Two Horses

Problem Description

In board games a piece always moves in a fixed way; for example, in Chinese chess the horse moves in the 日 shape. A schoolboy wondered whether the game would be more fun if the horse had two kinds of moves. So he ruled that the horse may move either in the 日 shape or, like the elephant, in the 田 shape.

His desk-mate, who likes Go, found this interesting and decided to try it on a $100 \times 100$ Go board. Choose two points $A$ and $B$; put a black stone at $A$ and a white stone at $B$, representing the two horses. A piece may move in either the 日 or the 田 shape. One player moves the black horse, the other moves the white horse. Whoever reaches the upper-left corner $(1,1)$ in the fewest moves wins.

Given the coordinates of $A$ and $B$, find the minimum number of moves each horse needs to reach $(1,1)$.

Input Format

The coordinates of points $A$ and $B$.

Output Format

The minimum number of moves for each horse.

Sample Input

12 16
18 10

Sample Output

8
9

Limitation

1 s, 1024 KiB for each test case.