Score : $200$ points

问题描述

给定从 $1$ 到 $N$ 编号的 $N$ 个序列。
第 $i$ 个序列的长度为 $L_i$，其第 $j$ 个元素 $(1 \leq j \leq L_i)$ 为 $a_{i,j}$。

若满足以下条件，则认为序列 $i$ 和序列 $j$ 相同：$L_i = L_j$ 且对于所有 $k$ $(1 \leq k \leq L_i)$，有 $a_{i,k} = a_{j,k}$。
请问从序列 $1$ 到序列 $N$ 中有多少种不同的序列？

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

You are given $N$ sequences numbered $1$ to $N$.
Sequence $i$ has a length of $L_i$ and its $j$-th element $(1 \leq j \leq L_i)$ is $a_{i,j}$.

Sequence $i$ and Sequence $j$ are considered the same when $L_i = L_j$ and $a_{i,k} = a_{j,k}$ for every $k$ $(1 \leq k \leq L_i)$.
How many different sequences are there among Sequence $1$ through Sequence $N$?

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq L_i \leq 2 \times 10^5$ $(1 \leq i \leq N)$
• $0 \leq a_{i,j} \leq 10^{9}$ $(1 \leq i \leq N, 1 \leq j \leq L_i)$
• The total number of elements in the sequences, $\sum_{i=1}^N L_i$, does not exceed $2 \times 10^5$.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$L_1$ $a_{1,1}$ $a_{1,2}$ $\dots$ $a_{1,L_1}$

$L_2$ $a_{2,1}$ $a_{2,2}$ $\dots$ $a_{2,L_2}$

$\vdots$

$L_N$ $a_{N,1}$ $a_{N,2}$ $\dots$ $a_{N,L_N}$

Output

Print the number of different sequences.

Sample Input 1

4
2 1 2
2 1 1
2 2 1
2 1 2

Sample Output 1

3

Sample Input $1$ contains four sequences:

• Sequence $1$ : $(1, 2)$
• Sequence $2$ : $(1, 1)$
• Sequence $3$ : $(2, 1)$
• Sequence $4$ : $(1, 2)$

Except that Sequence $1$ and Sequence $4$ are the same, these sequences are pairwise different, so we have three different sequences.

Sample Input 2

5
1 1
1 1
1 2
2 1 1
3 1 1 1

Sample Output 2

4

Sample Input $2$ contains five sequences:

• Sequence $1$ : $(1)$
• Sequence $2$ : $(1)$
• Sequence $3$ : $(2)$
• Sequence $4$ : $(1, 1)$
• Sequence $5$ : $(1, 1, 1)$

Sample Input 3

1
1 1

Sample Output 3

1

update @ 2024/3/10 09:54:49