Contest Duration: - (local time) (100 minutes) Back to Home
D - Prime Sum Game /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

• まず、高橋君が A 以上 B 以下の好きな整数を選び、青木君に伝える
• 次に、青木君が C 以上 D 以下の好きな整数を選ぶ
• 二人の選んだ整数の和が素数なら青木君の勝ち、そうでなければ高橋君の勝ち

### 制約

• 1 \leq A \leq B \leq 100
• 1 \leq C \leq D \leq 100
• 入力に含まれる値は全て整数である

### 入力

A B C D


### 入力例 1

2 3 3 4


### 出力例 1

Aoki


### 入力例 2

1 100 50 60


### 出力例 2

Takahashi


### 入力例 3

3 14 1 5


### 出力例 3

Aoki


Score : 400 points

### Problem Statement

Takahashi and Aoki are playing a game.

• First, Takahashi chooses an integer between A and B (inclusive) and tells it to Aoki.
• Next, Aoki chooses an integer between C and D (inclusive).
• If the sum of these two integers is a prime, then Aoki wins; otherwise, Takahashi wins.

When the two players play optimally, which player will win?

### Constraints

• 1 \leq A \leq B \leq 100
• 1 \leq C \leq D \leq 100
• All values in input are integers.

### Input

Input is given from Standard Input in the following format:

A B C D


### Output

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

### Sample Input 1

2 3 3 4


### Sample Output 1

Aoki


For example, if Takahashi chooses 2, Aoki can choose 3 to make the sum 5, which is a prime.

### Sample Input 2

1 100 50 60


### Sample Output 2

Takahashi


If they play optimally, Takahashi always wins.

### Sample Input 3

3 14 1 5


### Sample Output 3

Aoki