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):
##    print(n)
    for i in range(2,int(n**0.5)+1):
        if n%i==0:
            return False
    return True
def solve(n,p):
##    print(str(n)+" "+str(p))
    if n%2==1:
        if n==1:
            print("FastestFinger") 
            return 
        else:
            print("Ashishgup")
            return 
    else:
        if (n&(n-1))==0:
            if n==2:
                print("Ashishgup") 
                return 
            else:    
                print("FastestFinger") 
                return 
        else:
            if n%4==0:
                print("Ashishgup") 
                return
            else:
                if isprime(n//2):
                    print("FastestFinger") 
                    return
                else:
                    print("Ashishgup") 
                return
                    
T=int(input())
for  x in range(T):
    n=int(input())
    solve(n,0)
                
            

        
        
    
##12
##6
##10
##12
##14
##18
##20
##22
##24
##26
##28
##30
##34
