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 os
import sys
if os.path.exists('/mnt/c/Users/Square/square/codeforces'):
    f = iter(open('C.txt').readlines())
    def input():
        return next(f).strip()
    # input = lambda: sys.stdin.readline().strip()  
else:
    input = lambda: sys.stdin.readline().strip()

fprint = lambda *args: print(*args, flush=True)

def is_power_two(x):
	while x % 2 == 0:
		x //= 2
	return x == 1

def primes(n):
	A = [1] * (n+1)
	A[0] = A[1] = 1
	primes = []
	lenA = len(A)
	for i in range(2, lenA):
		if A[i] == 1:
			primes.append(i)
		for j in range(i*2, lenA, i):
			A[j] = 0
	return primes

ps = primes(25000)


gamers = ['FastestFinger', 'Ashishgup']
# gamers = ['Loss', 'Win']
for _ in range(int(input())):
# for n in range(1, 100):
# 	print(n)
	n = int(input())
	if n == 1:
		print(gamers[0])
	elif n == 2:
		print(gamers[1])
	elif n % 2 == 1:
		print(gamers[1])
	elif is_power_two(n):
		print(gamers[0])
	elif n % 4 == 0:
		print(gamers[1])
	else:
		n //= 2
		divisors = []
		for i in ps:
			while n % i == 0:
				n //= i
				divisors.append(i)
		if n > 1:
			divisors.append(n)
		if len(divisors) == 1:
			print(gamers[0])
		else:
			print(gamers[1])
