{"raw_statement":[{"iden":"statement","content":"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.\n\nDetermine the number _m_ — the smallest number of points you should add on the line to make the distances between all neighboring points equal."},{"iden":"input","content":"The first line contains a single integer _n_ (3 ≤ _n_ ≤ 100 000) — the number of points.\n\nThe 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."},{"iden":"output","content":"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."},{"iden":"examples","content":"Input\n\n3\n-5 10 5\n\nOutput\n\n1\n\nInput\n\n6\n100 200 400 300 600 500\n\nOutput\n\n0\n\nInput\n\n4\n10 9 0 -1\n\nOutput\n\n8"},{"iden":"note","content":"In the first example you can add one point with coordinate 0.\n\nIn the second example the distances between all neighboring points are already equal, so you shouldn't add anything."}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":null,"simple_statement":null,"has_page_source":false}