CF1370C.Number Game

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).

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 $3$ .