Gomamayo Sequence

AtCoder

IDabc346_d

Time2000ms

Memory256MB

Difficulty—

You are given a string $S$ of length $N$ consisting of `0` and `1`. A string $T$ of length $N$ consisting of `0` and `1` is a **good string** if and only if it satisfies the following condition: * There is exactly one integer $i$ such that $1 \leq i \leq N - 1$ and the $i$\-th and $(i + 1)$\-th characters of $T$ are the same. For each $i = 1,2,\ldots, N$, you can choose whether or not to perform the following operation once: * If the $i$\-th character of $S$ is `0`, replace it with `1`, and vice versa. The cost of this operation, if performed, is $C_i$. Find the minimum total cost required to make $S$ a good string. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $S$ is a string of length $N$ consisting of `0` and `1`. * $1 \leq C_i \leq 10^9$ * $N$ and $C_i$ are integers. ## Input The input is given from Standard Input in the following format: $N$ $S$ $C_1$ $C_2$ $\ldots$ $C_N$ [samples]

Samples

Input #1

5
00011
3 9 2 6 4

Output #1

7

Performing the operation for $i = 1, 5$ and not performing it for $i = 2, 3, 4$ makes $S =$ `10010`, which is a good string. The cost incurred in this case is $7$, and it is impossible to make $S$ a good string for less than $7$, so print $7$.

Input #2

4
1001
1 2 3 4

Output #2

Input #3

11
11111100111
512298012 821282085 543342199 868532399 690830957 973970164 928915367 954764623 923012648 540375785 925723427

Output #3

2286846953

API Response (JSON)

{
  "problem": {
    "name": "Gomamayo Sequence",
    "description": {
      "content": "You are given a string $S$ of length $N$ consisting of `0` and `1`. A string $T$ of length $N$ consisting of `0` and `1` is a **good string** if and only if it satisfies the following condition: *   ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc346_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a string $S$ of length $N$ consisting of `0` and `1`.\nA string $T$ of length $N$ consisting of `0` and `1` is a **good string** if and only if it satisfies the following condition:\n\n*   ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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