DWITE Online Computer Programming Contest, December 2010, Problem 1

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 will contain 5 lines, each line having 4 integers $-1000\le A,B,X,Y\le 1000$, where $(A,B)$ describes one endpoint of a line, and $(X,Y)$ describes another.

The output will contain 5 lines, each line containing the number of points along the line (not including the endpoints) that fall on the integer coordinates.

Sample Input

0 0 2 2
-1 -2 1 1

Sample Output

1
0

Problem Resource: DWITE