Arithmetic Progression Subsequence

AtCoder

IDarc170_b

Time2000ms

Memory256MB

Difficulty—

You are given a sequence $A$ of length $N$ consisting of integers between $1$ and $\textbf{10}$, inclusive. A pair of integers $(l,r)$ satisfying $1\leq l \leq r\leq N$ is called a good pair if it satisfies the following condition: * The sequence $(A_l,A_{l+1},\ldots,A_r)$ contains a (possibly non-contiguous) arithmetic subsequence of length $3$. More precisely, there is a triple of integers $(i,j,k)$ with $l \leq i < j < k\leq r$ such that $A_j - A_i = A_k - A_j$. Find the number of good pairs. ## Constraints * $3 \leq N \leq 10^5$ * $1\leq A_i \leq 10$ * All input numbers are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $\ldots$ $A_N$ [samples]

Samples

Input #1

5
5 3 4 1 5

Output #1

3

There are three good pairs: $(l,r)=(1,4),(1,5),(2,5)$.
For example, the sequence $(A_1,A_2,A_3,A_4)$ contains an arithmetic subsequence of length $3$, which is $(5,3,1)$, so $(1,4)$ is a good pair.

Input #2

3
1 2 1

Output #2

0

There may be cases where no good pairs exist.

Input #3

9
10 10 1 3 3 7 2 2 5

Output #3

API Response (JSON)

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    "name": "Arithmetic Progression Subsequence",
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      "content": "You are given a sequence $A$ of length $N$ consisting of integers between $1$ and $\\textbf{10}$, inclusive. A pair of integers $(l,r)$ satisfying $1\\leq l \\leq r\\leq N$ is called a good pair if it sat",
      "description_type": "Markdown"
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    "difficulty": "None",
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      "statement_type": "Markdown",
      "content": "You are given a sequence $A$ of length $N$ consisting of integers between $1$ and $\\textbf{10}$, inclusive.\nA pair of integers $(l,r)$ satisfying $1\\leq l \\leq r\\leq N$ is called a good pair if it sat...",
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