B"There are n points on a straight line, and the i-th point among them is located at xi. 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 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89100 xe2 x80 x89000) -- the number of points. The second line contains a sequence of integers x1, xe2 x80 x89x2, xe2 x80 x89..., xe2 x80 x89xn ( xe2 x80 x89- xe2 x80 x89109 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89xi xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89109) -- 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. 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. "...