Add and Remove

AtCoder

IDagc035_d

Time2000ms

Memory256MB

Difficulty—

There is a stack of $N$ cards, each of which has a non-negative integer written on it. The integer written on the $i$\-th card from the top is $A_i$. Snuke will repeat the following operation until two cards remain: * Choose three consecutive cards from the stack. * Eat the middle card of the three. * For each of the other two cards, replace the integer written on it by the sum of that integer and the integer written on the card eaten. * Return the two cards to the original position in the stack, without swapping them. Find the minimum possible sum of the integers written on the last two cards remaining. ## Constraints * $2 \leq N \leq 18$ * $0 \leq A_i \leq 10^9 (1\leq i\leq N)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $...$ $A_N$ [samples]

Samples

Input #1

4
3 1 4 2

Output #1

16

We can minimize the sum of the integers written on the last two cards remaining by doing as follows:

*   Initially, the integers written on the cards are $3$, $1$, $4$, and $2$ from top to bottom.
*   Choose the first, second, and third card from the top. Eat the second card with $1$ written on it, add $1$ to each of the other two cards, and return them to the original position in the stack. The integers written on the cards are now $4$, $5$, and $2$ from top to bottom.
*   Choose the first, second, and third card from the top. Eat the second card with $5$ written on it, add $5$ to each of the other two cards, and return them to the original position in the stack. The integers written on the cards are now $9$ and $7$ from top to bottom.
*   The sum of the integers written on the last two cards remaining is $16$.

Input #2

6
5 2 4 1 6 9

Output #2

Input #3

10
3 1 4 1 5 9 2 6 5 3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Add and Remove",
    "description": {
      "content": "There is a stack of $N$ cards, each of which has a non-negative integer written on it. The integer written on the $i$\\-th card from the top is $A_i$. Snuke will repeat the following operation until tw",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc035_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a stack of $N$ cards, each of which has a non-negative integer written on it. The integer written on the $i$\\-th card from the top is $A_i$.\nSnuke will repeat the following operation until tw...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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