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.

def isPrime(n) :  
    if n == 3:  
        return True 
    
    
    
    # This is checked so that we can skip   
    # middle five numbers in below loop  
    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 = i + 6
    
    return True
    


def isPT (x): 
  
    # First x in the below expression  
    # is for the case when x is 0  
    return (x and (not(x & (x - 1))) ) 




t=int(input())
while t:
    t-=1
    n=int(input())
    if n==1:
        print("FastestFinger")
    elif n>1 and n%2!=0:
        print("Ashishgup")
    else:
        if isPT(n) and n>2:
            print("FastestFinger")

        else:
            k=n/2
            if isPrime(k) and k >1:
                print("FastestFinger")

            else:
                print("Ashishgup")
        
            
            
                
        
    