Election

AtCoder

IDarc172_c

Time2000ms

Memory256MB

Difficulty—

This year's AtCoder mayoral election has two candidates, A and B, and $N$ voters have cast their votes. The voters are assigned numbers from $1$ to $N$, and voter $i$ $(1 \leq i \leq N)$ voted for candidate $c_i$. Now, the votes will be counted. As each vote is counted, the provisional result will be announced as one of the following three outcomes: * **Result A:** Currently, candidate A has more votes. * **Result B:** Currently, candidate B has more votes. * **Result C:** Currently, candidates A and B have the same number of votes. There is a rule regarding the order of vote counting: votes from all voters except voter $1$ must be counted in ascending order of their voter numbers. (The vote from voter $1$ may be counted at any time.) How many different sequences of provisional results could be announced? What is a sequence of provisional results?Let $s_i$ be the result (`A`, `B`, or `C`) reported when the $i$\-th vote $(1 \leq i \leq N)$ is counted. The sequence of provisional results refers to the string $s_1 s_2 \dots s_N$. ## Constraints * $N$ is an integer such that $2 \leq N \leq 1000000$. * Each of $c_1, c_2, \dots, c_N$ is `A` or `B`. ## Input The input is given from Standard Input in the following format: $N$ $c_1 c_2 \cdots c_N$ [samples]

Samples

Input #1

4
AABB

Output #1

3

In this sample input, there are four possible orders in which the votes may be counted:

*   The votes are counted in the order of voter $1 \to 2 \to 3 \to 4$.
*   The votes are counted in the order of voter $2 \to 1 \to 3 \to 4$.
*   The votes are counted in the order of voter $2 \to 3 \to 1 \to 4$.
*   The votes are counted in the order of voter $2 \to 3 \to 4 \to 1$.

The sequences of preliminary results for these will be `AAAC`, `AAAC`, `ACAC`, `ACBC` from top to bottom, so there are three possible sequences of preliminary results.

Input #2

4
AAAA

Output #2

1

No matter the order of counting, the sequence of preliminary results will be `AAAA`.

Input #3

10
BBBAAABBAA

Output #3

Input #4

172
AABAAAAAABBABAABBBBAABBAAABBABBABABABBAAABAAABAABAABBBBABBBABBABBBBBBBBAAABAAABAAABABBBAABAAAABABBABBABBBBBABAABAABBBABABBAAAABAABABBBABAAAABBBBABBBABBBABAABBBAAAABAAABAAAB

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Election",
    "description": {
      "content": "This year's AtCoder mayoral election has two candidates, A and B, and $N$ voters have cast their votes. The voters are assigned numbers from $1$ to $N$, and voter $i$ $(1 \\leq i \\leq N)$ voted for can",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc172_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "This year's AtCoder mayoral election has two candidates, A and B, and $N$ voters have cast their votes. The voters are assigned numbers from $1$ to $N$, and voter $i$ $(1 \\leq i \\leq N)$ voted for can...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments