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 io,os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
I = lambda : list(map(int,input().split()))


t,=I()
for _ in range(t):
	f=0
	n,=I()
	if n%2:
		f=1 if n!=1 else 0
	else:
		d=0;r=int(n**0.5)+1;c=0
		while n%2==0:
			n//=2;c+=1
		for i in range(3,r,2):
			while n%i==0 and i%2:
				n//=i;d+=1
		d = d+1 if n!=1 else d
		if c!=1:
			if d!=0:
				f=1
		else:
			if d==0 or d>1:
				f=1
	if f:
		print("Ashishgup") 
	else:
		print("FastestFinger")