Lucky 7 Battle

AtCoder

IDabc195_e

Time2000ms

Memory256MB

Difficulty—

We have a string $S$ of length $N$ consisting of `0`, $\ldots$, `9`, and a string $X$ of length $N$ consisting of `A` and `T`. Additionally, there is a string $T$, which is initialized to an empty string. Takahashi and Aoki will play a game using these. The game consists of $N$ rounds. In the $i$\-th round $(1\leq i \leq N)$, the following happens: * If $X_i$ is `A`, Aoki does the operation below; if $X_i$ is `T`, Takahashi does it. * Operation: append $S_i$ or `0` at the end of $T$. After $N$ operations, $T$ will be a string of length $N$ consisting of `0`, $\ldots$, `9`. If $T$ is a multiple of $7$ as a base-ten number (after removing leading zeros), Takahashi wins; otherwise, Aoki wins. Determine the winner of the game when the two players play optimally. ## Constraints * $1 \leq N \leq 2\times 10^5$ * $S$ and $X$ have a length of $N$ each. * $S$ consists of `0`, $\ldots$, `9`. * $X$ consists of `A` and `T`. ## Input Input is given from Standard Input in the following format: $N$ $S$ $X$ [samples]

Samples

Input #1

2
35
AT

Output #1

Takahashi

In the $1$\-st round, Aoki appends `3` or `0` at the end of $T$. In the $2$\-nd round, Takahashi appends `5` or `0` at the end of $T$.
If Aoki appends `3`, Takahashi can append `5` to make $T$ `35`, a multiple of $7$.
If Aoki appends `0`, Takahashi can append `0` to make $T$ `00`, a multiple of $7$.
Thus, Takahashi can always win.

Input #2

5
12345
AAAAT

Output #2

Aoki

Input #3

5
67890
TTTTA

Output #3

Takahashi

Input #4

5
12345
ATATA

Output #4

Aoki

API Response (JSON)

{
  "problem": {
    "name": "Lucky 7 Battle",
    "description": {
      "content": "We have a string $S$ of length $N$ consisting of `0`, $\\ldots$, `9`, and a string $X$ of length $N$ consisting of `A` and `T`. Additionally, there is a string $T$, which is initialized to an empty str",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc195_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a string $S$ of length $N$ consisting of `0`, $\\ldots$, `9`, and a string $X$ of length $N$ consisting of `A` and `T`. Additionally, there is a string $T$, which is initialized to an empty str...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments