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
input = sys.stdin.readline
import math

def prime(a):
	if a==2:
		return True
	elif a==0:
		return False
	for i in range(2,int(math.sqrt(a))+1):
		if a%i==0:
			return False
	return True
# def is_power_two(x):
# 	while x % 2 == 0:
# 		x //= 2
# 	return x == 1
for _ in range(int(input())):
	n = int(input())
	if n==1:
		print("FastestFinger")
	elif n==2 or n%2==1:
		print("Ashishgup")
	else:
		I = 0
		p =0 
		while n % 2 == 0:
			n //= 2
			p+=1
		if n==1:
			print("FastestFinger")
		elif p>=2:
			print("Ashishgup")
		elif prime(n):
			print("FastestFinger")
		else:
			print("Ashishgup")
		# elif n%4==0 and I!=0:
		# 	print("Ashishgup")
		# elif prime(I):	
		# 	print("FastestFinger")
		# else:
		# 	print("Ashishgup")