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.
# Python program to print prime factors 
  
import math 
  
# A function to print all prime factors of  
# a given number n 
def primeFactors(n): 
	r = []
	while n % 2 == 0:
		r.append(2)
		n = n // 2
	for i in range(3,int(math.sqrt(n))+1,2): 
		while n % i== 0: 
			r.append(int(i))
			n = n // i 
	if n > 2: 
		r.append(n)
	return r 
  
# n =30
# print(primeFactors(n))
  
# This code is contributed by Harshit Agrawal 

for _ in range(0, int(input())):
	n = int(input())
	if n == 1:
		print("FastestFinger")
	elif n == 2:
		print("Ashishgup")
	else:
		if n %  2 != 0:
			print("Ashishgup")
		else:
			p = primeFactors(n)
			twos = p.count(2)
			not_twos = len(p) - twos 
			if twos == len(p):
				print("FastestFinger")
			else:
				if twos == 1:
					if not_twos == 1:
						print("FastestFinger")
					else:
						print("Ashishgup")
				else:
					print("Ashishgup")