CF1284B.New Year and Ascent Sequence

A sequence $a = [a_1, a_2, \ldots, a_l]$ of length $l$ has an ascent if there exists a pair of indices $(i, j)$ such that $1 \le i \lt j \le l$ and $a_i \lt a_j$. For example, the sequence $[0, 2, 0, 2, 0]$ has an ascent because of the pair $(1, 4)$, but the sequence $[4, 3, 3, 3, 1]$ doesn't have an ascent.

Let's call a concatenation of sequences $p$ and $q$ the sequence that is obtained by writing down sequences $p$ and $q$ one right after another without changing the order. For example, the concatenation of the $[0, 2, 0, 2, 0]$ and $[4, 3, 3, 3, 1]$ is the sequence $[0, 2, 0, 2, 0, 4, 3, 3, 3, 1]$. The concatenation of sequences $p$ and $q$ is denoted as $p+q$.

Gyeonggeun thinks that sequences with ascents bring luck. Therefore, he wants to make many such sequences for the new year. Gyeonggeun has $n$ sequences $s_1, s_2, \ldots, s_n$ which may have different lengths.

Gyeonggeun will consider all $n^2$ pairs of sequences $s_x$ and $s_y$ ($1 \le x, y \le n$), and will check if its concatenation $s_x + s_y$ has an ascent. Note that he may select the same sequence twice, and the order of selection matters.

Please count the number of pairs ($x, y$) of sequences $s_1, s_2, \ldots, s_n$ whose concatenation $s_x + s_y$ contains an ascent.

长度为 $l$ 的序列 $a = [a_1, a_2, \ldots, a_l]$ 若存在一对下标 $(i, j)$ 满足 $1 \le i \lt j \le l$ 且 $a_i \lt a_j$，则称该序列具有上升段（ascent）。例如，序列 $[0, 2, 0, 2, 0]$ 具有上升段，因为存在下标对 $(1, 4)$；而序列 $[4, 3, 3, 3, 1]$ 则不具有上升段。

我们把序列 $p$ 和 $q$ 的**拼接（concatenation）**定义为将 $p$ 和 $q$ 按原有顺序依次写在一起所得到的序列。例如，序列 $[0, 2, 0, 2, 0]$ 与 $[4, 3, 3, 3, 1]$ 的拼接结果为 $[0, 2, 0, 2, 0, 4, 3, 3, 3, 1]$。序列 $p$ 与 $q$ 的拼接记作 $p+q$。

京根认为具有上升段的序列会带来好运。因此，他希望在新年到来之际构造尽可能多的此类序列。京根手头有 $n$ 个序列 $s_1, s_2, \ldots, s_n$，它们的长度可能各不相同。

京根将考察所有 $n^2$ 对序列 $(s_x, s_y)$（其中 $1 \le x, y \le n$），并检查其拼接序列 $s_x + s_y$ 是否具有上升段。注意：他允许选择同一个序列两次，且顺序是有区别的（即 $(x,y)$ 与 $(y,x)$ 被视为不同对）。

请统计满足条件的序列对 $(x, y)$ 的数量，即拼接序列 $s_x + s_y$ 中包含上升段的对数。

The first line contains the number $n$ ($1 \le n \le 100\,000$) denoting the number of sequences.

The next $n$ lines contain the number $l_i$ ($1 \le l_i$) denoting the length of $s_i$, followed by $l_i$ integers $s_{i, 1}, s_{i, 2}, \ldots, s_{i, l_i}$ ($0 \le s_{i, j} \le 10^6$) denoting the sequence $s_i$.

It is guaranteed that the sum of all $l_i$ does not exceed $100\,000$.

第一行包含一个整数 $n$（$1 \le n \le 100\,000$），表示序列的个数。

接下来的 $n$ 行中，每行首先给出一个整数 $l_i$（$1 \le l_i$），表示序列 $s_i$ 的长度，随后是 $l_i$ 个整数 $s_{i, 1}, s_{i, 2}, \ldots, s_{i, l_i}$（$0 \le s_{i, j} \le 10^6$），表示序列 $s_i$。

保证所有 $l_i$ 的总和不超过 $100\,000$。

Print a single integer, the number of pairs of sequences whose concatenation has an ascent.

输出一个整数，表示满足其连接序列具有上升段的序列对的数量。

For the first example, the following $9$ arrays have an ascent: $[1, 2], [1, 2], [1, 3], [1, 3], [1, 4], [1, 4], [2, 3], [2, 4], [3, 4]$. Arrays with the same contents are counted as their occurences.

对于第一个样例，以下 $9$ 个数组具有上升段（ascent）：$[1, 2], [1, 2], [1, 3], [1, 3], [1, 4], [1, 4], [2, 3], [2, 4], [3, 4]$。内容相同的数组按其出现次数分别计数。