[ICPC 2022 Xi'an R] Strange Sum

Luogu

IDLGP9367

Time1000ms

Memory512MB

DifficultyP2

2022O2优化ICPC西安

Given a sequence $a_1, a_2, \ldots, a_n$. You are going to select zero or more elements of $a$ so that: if you select $a_i$, then in any interval of length $i$ (formally, in $a[j, j + i - 1]$ for any $1 \le j \le n - i + 1$) you can select at most $2$ elements. Calculate the maximal sum of the elements you select. ## Input The first line contains an integer $n$ ($2 \leq n \leq 10^5$). The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($-10^9 \leq a_i \leq 10^9$). ## Output Output a single integer denoting the answer. [samples] ## Note **Source**: The 2022 ICPC Asia Xi'an Regional Contest Problem J. **Author**: JohnVictor.

Samples

Input #1

4
1 4 3 2

Output #1

Input #2

3
-10 -10 -10

Output #2

API Response (JSON)

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  "problem": {
    "name": "[ICPC 2022 Xi'an R] Strange Sum",
    "description": {
      "content": "Given a sequence $a_1, a_2, \\ldots, a_n$. You are going to select zero or more elements of $a$ so that: if you select $a_i$, then in any interval of length $i$ (formally, in $a[j, j + i - 1]$ for any",
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    "platform": "Luogu",
    "limit": {
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      "memory_limit": 524288
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    "difficulty": {
      "LuoguStyle": "P2"
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    "is_remote": true,
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    "sync_url": null,
    "sign": "LGP9367"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given a sequence $a_1, a_2, \\ldots, a_n$.\n\nYou are going to select zero or more elements of $a$ so that: if you select $a_i$, then in any interval of length $i$ (formally, in $a[j, j + i - 1]$ for any...",
      "is_translate": false,
      "language": "English"
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}

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