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?

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.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分