Problem Statement

There are $N squares called square 1, square 2, \ldots, square N$, where square i and square i+1 are adjacent for each $i = 1, 2, \ldots, N-1$.
Initially, M of the squares have 0 or 1 written on them.
Specifically, for each $i = 1, 2, \ldots, M, Y_i$ is written on square X_i.
The other N-M squares have nothing written on them.
Takahashi and Aoki will play a game against each other.
The two will alternately act as follows, with Takahashi going first.

• Choose a square with nothing written yet, and write 0 or 1 on that square.
  Here, it is forbidden to make two adjacent squares have the same digit written on them.

The first player to be unable to act loses; the other player wins.
Determine the winner when both players adopt the optimal strategy for their own victory.

Input

The input is given from Standard Input in the following format:
N M
X_1 Y_1
X_2 Y_2
$\vdots$
X_M Y_M

Output

If Takahashi wins, print Takahashi; if Aoki wins, print Aoki.

Constraints

• $1 \leq N \leq 10^{18}$
• $0 \leq M \leq \min\lbrace N, 2 \times 10^5 \rbrace$
• $1 \leq X_1 \lt X_2 \lt \cdots \lt X_M \leq N$
• $Y_i \in$ $\lbrace 0, 1\rbrace$
• $X_i + 1 = X_{i+1} \implies Y_i \neq Y_{i+1}$
• All values in the input are integers.

Sample Input 1

7 2
2 0
4 1

Sample Output 1

Takahashi

Here is one possible progression of the game.

• Takahashi writes 0 on square 6.
• Aoki writes 1 on square 1.
• Takahashi writes 1 on square 7.

Then, Aoki cannot write 0 or 1 on any square, so Takahashi wins.

Sample Input 2

3 3
1 1
2 0
3 1

Sample Output 2

Aoki

Since every square already has 0 or 1 written at the beginning, Takahashi, who goes first, cannot act, so Aoki wins.

Sample Input 3

1000000000000000000 0

Sample Output 3

Aoki

见题面 Input 部分

见题面 Output 部分