Number Game

2000ms

262144K

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.

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).

Sample Input:

Sample Output:

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 $$$3$$$.

Informação

Provedor Codeforces

Código CF1370C