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 sys, math

def func(n):
	while n%2==0:
		n=n//2
	if n==1:
		return 1
	else:
		return n

def no_of_odd(n):
	no=0
	while n%2==0:
		n=n//2
	for i in range(3,math.floor(math.sqrt(n))+2,2):
		if n%i==0:
			no+=1
			return no+1

	return 1

input=sys.stdin.readline()
t=int(input)
while t>0:
    t-=1
    n=int(sys.stdin.readline())
    turn=1
    flag=0
    y=func(n)
#    print(n,y)
    if n==1:
    	print("FastestFinger")
    elif n==2:
    	print('Ashishgup')
    elif n%2!=0:
    	print("Ashishgup")
    elif y==1:
    	print("FastestFinger")
    else:
    	x=no_of_odd(y)
    	if x>1:
    		print("Ashishgup")
    	elif x==1:
    		if n%4==0:
    			print("Ashishgup")
    		else:
    			print("FastestFinger")