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(x) :
    i=3
    while(i*i<=x) :
        if x%i==0 :
            return False
        i+=1
    return True
    
    
    
t=int(input())
while t>0 :
    n=int(input())
    num=n
    if n==1 :
        print("FastestFinger")
    elif n==2 :
        print("Ashishgup")
    elif n%2==1 :
        print("Ashishgup")
    else :
        while (n%2==0) :
            n=n//2
        if n==1 :
            print("FastestFinger")
        else :
            if num//n==2 :
                if isPrime(n) :
                    print("FastestFinger")
                else :
                    print("Ashishgup")
            else :
                print("Ashishgup")
    t-=1