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.
from functools import lru_cache

def odd_div(x):
    if bin(x).count('1') == 1:
        return False
    cnt2 = 0
    while x&1==0:
        x >>= 1
        cnt2 += 1

    i = 3
    num_prime = 0
    while i*i <= x:
        while x % i == 0:
            num_prime += 1
            x //= i
        i += 1
    if x != 1 or num_prime == 0:
        num_prime += 1

    if cnt2 == 1 and num_prime <= 1:
        return False
    else:
        return True

def main():
    for __ in [0]*int(input()):
        n = int(input())

        if n == 1:
            print('FastestFinger')
        elif n == 2:
            print('Ashishgup')
        elif n & 1:
            print('Ashishgup')
        elif odd_div(n):
            print('Ashishgup')
        else:
            print('FastestFinger')


if __name__ == '__main__':
    main()

