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Problem Statement

We have a deck of $N$ cards.
Each of these cards is good or bad.

Using this deck, Takahashi and Aoki will play a game against each other.
In the game, the players alternately draw the topmost card and eat it.
The player who first gets to eat a bad card loses the game. (Here, it is guaranteed that the deck contains at least one bad card.)

You are given a string $S$ consisting of 0 and 1. For each $i = 1, 2, \ldots, N$,

• if the $i$-th character of $S$ is 0, it means that the $i$-th card from the top of the deck is good;
• if the $i$-th character of $S$ is 1, it means that the $i$-th card from the top of the deck is bad.

Which player will lose when Takahashi goes first in the game?

Constraints

• $1 \leq N \leq 10^5$
• $N$ is an integer.
• $S$ is a string of length $N$ consisting of 0 and 1.
• $S$ contains at least one occurrence of 1.

Sample Input 1

5
00101

Sample Output 1

Takahashi

First, Takahashi will eat a good card. Next, Aoki will eat a good card. Then, Takahashi will eat a bad card.
Thus, Takahashi will be the first to eat a bad card, so we should print Takahashi.

Sample Input 2

3
010

Sample Output 2

Aoki