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 sqrt
for T in range(int(input())) :
    n = int(input())
    if n ==1 :
        print("FastestFinger")
    elif n == 2  :
        print("Ashishgup")
        
    elif (n%2 == 1) :
        print("Ashishgup")
    else :
        cnt = 0
        while (n%2 ==0 ):
            cnt +=1
            n //=2
        if n == 1 :
            print("FastestFinger")
            continue
        odd = 0 
        for i in range (3 ,int(sqrt(n)) +1 ,2):
            if n%i ==0 :
                while n%i == 0 :
                    odd +=1
                    n //=i
            if odd >=2 :
                break
        if n >1 :
            odd +=1
        if cnt ==1  and  odd ==1 :
            print("FastestFinger")
            
            
        else  :
            print("Ashishgup")
            
            
            
            
            
    
            

        

    
            
        
     
        
        

    


    
        
        
        
            

    
    


    
    




        
                
                  
                
            
            
    
    
        
