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
for case in range(int(input())):
    n = int(input())
    temp = n
    if n == 1:
        print("FastestFinger")
    elif n == 2:
        print("Ashishgup")
    elif n % 2 == 1:
        print("Ashishgup")
    else:
        odd_factors = 0
        while n % 2 == 0:
            n //= 2
        for i in range(3, int(math.sqrt(n))+1, 2):
            while n % i == 0:
                odd_factors += 1
                n //= i
        if n > 1 and n % 2 == 1:
            odd_factors += 1 
        if odd_factors == 0:
            print("FastestFinger")
        elif odd_factors > 1:
            print("Ashishgup")
        else:
            if temp % 4 == 0:
                print("Ashishgup")
            else:
                print("FastestFinger")