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 isPrime(n) : 
	if (n <= 1) : 
		return False
	if (n <= 3) : 
		return True
	if (n % 2 == 0 or n % 3 == 0) : 
		return False  
	i = 5
	while(i * i <= n) : 
		if (n % i == 0 or n % (i + 2) == 0) : 
			return False
		i = i + 6  
	return True

def help():
	n = int(input())
	
	t1 = bin(n)
	if(n == 1):
		print("FastestFinger")
		return
	if(n%2 == 1):
		print("Ashishgup")
		return
	if(t1.count('1')==1):
		if(n == 2):
			print("Ashishgup")
		else:
			print("FastestFinger")
	else:
		if(n%4 == 0):
			print("Ashishgup")
		else:
			n = n//2
			if(isPrime(n)):
				print("FastestFinger")
			else:
				print("Ashishgup")


for _ in range(int(input())):
	help()