Count Arithmetic Subsequences

AtCoder

IDabc362_e

Time2000ms

Memory256MB

Difficulty—

You are given a sequence $A = (A_1, A_2, \dots, A_N)$ of length $N$. For each $k = 1, 2, \dots, N$, find the number, modulo $998244353$, of (not necessarily contiguous) subsequences of $A$ of length $k$ that are arithmetic sequences. Two subsequences are distinguished if they are taken from different positions, even if they are equal as sequences. What is a subsequence? A subsequence of a sequence $A$ is a sequence obtained by deleting zero or more elements from $A$ and arranging the remaining elements without changing the order. ## Constraints * $1 \leq N \leq 80$ * $1 \leq A_i \leq 10^9$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

5
1 2 3 2 3

Output #1

5 10 3 0 0

*   There are $5$ subsequences of length $1$, all of which are arithmetic sequences.
*   There are $10$ subsequences of length $2$, all of which are arithmetic sequences.
*   There are $3$ subsequences of length $3$ that are arithmetic sequences: $(A_1, A_2, A_3)$, $(A_1, A_2, A_5)$, and $(A_1, A_4, A_5)$.
*   There are no arithmetic subsequences of length $4$ or more.

Input #2

4
1 2 3 4

Output #2

4 6 2 1

Input #3

1
100

Output #3

API Response (JSON)

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    "name": "Count Arithmetic Subsequences",
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      "memory_limit": 262144
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      "statement_type": "Markdown",
      "content": "You are given a sequence $A = (A_1, A_2, \\dots, A_N)$ of length $N$. For each $k = 1, 2, \\dots, N$, find the number, modulo $998244353$, of (not necessarily contiguous) subsequences of $A$ of length $...",
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