CF1190D.Tokitsukaze and Strange Rectangle

There are $n$ points on the plane, the $i$-th of which is at $(x_i, y_i)$. Tokitsukaze wants to draw a strange rectangular area and pick all the points in the area.

The strange area is enclosed by three lines, $x = l$, $y = a$ and $x = r$, as its left side, its bottom side and its right side respectively, where $l$, $r$ and $a$ can be any real numbers satisfying that $l \lt r$. The upper side of the area is boundless, which you can regard as a line parallel to the $x$-axis at infinity. The following figure shows a strange rectangular area.

A point $(x_i, y_i)$ is in the strange rectangular area if and only if $l \lt x_i \lt r$ and $y_i \gt a$. For example, in the above figure, $p_1$ is in the area while $p_2$ is not.

Tokitsukaze wants to know how many different non-empty sets she can obtain by picking all the points in a strange rectangular area, where we think two sets are different if there exists at least one point in one set of them but not in the other.

平面上有 $n$ 个点，其中第 $i$ 个点的坐标为 $(x_i, y_i)$。Tokitsukaze 想画出一个特殊的矩形区域，并选取该区域内所有的点。

该特殊区域由三条直线 $x = l$、$y = a$ 和 $x = r$ 围成，分别作为其左侧边、底边和右侧边，其中 $l$、$r$ 和 $a$ 可取任意满足 $l \lt r$ 的实数。该区域的上边界无界，可视为一条在无穷远处、平行于 $x$ 轴的直线。下图展示了一个这样的特殊矩形区域。

当且仅当 $l \lt x_i \lt r$ 且 $y_i \gt a$ 时，点 $(x_i, y_i)$ 位于该特殊矩形区域内。例如，在上图中，$p_1$ 在该区域内，而 $p_2$ 不在。

Tokitsukaze 想知道：通过选取某个特殊矩形区域内的所有点，她最多能得到多少个互不相同的非空点集？这里认为两个点集不同，当且仅当其中至少有一个点属于其中一个集合但不属于另一个集合。

The first line contains a single integer $n$ ($1 \leq n \leq 2 \times 10^5$) — the number of points on the plane.

The $i$-th of the next $n$ lines contains two integers $x_i$, $y_i$ ($1 \leq x_i, y_i \leq 10^9$) — the coordinates of the $i$-th point.

All points are distinct.

第一行包含一个整数 $n$（$1 \leq n \leq 2 \times 10^5$）—— 表示平面上的点的数量。

接下来的 $n$ 行中，第 $i$ 行包含两个整数 $x_i$、$y_i$（$1 \leq x_i, y_i \leq 10^9$）—— 表示第 $i$ 个点的坐标。

所有点互不相同。

Print a single integer — the number of different non-empty sets of points she can obtain.

输出一个整数——她能得到的不同非空点集的个数。

For the first example, there is exactly one set having $k$ points for $k = 1, 2, 3$, so the total number is $3$.

For the second example, the numbers of sets having $k$ points for $k = 1, 2, 3$ are $3$, $2$, $1$ respectively, and their sum is $6$.

For the third example, as the following figure shows, there are

• $2$ sets having one point;
• $3$ sets having two points;
• $1$ set having four points.

Therefore, the number of different non-empty sets in this example is $2 + 3 + 0 + 1 = 6$.

第一个样例中，恰好存在一个包含 $k$ 个点的集合，其中 $k = 1, 2, 3$，因此总数为 $3$。

第二个样例中，包含 $k$ 个点的集合的数量（$k = 1, 2, 3$）分别为 $3$、$2$、$1$，其总和为 $6$。

第三个样例中，如下图所示，存在：

• $2$ 个仅含一个点的集合；
• $3$ 个含有两个点的集合；
• $1$ 个含有四个点的集合。

因此，本样例中不同的非空集合数量为 $2 + 3 + 0 + 1 = 6$。