Number Game

题意翻译

有一个正整数 $n$。 两名玩家轮流操作。每次操作可以执行以下一种： - 将 $n$ 除以一个 $n$ 的大于 $1$ 的奇数因子。 - 将 $n$ 减去 $1$（若 $n\gt1$）。 无法操作者输。 问先手是否有必胜策略。如果先手有必胜策略，输出 `Ashishgup `，否则输出 `FastestFinger `。 多组数据，数据组数 $t \leq 100$，$1 \leq n \leq 10^9$ 翻译 by Meatherm

题目描述

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.

输入输出格式

输入格式

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 $ ).

输出格式

For each test case, print "Ashishgup" if he wins, and "FastestFinger" otherwise (without quotes).

输入输出样例

输入样例 #1

7
1
2
3
4
5
6
12

输出样例 #1

FastestFinger
Ashishgup
Ashishgup
FastestFinger
Ashishgup
FastestFinger
Ashishgup

说明

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 $ .

题意翻译

有一个正整数 $n$。 两名玩家轮流操作。每次操作可以执行以下一种： - 将 $n$ 除以一个 $n$ 的大于 $1$ 的奇数因子。 - 将 $n$ 减去 $1$（若 $n\gt1$）。 无法操作者输。 问先手是否有必胜策略。如果先手有必胜策略，输出 `Ashishgup `，否则输出 `FastestFinger `。 多组数据，数据组数 $t \leq 100$，$1 \leq n \leq 10^9$ 翻译 by Meatherm