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
inputr = lambda: input().rstrip('\n')

INF = 10 ** 18

from functools import lru_cache

@lru_cache(maxsize=None)
def f(n):
	if n == 1: return False
	elif n == 2: return True
	elif n % 2 == 1: return True

	for d in range(2, n):
		if d * d > n: break
		if n % d == 0:
			if d % 2 == 1 and not f(n//d):
				return True

			od = n // d
			if od % 2 == 1 and not f(n//od):
				return True

	return False

for _ in range(int(input())):
	n = int(input())

	print('Ashishgup' if f(n) else 'FastestFinger')
