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
from collections import defaultdict, Counter, deque

INF = float('inf')

def gcd(a, b):
	while b:
		a, b = b, a%b
	return a

def isPrime(n):
	if (n <= 1): 
		return False
	i = 2
	while i ** 2 <= n:
		if n % i == 0:
			return False
		i += 1
	return True

def primeFactor(n):
	if n % 2 == 0:
		return 2
	i = 3
	while (i ** 2) <= n:
		if n % i == 0:
			return i 
		i += 1
	return n

def main():
	n = int(input())

	if n <= 1:
		print("FastestFinger")
		return
	elif n <= 3:
		print("Ashishgup")
		return

	if n % 2 == 1:
		print("Ashishgup")
	elif 2 ** int(math.log(n, 2)) == n:
		
		print("FastestFinger")
	elif isPrime(n // 2):
		
		print("FastestFinger")
	else:
		print("Ashishgup") 
	

if __name__ == "__main__":
	t = int(input())
	# t = 1
	for _ in range(t):
		main()







