Forest

AtCoder

IDarc211_c

Time2000ms

Memory256MB

Difficulty—

You are given a positive integer $N$, a string $S$ of length $N$ consisting of `#` and `.`, and a length-$N$ sequence of positive integers $R=(R_1,R_2,\dots,R_N)$. There is a forest with $N$ sections arranged in a single horizontal line. The sections are numbered $1,2,\dots,N$ from left to right. Some sections have trees. Specifically, section $i$ has a tree if and only if the $i$\-th character of $S$ is `#`. It is guaranteed that the following operation can be performed at least once. You can repeat the following operation as many times as you like: * Choose two sections without trees. Let sections $i$ and $j$ (where $i < j$) be the chosen sections from left to right. Then, all trees between sections $i$ and $j$ are removed, and you gain a reward of $R_i+R_j$. Here, you cannot perform an operation that removes no trees. Find the number of ways to perform the **first** operation to achieve the maximum possible total reward. Two ways are considered distinct if and only if there exists a section chosen in one way but not in the other. ## Constraints * $3\leq N\leq 2\times 10^5$ * The length of $S$ is $N$, and each character is `#` or `.`. * $1\leq R_i\leq 10^9$ $(1\leq i\leq N)$ * The operation can be performed at least once. * $N$ and $R_i$ are integers. ## Input The input is given from Standard Input in the following format: $N$ $S$ $R_1$ $R_2$ $\dots$ $R_N$ [samples]

Samples

Input #1

8
...###..
20 25 1 1 30 2 1 1

Output #1

2

There are six ways to perform the first operation, as follows:

*   Choose sections $1$ and $7$. The trees at sections $4,5,6$ are removed, and you gain a reward of $21$.
*   Choose sections $1$ and $8$. The trees at sections $4,5,6$ are removed, and you gain a reward of $21$.
*   Choose sections $2$ and $7$. The trees at sections $4,5,6$ are removed, and you gain a reward of $26$.
*   Choose sections $2$ and $8$. The trees at sections $4,5,6$ are removed, and you gain a reward of $26$.
*   Choose sections $3$ and $7$. The trees at sections $4,5,6$ are removed, and you gain a reward of $2$.
*   Choose sections $3$ and $8$. The trees at sections $4,5,6$ are removed, and you gain a reward of $2$.

No matter which operation is performed, all trees are removed, so a second operation cannot be performed. The maximum possible total reward is $26$.

Input #2

5
.#.#.
211 182 192 182 211

Output #2

2

The maximum possible total reward is $825$.
Note that the goal is not to maximize the reward obtained in the first operation. If you choose sections $1$ and $5$ first, you can gain a reward of $422$, but no operation can be performed afterwards, and the total reward cannot reach $825$.

Input #3

11
#..#.##.#..
192 192 192 211 182 192 182 192 182 211 182

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Forest",
    "description": {
      "content": "You are given a positive integer $N$, a string $S$ of length $N$ consisting of `#` and `.`, and a length-$N$ sequence of positive integers $R=(R_1,R_2,\\dots,R_N)$. There is a forest with $N$ sections ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc211_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a positive integer $N$, a string $S$ of length $N$ consisting of `#` and `.`, and a length-$N$ sequence of positive integers $R=(R_1,R_2,\\dots,R_N)$.\nThere is a forest with $N$ sections ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments