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 isPrime(n) :  
    if (n <= 1) :  
        return False
    if (n <= 3) :  
        return True  
    if (n % 2 == 0 or n % 3 == 0) :  
        return False
    i = 5
    while(i * i <= n) :  
        if (n % i == 0 or n % (i + 2) == 0) :  
            return False
        i = i + 6
    return True

def isit(a):
	i=1
	for i in range(34):
		if(a==2**i):
			return(True)
	return(False)

def stat(n):
	dn=int(n)
	pt=0
	while(dn%2==0):
		dn/=2
		pt+=1
	kk=isPrime(dn)
	return([pt,kk])


a='Ashishgup'
b='FastestFinger'
t=int(input())
for tt in range(t):
	n=int(input())
	if(n==1):
		print(b)
	elif(n==2):
		print(a)
	else:
		if(isit(n)):
			print(b)
		else:
			if(stat(n)[0]==1):
				if(stat(n)[1]):
					print(b)
				else:
					print(a)
			else:
				print(a)
