Select Half

AtCoder

IDabc162_f

Time2000ms

Memory256MB

Difficulty—

Given is an integer sequence $A_1, ..., A_N$ of length $N$. We will choose exactly $\left\lfloor \frac{N}{2} \right\rfloor$ elements from this sequence so that no two adjacent elements are chosen. Find the maximum possible sum of the chosen elements. Here $\lfloor x \rfloor$ denotes the greatest integer not greater than $x$. ## Constraints * $2 \leq N \leq 2\times 10^5$ * $|A_i|\leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $...$ $A_N$ [samples]

Samples

Input #1

6
1 2 3 4 5 6

Output #1

12

Choosing $2$, $4$, and $6$ makes the sum $12$, which is the maximum possible value.

Input #2

5
-1000 -100 -10 0 10

Output #2

0

Choosing $-10$ and $10$ makes the sum $0$, which is the maximum possible value.

Input #3

10
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Output #3

5000000000

Watch out for overflow.

Input #4

27
18 -28 18 28 -45 90 -45 23 -53 60 28 -74 -71 35 -26 -62 49 -77 57 24 -70 -93 69 -99 59 57 -49

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Select Half",
    "description": {
      "content": "Given is an integer sequence $A_1, ..., A_N$ of length $N$. We will choose exactly $\\left\\lfloor \\frac{N}{2} \\right\\rfloor$ elements from this sequence so that no two adjacent elements are chosen. Fin",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc162_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is an integer sequence $A_1, ..., A_N$ of length $N$.\nWe will choose exactly $\\left\\lfloor \\frac{N}{2} \\right\\rfloor$ elements from this sequence so that no two adjacent elements are chosen.\nFin...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments