Avoid Boring Matches

AtCoder

IDarc169_e

Time2000ms

Memory256MB

Difficulty—

There is a tournament with $2^N$ participants, numbered $1$ to $2^N$. The tournament proceeds as follows: * First, each participant is given a red or blue hat. You are given the color of the hat for each participant as the string $S$. Specifically, participant $i$ is given a red hat if the $i$\-th character ($1 \leq i \leq 2^N$) of $S$ is `R`, and a blue hat if it is `B`. * Then, the following operation is repeated until there is only one participant remaining: * Let $2k$ be the current number of participants. Divide the participants into $k$ pairs. You can freely choose how to pair them. Then, a match is held for each pair; the winner remains, and the loser leaves the tournament. The participants are numbered in descending order of strength, so the participant with the **smaller** number always wins. A match between two participants wearing red hats is called a **boring** match. Your goal is to arrange the pairings so that no boring matches occur during the tournament. Whether the goal is achievable or not depends on the string $S$. Hence, you have decided to tamper with $S$ before the start of the tournament. Specifically, you can perform the following operation zero or more times: * Choose two adjacent characters in $S$ and swap them. Determine whether it is possible to achieve the goal after operations. If it is, find the minimum number of operations required. ## Constraints * $1 \leq N \leq 18$ * $S$ is a string of length $2^N$ consisting of `R` and `B`. * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $S$ [samples]

Samples

Input #1

2
RRBB

Output #1

1

Without performing any operations, you cannot achieve the goal.
If you swap the second and third characters of $S$, making $S=$`RBRB`, you can achieve the goal as follows:

*   Give red, blue, red, and blue hats to participants $1$, $2$, $3$, and $4$, respectively.
*   Divide the four participants into two pairs $(1,4),(2,3)$. No boring matches occur here. After the matches, participants $1$ and $2$ remain.
*   Divide the two participants into one pair $(1,2)$. No boring matches occur here. After the match, participant $1$ remains.

Therefore, the answer is $1$.

Input #2

1
RR

Output #2

\-1

Input #3

4
RBBRRBRBBRBBBRBR

Output #3

Input #4

5
RBRRBRRRBRRRRRRRRRBBBBBBBBBBBBBB

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Avoid Boring Matches",
    "description": {
      "content": "There is a tournament with $2^N$ participants, numbered $1$ to $2^N$. The tournament proceeds as follows: *   First, each participant is given a red or blue hat. You are given the color of the hat fo",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc169_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a tournament with $2^N$ participants, numbered $1$ to $2^N$.\nThe tournament proceeds as follows:\n\n*   First, each participant is given a red or blue hat. You are given the color of the hat fo...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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