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.
#numbers game

def solve(n):
    if(n==1):
        return False
    if(n%2!=0):
        return True
    ans=False
    if(n-1==1):
        return True
    l=list()
    i=2
    while(i*i<=n):
        if(n%i==0):
            l.append(i)
            if(n//i!=i):
                l.append(n//i)
        i+=1
    for i in l:
        if(i%2!=0):
            if(not solve(n//i)):
                return True
            
    
    return False
                
                

if __name__=="__main__": 
    t=int(input())
    for i in range(t):
        n=int(input())
        f=solve(n)
        if(f):
            print('Ashishgup')
        else:
            print('FastestFinger')
