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 sys
import bisect as b
import math
from collections import defaultdict as dd
input=sys.stdin.readline
#sys.setrecursionlimit(10**7)
def cin():
    return map(int,sin().split())
def ain():            
    return list(map(int,sin().split()))
def sin():
    return input()
def inin():
    return int(input())
def Solve(n) :
    l = []  
    for i in range(3, int(math.sqrt(n) + 1)) :
        if (n % i == 0 ) : 
            if (i%2==1 or n//i%2==1) : 
                return True 
    return False
for _ in range(inin()):
    n=inin()
    k=n
    f=0
    if(n==1):
        f=0
    elif(n==2 or n%2==1):
        f=1
    elif(k&(k-1)==0):
        f=0
    elif(k%4==0):
        f=1
    else:
        f=Solve(n)
    if(f):
        print("Ashishgup")
    else:
        print("FastestFinger")
        
        
            
            
        
        
    
    
    
            
    
        
        
        
    
            
    
    
    
    
        
                
            
        
        
        
    
            
            
        
    
    
        
    

        
        
    
                
                
                
                

        
            
            
                
            
                
    
 
        
    
    
    
    




    


   
        
    
    
    
    




    


