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 math import log2


def isPrime(n):
    if n <= 1:
        return False
    if n <= 3:
        return True
    if (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


def play(i):

    if i == 1:
        to_return = 1       # opponent wins

    elif i == 2:
        to_return = 0

    elif i & 1:       # odd
        to_return = 0       # starting player wins4

    elif log2(i) == int(log2(i)):   # no odd divisor
        to_return = 1

    else:
        if i % 4 == 0:
            to_return = 0
        else:
            if isPrime(i // 2):
                to_return = 1
            else:
                to_return = 0
    return to_return


d = {0: 'Ashishgup', 1: 'FastestFinger'}
t = int(input())
l = []
for _ in range(t):
    n = int(input())
    print(d[play(n)])
