Czech Technical University in Prague

Faculty of Mathematics and Physics, Charles University in Prague

Faculty of Electrical Engineering and Computer Science, Technical University of Ostrava

Faculty of Informatics and Information Technologies, Slovak University of Technology

acm

Faculty of Informatics, Masaryk University

Faculty of Management Science and Informatics, University of Zilina

CTU Open Contest 2009

Arable Area

aa.c, aa.C, aa.java, aa.p

The prime minister has recently bought a piece of valuable agricultural land, which is situated

in a valley forming a regular grid of unit square fields. ACM would like to verify the transac-

tion, especially whether the price corresponds to the market value of the land, which is always

determined as the number of unit square fields fully contained in it.

Your task is to write a program that computes the market value. The piece of land forms a closed

polygon, whose vertices lie in the corners of unit fields.

For example, the polygon in the picture (it corresponds to the first scenario in Sample Input)

contains three square fields.

Input Specification

The input consists of several test scenarios. Each scenario starts with a line containing one

integer number N (3 ≤ N ≤ 100), the number of polygon vertices. Each of the following N

lines contains a pair of integers Xi and Yi, giving the coordinates of one vertex. The vertices

are listed in the order they appear along the boundary of the polygon. You may assume that

no coordinate will be less then -100 or more than 100 and that the boundary does not touch

or cross itself.

The last scenario is followed by a line containing single zero.

Output Specification

For each scenario, output one line with an integer number -- the number of unit squares that

are completely inside the polygon.

Sample Input

0 -50

-50 -51

-51 -50

-50 0

Output for Sample Input

2500