# Problem C

Clumsy Cardinals

Everyone knows that in the game *chess*, a bishop
moves diagonally. Boring! Consider a new piece called a
**cardinal**. A cardinal moves diagonally, like a
bishop but they are clumsy. If its movement brings a cardinal
adjacent to another piece, it *trips* and falls on the
other piece. This results in the other piece being captured and
removed from the board. The cardinal that was moving then rests
on the captured piece’s square. Note two squares are adjacent
if they share a side, meaning they are directly horizontal or
vertical from one another. A cardinal can also capture pieces
like a bishop if the other piece lies on the same diagonal. A
cardinal can only move if the movement results in the capture
of another piece.

In this problem, you are given the initial locations of cardinal pieces on an infinite chessboard. Determine the minimum number of cardinals that remain on the board under some sequence of valid moves.

## Input

The first line of input contains a single integer $N$ ($1 \leq N \leq 10^5$), which is the number of cardinal pieces to consider.

The next line contains $2N$ space-separated integers $r_1, c_1, r_2, c_2, \ldots , r_ N, c_ N$ ($-10^{9} \leq r_ i, c_ i \leq 10^9$). These give the initial cardinal locations, so cardinal $i$ initially lies on square $(r_ i, c_ i)$. Furthermore, $|r_ i-r_ j| \geq 2$ or $|c_ i-c_ j| \geq 2$ (or both) for any $1 \leq i < j \leq N$.

## Output

Display the minimum number of cardinals that remain on the board though some sequence of valid moves.

Sample Input 1 | Sample Output 1 |
---|---|

3 -1 0 4 4 7 1 |
1 |

Sample Input 2 | Sample Output 2 |
---|---|

4 0 0 4 4 10 12 30 -7 |
2 |

Sample Input 3 | Sample Output 3 |
---|---|

7 1 0 1 2 1 7 3 4 3 7 7 1 7 5 |
3 |