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.

Input is given from Standard Input in the following format:

```
$N$
$S$
$X$
```

If Takahashi wins when the two players play optimally, print `Takahashi`; if Aoki wins, print `Aoki`.

-   $1 \leq N \leq 2\times 10^5$
-   $S$ and $X$ have a length of $N$ each.
-   $S$ consists of `0`, $\ldots$, `9`.
-   $X$ consists of `A` and `T`.

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.