Czech ACM Student Chapter

Czech Technical University in Prague

Charles University in Prague

Technical University of Ostrava

ˇ

Slovak University of Technology

University of Zilina

Masaryk University

University of West Bohemia

CTU Open Contest 2017

Punching Power

power.c, power.cpp, power.c11, Power.java, power.py

The park management finally decided to install some popular boxing machines at various strate-

gic places in the park. In fact, to compensate for the previous lack of machines, they decided to

install as many machines as possible. Surprisingly enough, the park is not going to be choked

with new machines because there are some quite serious legal limitations regarding the locations

of the machines. The management has marked all possible boxing machine locations and their

respective coordinates on the park plan. Additionally, they also have to respect manufacturer

security rule: The distance between any two boxing machines has to be at least 1.3 meters.

Help the management to establish the maximum possible number of boxing machines which can

be installed in the park.

Input Specification

There are several test cases. Each case starts with a line containing one integer N which specifies

the number of possible boxing machine locations in the park (1 ≤ N ≤ 2000). Next, there are N

lines representing the location coordinates, each line describes one location by a pair of integer

coordinates in meters. All locations in one test case are unique. Each coordinate is non-negative

and less than or equal to 109.

You are guaranteed that all locations form a single connected group, that is, it is possible to

start in any location and reach any other location by a sequence of steps, each of which changes

exactly one coordinate by 1, without leaving the area suitable for placing boxing machines.

Output Specification

For each test case, print a single line with one integer representing the maximum number of

boxing machines which can be installed in the park.

Sample Input

4

0

0

0

1

1

0

1

1

6

0

1

1

0

1

1

1

2

1

3

2

2

Output for Sample Input

2

4