Takahashi and Animals

AtCoder

IDabc251_e

Time2000ms

Memory256MB

Difficulty—

Takahashi is with $N$ animals. The $N$ animals are called Animal $1$, Animal $2$, $\ldots$, Animal $N$. Takahashi will perform the following $N$ kinds of action. Each action can be performed any number of (possibly zero) times. * Pay $A_1$ yen (the currency in Japan) to feed Animals $1$ and $2$. * Pay $A_2$ yen to feed Animals $2$ and $3$. * Pay $A_3$ yen to feed Animals $3$ and $4$. * $\cdots$ * Pay $A_i$ yen to feed Animals $i$ and $(i+1)$. * $\cdots$ * Pay $A_{N-2}$ yen to feed Animals $(N-2)$ and $(N-1)$. * Pay $A_{N-1}$ yen to feed Animals $(N-1)$ and $N$. * Pay $A_N$ yen to feed Animals $N$ and $1$. Note that the $N$\-th action above feeds "Animals $N$ and $1$." Print the minimum possible total cost to feed every animal at least once. ## Constraints * $2 \leq N \leq 3 \times 10^5$ * $1 \leq A_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\ldots$ $A_N$ [samples]

Samples

Input #1

5
2 5 3 2 5

Output #1

7

If Takahashi performs the $1$\-st, $3$\-rd, and $4$\-th actions once each, Animals $1$, $2$, $3$, $4$, and $5$ are fed once, once, once, twice, once, respectively, so every animal is fed at least once. The total cost to do so is $A_1 + A_3 + A_4 = 2 + 3 + 2 = 7$ yen, which is the minimum possible.

Input #2

20
29 27 79 27 30 4 93 89 44 88 70 75 96 3 78 39 97 12 53 62

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Takahashi and Animals",
    "description": {
      "content": "Takahashi is with $N$ animals. The $N$ animals are called Animal $1$, Animal $2$, $\\ldots$, Animal $N$. Takahashi will perform the following $N$ kinds of action. Each action can be performed any numbe",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc251_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi is with $N$ animals. The $N$ animals are called Animal $1$, Animal $2$, $\\ldots$, Animal $N$.\nTakahashi will perform the following $N$ kinds of action. Each action can be performed any numbe...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments