Codeforces Round 651 (Div. 2) |
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Finished |
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:
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).
7 1 2 3 4 5 6 12
FastestFinger Ashishgup Ashishgup FastestFinger Ashishgup FastestFinger Ashishgup
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 $$$3$$$.
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