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 math import sqrt
from itertools import count, islice

def is_prime(n):
    if n < 2:
        return False

    for number in islice(count(2), int(sqrt(n) - 1)):
        if n % number == 0:
            return False

    return True
def solve():
	n = int(input())
	#a = list(map(int, input().split()))
	#s = list(input())
	if n&1:
		if n!=1:
			print('Ashishgup')
		else: print('FastestFinger')
	else:
		if n==2:
			print('Ashishgup')
		else:
			if bin(n)[2::].count('1') == 1:
				print('FastestFinger')
			else:
				if n%2==0 and (n//2)%2!=0:
					if not is_prime(n//2):
						print('Ashishgup')
					else:
						print('FastestFinger')
				else:
					print('Ashishgup')
	
	


##################################################################
if __name__ == "__main__":
	t = 1
	t = int(input())
	for _ in range(t): solve()