A13479 | Number Game
时间限制1s
内存限制256MB
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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.
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 — $n$ ( $1 \leq n \leq 10^9$ ).
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 #1
7 1 2 3 4 5 6 12
输出 #1
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 $3$ .
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 $3$ .
C++ 编辑器
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评测结果：Accepted