E - Shiritori

Score : $500$ points

Problem Statement

The Takahashi Dictionary lists $N$ words; the $i$-th word $(1 \leq i \leq N)$ is $s_i$.

Using this dictionary, Takahashi and Aoki will play $3$-shiritori, which goes as follows.

• Takahashi and Aoki alternately say words, with Takahashi going first.
• Each player must say a word beginning with the last three characters of the previous word. For example, if a player says Takahashi, the next player can say ship or shield along with other choices, but not Aoki, sing, or his.
• Uppercase and lowercase are distinguished. For example, a player cannot say ShIp following Takahashi.
• A player who becomes unable to say a word loses.
• A player cannot say a word not listed in the dictionary.
• The same word can be used multiple times.

For each $i$ $(1 \leq i \leq N)$, determine who will win when Takahashi starts the game by saying the word $s_i$. Here, we assume that both players play optimally. More specifically, each player gives first priority to avoiding his loss and second priority to defeating the opponent.

Constraints

• $N$ is an integer between $1$ and $2 \times 10^5$ (inclusive).
• $s_i$ is a string of length between $3$ and $8$ (inclusive) consisting of lowercase and uppercase English letters.

Input

Input is given from Standard Input in the following format:

$N$

$s_1$

$s_2$

$\vdots$

$s_N$

Output

Print $N$ lines. The $i$-th line $(1 \leq i \leq N)$ should contain Takahashi if Takahashi wins when Takahashi starts the game by saying the word $s_i$, Aoki if Aoki wins in that scenario, and Draw if the game continues forever with neither of them losing in that scenario.

3
abcd
bcda
ada

Aoki
Takahashi
Draw

When Takahashi starts the game by saying abcd, Aoki will say bcda next, and Takahashi will then have no word to say, resulting in Aoki's win. Thus, we should print Aoki.

When Takahashi starts the game by saying bcda, Aoki will have no word to say, resulting in Takahashi win. Thus, we should print Takahashi.

When Takahashi starts the game by saying ada, both players will repeat ada and never end the game. Thus, we should print Draw. Note that they can use the same word any number of times.

1
ABC

Draw

5
eaaaabaa
eaaaacaa
daaaaaaa
eaaaadaa
daaaafaa

Takahashi
Takahashi
Takahashi
Aoki
Takahashi