CF475F.Meta-universe

Consider infinite grid of unit cells. Some of those cells are planets.

Meta-universe M = {_p_1, _p_2, ..., p__k} is a set of planets. Suppose there is an infinite row or column with following two properties: 1) it doesn't contain any planet p__i of meta-universe M on it; 2) there are planets of M located on both sides from this row or column. In this case we can turn the meta-universe M into two non-empty meta-universes _M_1 and _M_2 containing planets that are located on respective sides of this row or column.

A meta-universe which can't be split using operation above is called a universe. We perform such operations until all meta-universes turn to universes.

Given positions of the planets in the original meta-universe, find the number of universes that are result of described process. It can be proved that each universe is uniquely identified not depending from order of splitting.

考虑一个无限大的单位格点网格，其中某些格点上存在行星。

元宇宙 $M = \{p_1, p_2, \dots, p_k\}$ 是一组行星的集合。假设存在一条无限长的行或列，满足如下两个条件：

1. 该行或列上不包含元宇宙 $M$ 中的任何行星 $p_i$；
2. 在该行或列的两侧均存在 $M$ 中的行星。
   此时，我们可以将元宇宙 $M$ 拆分为两个非空的元宇宙 $M_1$ 和 $M_2$，分别包含位于该行或列两侧的行星。

无法通过上述操作进一步拆分的元宇宙称为宇宙（universe）。我们持续执行该拆分操作，直至所有元宇宙都变为宇宙。

给定原始元宇宙中各行星的坐标，请计算最终得到的宇宙个数。可以证明，每个宇宙的划分结果是唯一的，与拆分顺序无关。

The first line of input contains an integer n, (1 ≤ n ≤ 105), denoting the number of planets in the meta-universe.

The next n lines each contain integers x__i and y__i, ( - 109 ≤ x__i, y__i ≤ 109), denoting the coordinates of the i-th planet. All planets are located in different cells.

输入的第一行包含一个整数 $n$（$1 \leq n \leq 10^5$），表示元宇宙中行星的数量。

接下来的 $n$ 行，每行包含两个整数 $x_i$ 和 $y_i$（$-10^9 \leq x_i, y_i \leq 10^9$），表示第 $i$ 颗行星的坐标。所有行星均位于不同的格子中。

Print the number of resulting universes.

输出最终的宇宙数量。

The following figure describes the first test case:

下图描述了第一个测试用例：