SP8132 STREETR - Street Trees

A group of trees is planted along a straight line. KOI is planning to plant more trees so that the distance between two adjacent trees is equal for all trees. For simplicity, each tree can only be planted on an integer coordinate. For example, if 4 trees were originally planted on coordinates (1, 3, 7, 13), and if KOI plants 3 more trees on coordinates (5, 9, 11), then the distance between two adjacent trees will equal for all trees. Your task is to calculate the minimal number of trees that KOI can plant so that the distance between two adjacent trees will equal for all trees.

The first line is an integer N (3

Output the minimal number of trees that must be planted.