Add Points

有一条数轴上有n个点。输入n和每个点的坐标，输出使每两个相邻点距离相同，最少要加入多少个点。 样例1解释：加入一个坐标为0的点，则$\text{0-(-5)=5-0=10-5=5}$，所以至少加入一个点。

There are $ n $ points on a straight line, and the $ i $ -th point among them is located at $ x_{i} $ . All these coordinates are distinct. Determine the number $ m $ — the smallest number of points you should add on the line to make the distances between all neighboring points equal.

The first line contains a single integer $ n $ ( $ 3<=n<=100000 $ ) — the number of points. The second line contains a sequence of integers $ x_{1},x_{2},...,x_{n} $ ( $ -10^{9}<=x_{i}<=10^{9} $ ) — the coordinates of the points. All these coordinates are distinct. The points can be given in an arbitrary order.

Print a single integer $ m $ — the smallest number of points you should add on the line to make the distances between all neighboring points equal.

3
-5 10 5

1

6
100 200 400 300 600 500

0

4
10 9 0 -1

8

In the first example you can add one point with coordinate $ 0 $ . In the second example the distances between all neighboring points are already equal, so you shouldn't add anything.