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 perfect_pow(n):
	n = n >> 2
	ind = 0
	while n > 0:
		if n%2:
			if ind:
				return False
			else:
				ind = 1
		n = n >> 1

	return True

def is_half_prime(n):
	n = n >> 1
	for i in range(2, int(n**0.5) + 1):
		if n%i == 0:
			return False
	return True

t = int(input())
while t:
	t -= 1
	n = int(input())

	if n%2:
		if n == 1:
			print("FastestFinger")
		else:
			print("Ashishgup")
	else:
		if n == 2:
			print("Ashishgup")
		elif n%4:
			if not is_half_prime(n):
				print("Ashishgup")
			else:
				print("FastestFinger")
		else:
			if perfect_pow(n):
				print("FastestFinger")
			else:
				print("Ashishgup")