human
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.

Input

The first line contains a single integer t (1 ≤ t ≤ 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 ≤ n ≤ 10^9).

Output

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

Example

Input

7
1
2
3
4
5
6
12

Output

FastestFinger
Ashishgup
Ashishgup
FastestFinger
Ashishgup
FastestFinger
Ashishgup

Note

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.
Solve the task in PYTHON3.
 ... Can you provide a Python code to determine the winner of the game if both of them play optimally?
assistant
#Here is Python code to determine the winner of the game if both of them play optimally.

from sys import stdin, gettrace

if gettrace():
    inputi = input
else:
    def input():
        return next(stdin)[:-1]

    def inputi():
        return stdin.buffer.readline()

def main():
    def solve():
        n = int(input())
        if n == 1:
            print("FastestFinger")
            return
        if n == 2:
            print("Ashishgup")
            return
        if n%2 == 1:
            # divide by self
            print("Ashishgup")
            return
        tc = 0
        while n%2 == 0:
            tc += 1
            n = n//2
        if n == 1:
            # Only choice is sub 1, hence giving an odd number
            print("FastestFinger")
            return
        if tc > 1:
            # Divide by largest odd factor, giving a power of 2 > 2
            print("Ashishgup")
            return
        i = 3
        while(i*i <= n):
            if n%i == 0:
                # Two or more odd factors, divide by all but one giving twice a prime
                print("Ashishgup")
                return
            i += 2
        # Twice prime, divide by prime gives 2, sub 1 gives odd
        print("FastestFinger")


    t = int(inputi())
    for _ in range(t):
        solve()

if __name__ == "__main__":
    main()