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.
t= int(input())
import math
for i in range(t):
	n= int(input())
	arr_prime=[]
	if n==1:
		print("FastestFinger")
	elif n==2:
		print("Ashishgup")
	elif n%2==1:
		print("Ashishgup")
	else:
		c=0
		while(n%2==0):
			c+=1
			n=n//2
		for i in range(3,int(math.sqrt(n))+1,2):
			while n%i==0:
				n=n/i
				arr_prime.append(i)
		if n > 2:
			arr_prime.append(i)

		if (len(arr_prime)==0):
			print("FastestFinger")
		elif(len(arr_prime)==1 and c==1):
			print("FastestFinger")
		else:
			print("Ashishgup")
