#P1370C. Number Game
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ID: 5431
Type: RemoteJudge
2000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Number Game
No submission language available for this problem.
Description
Ashishgup and FastestFinger play a game.
They start with a number $n$ and play in turns. In each turn, a player can make any one of the following moves:
- Divide $n$ by any of its odd divisors greater than $1$.
- Subtract $1$ from $n$ if $n$ is greater than $1$.
Divisors of a number include the number itself.
The player who is unable to make a move loses the game.
Ashishgup moves first. Determine the winner of the game if both of them play optimally.
The first line contains a single integer $t$ ($1 \leq t \leq 100$) — the number of test cases. The description of the test cases follows.
The only line of each test case contains a single integer — $n$ ($1 \leq n \leq 10^9$).
For each test case, print "Ashishgup" if he wins, and "FastestFinger" otherwise (without quotes).
Input
The first line contains a single integer $t$ ($1 \leq t \leq 100$) — the number of test cases. The description of the test cases follows.
The only line of each test case contains a single integer — $n$ ($1 \leq n \leq 10^9$).
Output
For each test case, print "Ashishgup" if he wins, and "FastestFinger" otherwise (without quotes).
Samples
7
1
2
3
4
5
6
12
FastestFinger
Ashishgup
Ashishgup
FastestFinger
Ashishgup
FastestFinger
Ashishgup
Note
In the first test case, $n = 1$, Ashishgup cannot make a move. He loses.
In the second test case, $n = 2$, Ashishgup subtracts $1$ on the first move. Now $n = 1$, FastestFinger cannot make a move, so he loses.
In the third test case, $n = 3$, Ashishgup divides by $3$ on the first move. Now $n = 1$, FastestFinger cannot make a move, so he loses.
In the last test case, $n = 12$, Ashishgup divides it by $3$. Now $n = 4$, FastestFinger is forced to subtract $1$, and Ashishgup gets $3$, so he wins by dividing it by $3$.