Counting Arrays

AtCoder

IDabc226_b

Time2000ms

Memory256MB

Difficulty—

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: $N$ $L_1$ $a_{1,1}$ $a_{1,2}$ $\dots$ $a_{1,L_1}$ $L_2$ $a_{2,1}$ $a_{2,2}$ $\dots$ $a_{2,L_2}$ $\vdots$ $L_N$ $a_{N,1}$ $a_{N,2}$ $\dots$ $a_{N,L_N}$ [samples]

Samples

Input #1

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.

Input #2

Output #2

4

Sample Input $2$ contains five sequences:

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

Input #3

1
1 1

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Counting Arrays",
    "description": {
      "content": "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 ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc226_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given $N$ sequences numbered $1$ to $N$.  \nSequence $i$ has a length of $L_i$ and its $j$\\-th element $(1 \\leq j \\leq L_i)$ is $a_{i,j}$.\nSequence $i$ and Sequence $j$ are considered the same ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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