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 $ .