Rotate and Palindrome

AtCoder

IDabc286_c

Time2000ms

Memory256MB

Difficulty—

You are given a string $S$ of length $N$. Let $S_i\ (1\leq i \leq N)$ be the $i$\-th character of $S$ from the left. You may perform the following two kinds of operations zero or more times in any order: * Pay $A$ yen (the currency in Japan). Move the leftmost character of $S$ to the right end. In other words, change $S_1S_2\ldots S_N$ to $S_2\ldots S_NS_1$. * Pay $B$ yen. Choose an integer $i$ between $1$ and $N$, and replace $S_i$ with any lowercase English letter. How many yen do you need to pay to make $S$ a palindrome? What is a palindrome? A string $T$ is a palindrome if and only if the $i$\-th character from the left and the $i$\-th character from the right are the same for all integers $i$ ($1 \le i \le |T|$), where $|T|$ is the length of $T$. ## Constraints * $1\leq N \leq 5000$ * $1\leq A,B\leq 10^9$ * $S$ is a string of length $N$ consisting of lowercase English letters. * All values in the input except for $S$ are integers. ## Input The input is given from Standard Input in the following format: $N$ $A$ $B$ $S$ [samples]

Samples

Input #1

5 1 2
rrefa

Output #1

3

First, pay $2$ yen to perform the operation of the second kind once: let $i=5$ to replace $S_5$ with `e`. $S$ is now `rrefe`.
Then, pay $1$ yen to perform the operation of the first kind once. $S$ is now `refer`, which is a palindrome.
Thus, you can make $S$ a palindrome for $3$ yen. Since you cannot make $S$ a palindrome for $2$ yen or less, $3$ is the answer.

Input #2

8 1000000000 1000000000
bcdfcgaa

Output #2

4000000000

Note that the answer may not fit into a $32$\-bit integer type.

API Response (JSON)

{
  "problem": {
    "name": "Rotate and Palindrome",
    "description": {
      "content": "You are given a string $S$ of length $N$. Let $S_i\\ (1\\leq i \\leq N)$ be the $i$\\-th character of $S$ from the left. You may perform the following two kinds of operations zero or more times in any ord",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc286_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a string $S$ of length $N$. Let $S_i\\ (1\\leq i \\leq N)$ be the $i$\\-th character of $S$ from the left.\nYou may perform the following two kinds of operations zero or more times in any ord...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments