Problem Statement

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

Input is given from Standard Input in the following format:
N
S
X

Output

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

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.

Sample Input 1

2
35
AT

Sample 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.

Sample Input 2

5
12345
AAAAT

Sample Output 2

Aoki

Sample Input 3

5
67890
TTTTA

Sample Output 3

Takahashi

Sample Input 4

5
12345
ATATA

Sample Output 4

Aoki

见题面 Input 部分

见题面 Output 部分