Both Sides Merger

AtCoder

IDarc092_c

Time2000ms

Memory256MB

Difficulty—

You have an integer sequence of length $N$: $a_1, a_2, ..., a_N$. You repeatedly perform the following operation until the length of the sequence becomes $1$: * First, choose an element of the sequence. * If that element is at either end of the sequence, delete the element. * If that element is not at either end of the sequence, replace the element with the sum of the two elements that are adjacent to it. Then, delete those two elements. You would like to maximize the final element that remains in the sequence. Find the maximum possible value of the final element, and the way to achieve it. ## Constraints * All input values are integers. * $2 \leq N \leq 1000$ * $|a_i| \leq 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $a_2$ $...$ $a_N$ [samples]

Samples

Input #1

5
1 4 3 7 5

Output #1

11
3
1
4
2

The sequence would change as follows:

*   After the first operation: $4, 3, 7, 5$
*   After the second operation: $4, 3, 7$
*   After the third operation: $11(4+7)$

Input #2

4
100 100 -1 100

Output #2

200
2
3
1

*   After the first operation: $100, 200(100+100)$
*   After the second operation: $200$

Input #3

6
-1 -2 -3 1 2 3

Output #3

4
3
2
1
2

*   After the first operation: $-4, 1, 2, 3$
*   After the second operation: $1, 2, 3$
*   After the third operation: $4$

Input #4

9
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Both Sides Merger",
    "description": {
      "content": "You have an integer sequence of length $N$: $a_1, a_2, ..., a_N$. You repeatedly perform the following operation until the length of the sequence becomes $1$: *   First, choose an element of the sequ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc092_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You have an integer sequence of length $N$: $a_1, a_2, ..., a_N$.\nYou repeatedly perform the following operation until the length of the sequence becomes $1$:\n\n*   First, choose an element of the sequ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments