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 debug import  debug

t = int(input())

fas = "FastestFinger"
ash = "Ashishgup"
for _ in range(t):
	n = int(input())
	
	if n == 1:
		print(fas)
	elif n == 2:
		print(ash)
	elif n%2:
		print(ash)
	else:
		two = 1
		oth = 0

		if n%4 == 0:
			two = 2

		c = n
		i = 2
		while (i*i)<=c:
			while c%i == 0:
				c = c//i
				if i%2:
					oth+=1

				if oth >= 2:
					break
			i+=1
			if oth >= 2:
				break
		if(c>1 and oth<2):
			oth+=1
		# print(111, two, oth)

		if two == 1 and oth == 1:
			print(fas)
		elif two == 1 and oth == 2:
			print(ash)
		elif two == 2 and oth == 0:
			print(fas)
		elif two == 2 and oth >= 1:
			print(ash)

