Contest Duration: ~ (local time)
E - 方眼紙と線分 / Segment on Grid Paper

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

マス (A, B) の左下の点と マス (C, D) の左下の点を結んで線分を書くとき、線分が横切るマスの個数を求めてください。

ただし、線分があるマスの内側(境界は含まない)を通るとき、「線分がそのマスを横切る」と言います。

### 制約

• 1 \leq A, B, C, D \leq 10^9
• A \neq C もしくは B \neq D の少なくとも一方が成り立つ。

### 入力

A B C D


### 入力例 1

1 1 3 4


### 出力例 1

4


### 入力例 2

2 3 10 7


### 出力例 2

8


Score : 100 points

### 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