Touring Robot

TRobots Inc. fabricates and maintains touring robots. Every touring robot visits places in a Cartesian plane scene to accomplish its tasks. A task of a robot is a sequence of at least two points the robot must visit in a tour according to the following rules:

1. the robot starts at the first point of the task, facing the second one;
2. the robot moves in the direction it faces;
3. upon arrival to a point in the sequence, the robot turns counterclockwise an angle α, satisfying 0 ≤ α < 2π, until it faces the next point in the sequence (convention: the first point in a sequence is considered the following one for the last point in the sequence);
4. the robot ends at the first point of the sequence, facing the second one. As a net result of a tour, a robot completes an integer number of turns. TRobots Inc. finds the number of turns important as this number determines when a robot needs maintenance. Your job is to help TRobots Inc. calculating the number of turns a robot completes for a given tour. Input The input consists of several cases, each one comprising a set of lines with data that defines a task for a robot. A task for the robot is described by several input lines: • the first line defines the size N of the task, an integer satisfying 1 < N < 1000 and representing the number of places the robot must visit in the tour; • each of the following N lines has a pair of integer values, representing the Cartesian coordinates (x,y) of a point to visit in the tour (−106 ≤ x,y ≤ 106). It is guaranteed that each pair of consecutive points (considering the sequence as a circular list) are different. The end of the input is given by N = 0. Output For each given case, output one line with the number of turns a robot completes for the given tour. Sample Input 3 00 30 10 7 34 51 -2 -2 -2 2 -1 1 4 -1 1 -2 0

2/2 Sample Output 1 4