Source

This problem is adapted from Long Long OJ. All rights reserved.

Problem Description

Given two endpoints $(x_1,y_1)$ and $(x_2,y_2)$ of a line segment on a plane, find the number of points on this line segment (excluding the endpoints) where both the $x$-coordinate and $y$-coordinate are integers.

Input Format

This problem contains multiple test cases.

For each test case, input a line with four integers $x_1,y_1,x_2,y_2$ separated by spaces.

The input ends with EOF.

Output Format

For each test case, output a line containing the answer.

Samples

1 11 5 3
114 514 114 514

3
0

Data Range

For $100\%$ of the data: $-10^9\le x_1,x_2,y_1,y_2\le 10^9$, and the number of input test cases does not exceed $25$.