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.
#author: riyan

import math

def is_prime(n):
    sqn = int(math.ceil(math.sqrt(n)))
    for x in range(2, sqn + 1):
        if n % x == 0:
            return False
    return True

if __name__ == '__main__':
    ans = ['Ashishgup', 'FastestFinger']
    tc = int(input().strip())
    while tc:   
        n = int(input().strip())
        if n == 1:
            print(ans[1])
        elif n == 2:
            print(ans[0])
        elif n % 2 == 1:
            print(ans[0])
        elif (2 ** int(math.floor(math.log2(n)))) == n:
            print(ans[1])
        elif n % 4 == 0:
            print(ans[0])
        elif is_prime(n // 2):
            print(ans[1])
        else:
            print(ans[0])    
        tc -= 1