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.
def criba_eratostenes(n):
  multiplos = set()
  prime = set()
  for i in range(2, n+1):
    if i not in multiplos:
      prime.add(i)
      multiplos.update(range(i*i, n+1, i))
  return prime

primes = criba_eratostenes(31650)

two = {1<<i for i in range(2, 40)}
for i in range(int(input())):
	n = int(input())
	if n == 1:
		print("FastestFinger")
	elif n == 2:
		print("Ashishgup")
	elif n % 2:     # Si es impar gana el primero (2 jugadas)
		print("Ashishgup")
	elif n in two:	# Solo puede sustraer y luego pierde
		print("FastestFinger")
	elif n % 4:
		n /= 2
		t = True
		for i in primes:
			if not n%i:
				if n != i:
					print("Ashishgup")
					t = False
				break
		if t:
			print("FastestFinger")
	else:			# Si es par multiplo de 4 pero tiene divisores impares (not in two) divide por el divisor impar mas grande y deja n in two
		print("Ashishgup")