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 # Joueur 1 Ashishgup
# Joueur 2 FastestFinger
def nb_facteurs(n, p):
    if n==0 or n<p:
        return 0
    nb = 0
    while n%p==0:
        nb += 1
        n = int(n/p)
    return nb

nb_cases = int(input())
while nb_cases > 0:
    nb_cases -= 1

    n = int(input())


    if n==1:
        print("FastestFinger")
        continue
    if n==2:
        print("Ashishgup")
        continue
    # Impair
    if n%2==1:
        print("Ashishgup")
        continue
    # 4 * 2^k * impair
    if n%4==0 and n>2**nb_facteurs(n,2):
        print("Ashishgup")
        continue

    # 2 * 2^k * impair1 * impair 2
    nb_facteur_impair = 0
    for x in range(2, int(math.sqrt(n/nb_facteurs(n,2))+1)):
        if x%2==1:
            nb_facteur_impair += nb_facteurs(n,x)
        if nb_facteur_impair >= 1:
            break
    if nb_facteur_impair >= 1:
        print("Ashishgup")
    else:
        print("FastestFinger")
