All the Same

AtCoder

IDarc179_f

Time2000ms

Memory256MB

Difficulty—

You are given a string $S$ of length $N$ consisting of the characters `A` and `B`. For a string $X$ of length $N$ consisting of the characters `1`, `2`, and `3`, the **score** is determined by the following procedure: > First, initialize the variables $h_1, h_2, h_3, P$ to $0$. > Then, for $i = 1, 2, \dots, N$ in this order, perform the following operations: > > * If the $i$\-th character of $S$ is `A`, perform operation A; if it is `B`, perform operation B. Let $d$ be the number represented by the $i$\-th character of $X$. > * **Operation A**: Add $2$ to $h_d$. > > * **Operation B**: If $d = 2$ or $h_d \neq h_2$, set $P$ to $-10^{100}$. Otherwise, add $1$ to both $h_d$ and $h_2$. > > * If $h_1 = h_2 = h_3$, add $1$ to $P$. > > > The final value of $P$ is the score. Print one string $X$ that maximizes the score. You have $T$ test cases to solve. ## Constraints * $1 \leq T \leq 10^5$ * $1 \leq N \leq 10^6$ * $S$ is a string of length $N$ consisting of `A` and `B`. * $T$ and $N$ are integers. * The sum of $N$ across all test cases is at most $10^6$. ## Input The input is given from Standard Input in the following format. Here, $\mathrm{test}_i$ denotes the $i$\-th test case. $T$ $\mathrm{test}_1$ $\mathrm{test}_2$ $\vdots$ $\mathrm{test}_T$ Each test case is given in the following format: $N$ $S$ [samples]

Samples

Input #1

5
4
ABBA
5
AAAAA
6
BBBBBB
7
ABABABA
20
AAABBBBBBBBAAABBBABA

Output #1

1333
12321
333333
1313212
33311111133121111311

Let us describe the changes in $(h_1, h_2, h_3, P)$ as we proceed with $i = 1, 2, \dots, N$.

*   For the first test case, $(0,0,0,0) \rightarrow (2,0,0,0) \rightarrow (2,1,1,0) \rightarrow (2,2,2,1) \rightarrow (2,2,4,1)$. The maximum score is $1$.
*   For the second test case, $(0,0,0,0) \rightarrow (2,0,0,0) \rightarrow (2,2,0,0) \rightarrow (2,2,2,1) \rightarrow (2,4,2,1) \rightarrow (4,4,2,1)$. The maximum score is $1$.

For the third, fourth, and fifth test cases, the maximum scores are $0$, $0$, and $2$, respectively. There may be multiple strings $X$ that maximize the score, but you only need to print one of them.

API Response (JSON)

{
  "problem": {
    "name": "All the Same",
    "description": {
      "content": "You are given a string $S$ of length $N$ consisting of the characters `A` and `B`. For a string $X$ of length $N$ consisting of the characters `1`, `2`, and `3`, the **score** is determined by the fol",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc179_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a string $S$ of length $N$ consisting of the characters `A` and `B`.\nFor a string $X$ of length $N$ consisting of the characters `1`, `2`, and `3`, the **score** is determined by the fol...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments