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Problems

Lands of Antarctica

Lands of Antarctica

prb1685.gif

Dots on the map of Antarctica shows the n polar stations, each of which has natural coordinates in a rectangular grid. The transition between the two stations is possible if the distance between them in a straight line less than two unit segments of the map. Stations, between which there exists a direct or indirect paths, are united into the land. Each station belongs to one land only.

You must find the number k of Arctic lands.

Input

The first line contains the number n of stations. Each of the next n lines contains two numbers - the coordinates of each station. All values are natural and do not exceed 100.

Output

Print the number of lands.

Time limit 1 second
Memory limit 128 MiB
Input example #1
10
2 4
6 2
2 1
2 6
4 3
4 1
1 5
5 2
1 3
3 5
Output example #1
3
Author Matviychuk S.V.
Source Stage III All-Ukrainian School Olympiad 2010-2011, Round 2, Zhytomyr