Replace by Average

AtCoder

IDarc130_f

Time2000ms

Memory256MB

Difficulty—

Given is a sequence of $N$ positive integers $A = (A_1, A_2, \ldots, A_N)$. You can do the following operation on this sequence any number of times. * Choose integers $i, j, k$ such that $1\leq i < j < k \leq N$ and $j = \frac{i+k}{2}$. Replace $A_j$ with $\lfloor\frac{A_i+A_k}{2}\rfloor$. Find the minimum possible value of $\sum_{i=1}^N A_i$ after the operations. ## Constraints * $3\leq N\leq 3\times 10^5$ * $1\leq A_i\leq 10^{12}$ ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\ldots$ $A_N$ [samples]

Samples

Input #1

5
2 2 5 5 4

Output #1

13

The following operations achieves $\sum_{i=1}^N A_i = 13$.

*   Do the operation with $(i,j,k) = (1,3,5)$. The sequence $A$ is now $(2,2,3,5,4)$.
*   Do the operation with $(i,j,k) = (3,4,5)$. The sequence $A$ is now $(2,2,3,3,4)$.
*   Do the operation with $(i,j,k) = (2,3,4)$. The sequence $A$ is now $(2,2,2,3,4)$.

Input #2

5
3 1 4 1 5

Output #2

Input #3

3
3 1 3

Output #3

Input #4

3
3 5 3

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Replace by Average",
    "description": {
      "content": "Given is a sequence of $N$ positive integers $A = (A_1, A_2, \\ldots, A_N)$. You can do the following operation on this sequence any number of times. *   Choose integers $i, j, k$ such that $1\\leq i <",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc130_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a sequence of $N$ positive integers $A = (A_1, A_2, \\ldots, A_N)$.\nYou can do the following operation on this sequence any number of times.\n\n*   Choose integers $i, j, k$ such that $1\\leq i <...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments