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 _ in range(t):
	n=int(input())
	if(n==1):
		print("FastestFinger")
		continue

	if(n%2!=0):
		print("Ashishgup")
		continue


	if(n==2):
		print("Ashishgup")
		continue
	x=n
	c=0
	while(x%2==0):
		c+=1
		x/=2
	# print(x)
	if(x==1):
		print("FastestFinger")
		continue
	else:
		if(n%4==0):
			print("Ashishgup")
		else:
			o=0
			s=[]
			k=n//2
			# print(k)
			for i in range(3,int(math.sqrt(n))+1,2): 
				# print('j')
				while k % i== 0: 
				    o+=1
				    s.append(i)
				    k/=i
			if(k>2):
				o+=1
				s.append(k)
			# print(s,n)
			if(o>1):
				print("Ashishgup")
			else:
				print("FastestFinger")

          







