Problem7007--ABC269 —— D - Do use hexagon grid

7007: ABC269 —— D - Do use hexagon grid

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Time Limit : 1.000 sec  Memory Limit : 256 MiB

Description

We have an infinite hexagonal grid shown below. Initially, all squares are white.



A hexagonal cell is represented as $(i,j)$ with two integers $i$ and $j$.
Cell $(i,j)$ is adjacent to the following six cells:
  • $(i−1,j−1)$
  • $(i−1,j)$
  • $(i,j−1)$
  • $(i,j+1)$
  • $(i+1,j)$
  • $(i+1,j+1)$
Takahashi has painted $N$ cells $(X_1,Y_1),(X_2,Y_2),\dots,(X_N,Y_N)$ black.
Find the number of connected components formed by the black cells.
Two black cells belong to the same connected component when one can travel between those two black cells by repeatedly moving to an adjacent black cell.

Input

The input is given from Standard Input in the following format:
$N$
$X_1\ Y_1$
$X_2\ Y_2$
$\vdots$
$X_N\ Y_N$

Output

Print the answer as an integer.

Constraints

All values in the input are integers.
$1 \le N \le 1000$
$|X_i|,|Y_i| \le 1000$
The pairs $(X_i,Y_i)$ are distinct.

Sample 1 Input

6
-1 -1
0 1
0 2
1 0
1 2
2 0

Sample 1 Output

3
After Takahashi paints cells black, the grid looks as shown below.



The black squares form the following three connected components:
  • $(-1,-1)$
  • $(1,0),(2,0)$
  • $(0,1),(0,2),(1,2)$

Sample 2 Input

4
5 0
4 1
-3 -4
-2 -5

Sample 2 Output

4

Sample 3 Input

5
2 1
2 -1
1 0
3 1
1 -1

Sample 3 Output

1

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