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.
ganaA = "Ashishgup"
ganaB = "FastestFinger"

def fastio():
    import sys
    from io import StringIO
    from atexit import register
    global input
    sys.stdin = StringIO(sys.stdin.read())
    input = lambda : sys.stdin.readline().rstrip()
    sys.stdout = StringIO()
    register(lambda : sys.__stdout__.write(sys.stdout.getvalue()))
fastio()


def is_prime(n):
	d = 2
	while(d*d<=n):
		if n%d == 0:
			return False
		d+=1
	return True

def solve(n):
	if n == 1:
		print(ganaB)
		return
	if n & 1: 
		print(ganaA)
		return
	if n == 2:
		print(ganaA)
		return

	parteImpar = n
	alpha = 0
	while(parteImpar%2 == 0):
		parteImpar //=2
		alpha +=1

	if alpha == 1:
		#Parte impar con mas de un divisor
		if not is_prime(parteImpar):
			print(ganaA)
		else:
			print(ganaB)
	else:
		if parteImpar>1:
			print(ganaA)
		else:
			print(ganaB)



t = int(input())
for _ in range(t):
	n = int(input())
	solve(n)
