (`X`,`Y`) describe the two endpoints of the line segment.

The output file **OUT1.txt** will contain 5 lines, with each line containing the number of points along the line (excluding the endpoints) that fall on integer coordinates.

Sample Input (first 2 shown):

```
0 0 2 2
-1 -2 1 1
```

Sample Output (first 2 shown):

```
1
0
```