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 sys

def input():
	return sys.stdin.readline().rstrip()

def input_split():
	return [int(i) for i in input().split()]

testCases = int(input())
answers = []
player1 = 'Ashishgup'
player2 = 'FastestFinger'


def power_of_2_greater_than_2(a):
	start = 4

	for _ in range(50):
		if a== start:
			return True

		start = start*2
	
	return False

def remove_twos(a):
	while(a%2 == 0):
		a = a//2

	return a

def is_prime(a):
	for i in range(2, min(a, int(a**0.5) + 3)):
		if a%i == 0:
			return False
	return True


for _ in range(testCases):
	#take input
	n = int(input())
	if n == 1:
		ans = player2
	elif n ==2:
		ans = player1
	elif n%2 == 1:
		ans = player1
	else:
		if power_of_2_greater_than_2(n):
			ans = player2
		else:
			#even toh hai
			if (n % 4) != 0:
				#not necessary
				#Odd is not prime
				left_over = remove_twos(n)
				if is_prime(left_over):
					ans = player2
				else:
					ans = player1
			else:
				ans = player1

	answers.append(ans)

print(*answers, sep = '\n')
