P4671 [BalticOI 2011] Polygon (Day2)

题目描述

A simple polygon with NN vertices is drawn on an infinite rectangular grid. For such a polygon, only neighboring edges touch at their common vertex; no other of its edges intersect or touch. All vertices of the polygon lie on grid points, i.e., vertices have integer coordinates.

Your task is to find the total length of grid line segments which lie strictly inside the given polygon (these line segments are highlighted in the drawings below).

输入格式

The first line of input contains a single integer NN, the number of vertices of the polygon. Each of the following NN lines contains two integers xx and yy, the coordinates of one vertex. The vertices are given either in clockwise or counterclockwise order. All vertices are distinct, but more than two con