Problem Statement

Takahashi is drawing a segment on grid paper.

From a certain square, a square that is ~x~ squares to the right and ~y~ squares above, is denoted as square ~(x, y)~ .

When Takahashi draws a segment connecting the lower left corner of square ~(A, B)~ and the lower left corner of square ~(C, D)~ , find the number of the squares crossed by the segment.

Here, the segment is said to cross a square if the segment has non-empty intersection with the region within the square, excluding the boundary.

Constraints

• ~1 \leq A, B, C, D \leq 10^9~
• At least one of ~A \neq C~ and ~B \neq D~ holds.

Input

The input is given from Standard Input in the following format:

~A~ ~B~ ~C~ ~D~

Output

Print the number of the squares crossed by the segment.

Sample Input 1

1 1 3 4

Sample Output 1

4

Sample Input 2

2 3 10 7

Sample Output 2

8