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.
#map(int,input().split())
#int(x) for x in input().split()
import math
def prime(n): 
	l=[]
	while n % 2 == 0: 
		l.append(2)
		n = n / 2
	for i in range(3,int(math.sqrt(n))+1,2): 
		while n % i==0: 
			l.append(i)
			n = n / i  
	if n > 2:
		l.append(n)
	return l

for _ in range(int(input())):
	n=int(input())
	l=prime(n)
	if n==1:
		print('FastestFinger')
		continue
	if n==2:
		print('Ashishgup')
		continue		
	if n%2!=0:
		print('Ashishgup')
		continue
	eve=0
	odd=0
	for i in range(len(l)):
		if l[i]%2==0:
			eve+=1
		else:
			odd+=1
	if odd==0:
		print('FastestFinger')
		continue
	if eve>=2:
		print('Ashishgup')
		continue
	if odd>=2:
		print('Ashishgup')
		continue
	print('FastestFinger')

