Contest Duration: - (local time) (100 minutes) Back to Home
D - Do use hexagon grid /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

ある六角形のマスは 2 つの整数 i,j を用いて (i,j) と表されます。
マス (i,j) は以下の 6 つのマスと隣接します。

• (i-1,j-1)
• (i-1,j)
• (i,j-1)
• (i,j+1)
• (i+1,j)
• (i+1,j+1)

ただし、ある 2 つの黒いマスが同じ連結成分に属するとは、この 2 つの黒いマスの間をいくつかの隣接する黒いマスを辿って移動できることを指します。

### 制約

• 入力は全て整数
• 1 \le N \le 1000
• |X_i|,|Y_i| \le 1000
• (X_i,Y_i) は相異なる

### 入力

N
X_1 Y_1
X_2 Y_2
\vdots
X_N Y_N


### 入力例 1

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


### 出力例 1

3


• (-1,-1)
• (1,0),(2,0)
• (0,1),(0,2),(1,2)

### 入力例 2

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


### 出力例 2

4


### 入力例 3

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


### 出力例 3

1


Score : 400 points

### Problem Statement

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.

### 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.

### 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.

### Sample Input 1

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


### Sample Output 1

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 Input 2

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


### Sample Output 2

4


### Sample Input 3

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


### Sample Output 3

1