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.
cases = int(input())
def primechecker(number):
    if number == 1:
        return False
    if number == 2:
        return True
    for j in range(2, int(number**0.5)+1):
        if number%j == 0:
            return False
    return True

for i in range(cases):
    n = int(input())
    a = "Ashishgup"
    b = "FastestFinger"
    ptwo = [4]
    start = 3
    while max(ptwo)<=10**9:
        ptwo.append(2**start)
        start+=1

    if n == 1 or n in ptwo:
        print (b)
    elif n == 2 or n%2 == 1:
        print (a)
    elif n%2==0:
        num = int(n/2)
        if primechecker(num):
            print (b)
        else:
            print(a)