CF926B.Add Points

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.

一条直线上有 $n$ 个点，其中第 $i$ 个点的坐标为 $x_i$。所有这些坐标互不相同。

确定数 $m$ —— 即需要在该直线上添加的最少的点数，使得所有相邻点之间的距离均相等。

The first line contains a single integer n (3 ≤ n ≤ 100 000) — the number of points.

The second line contains a sequence of integers _x_1, _x_2, ..., x__n ( - 109 ≤ x__i ≤ 109) — the coordinates of the points. All these coordinates are distinct. The points can be given in an arbitrary order.

第一行包含一个整数 $n$（$3 \leq n \leq 100\,000$）—— 点的数量。

第二行包含一个整数序列 $x_1,\,x_2,\,...,\,x_n$（$-10^9 \leq x_i \leq 10^9$）—— 各点的坐标。所有坐标互不相同，且点的顺序是任意的。

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.

输出一个整数 m —— 为使所有相邻点之间的距离相等，需要在直线上添加的最少的点数。

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.

在第一个例子中，你可以添加一个坐标为 0 的点。

在第二个例子中，所有相邻点之间的距离已经相等，因此你无需添加任何点。