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 $1 \le i < j \le l$ and $a_i < a_j$. For example, the sequence $[0, 2, 0, 2, 0]$ has an ascent because of the pair $(1, 4)$, but the sequence $[4, 3, 3, 3, 1]$ does not have an ascent.

The concatenation of sequences $p$ and $q$ is the sequence obtained by writing down $p$ and $q$ one right after another without changing the order. For example, the concatenation of $[0, 2, 0, 2, 0]$ 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 $p+q$.

Gyeonggeun thinks that sequences with ascents bring luck. For the new year he wants to make many such sequences. 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 check whether the concatenation $s_x + s_y$ has an ascent. He may select the same sequence twice, and the order of selection matters.

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

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

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

The sum of all $l_i$ does not exceed $100\,000$.

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

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 once per occurrence.