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.
from __future__ import print_function, division
from sys import stdin, stdout
from fractions import gcd
from math import *
from collections import *
from operator import itemgetter, mul

rstr = lambda: stdin.readline().strip()
rstrs = lambda: [str(x) for x in stdin.readline().split()]
rint = lambda: int(stdin.readline())
rints = lambda: [int(x) for x in stdin.readline().split()]
arr_2d = lambda n: [rints() for i in range(n)]
out = []


def prime(n):
    if n in [2, 3]:
        return True

    if n < 2 or n % 2 == 0 or n % 3 == 0:
        return False

    i = 5
    while (i * i <= n):
        if n % i == 0 or n % (i + 2) == 0:
            return False
        i += 6
    return True


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

    if n == 1:
        print('FastestFinger')
    elif n % 2 or n == 2:
        print('Ashishgup')
    elif n % 4:
        if prime(n // 2):
            print('FastestFinger')
        else:
            print('Ashishgup')
    else:
        if n == (1 << n.bit_length() - 1):
            print('FastestFinger')
        else:
            print('Ashishgup')
