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.
import math
t = int(input())
for helloworld in range(t):
	n = int(input())
	hfd = int(n)
	d = []
	for i in range(2,int(math.sqrt(n)+1)):
		while n % i == 0:
			d.append(i)
			n = n // i
	if n > 1:
		d.append(n)
	dc = 0
	dce = 0
	for i in range(len(d)):
		if d[i] % 2 == 1:
			dc += 1
		else:
			dce += 1
	if dc > 1 or (hfd % 2 == 1 and hfd > 1) or hfd == 2:
		print('Ashishgup')
	else:
		if d.count(2) == 1 or dc == 0:
			print('FastestFinger')
		else:
			print('Ashishgup')