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Contest: Task: Related: TaskC TaskE

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