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 primes(n):
    onlytwo = True
    primfac = []
    d = 2
    while d*d <= n:
        while (n % d) == 0:
            if d!=2:
                onlytwo=False
            primfac.append(d)  # supposing you want multiple factors repeated
            n //= d
        d += 1
    if n > 1:
        if n!=2:
            onlytwo=False
        primfac.append(n)
    return primfac, onlytwo

def fret(n):
    ans = ["Ashishgup","FastestFinger"]
    b=0
    if n==1:
        b=1
    elif n==2 or n%2==1:
        b=0
    else:
        nos, onlytwo = primes(n)
        if onlytwo:
            b=1
        elif len(nos)>2:
            b=0
        else:
            b=1
    
    return ans[b]

for _ in range(int(input())):
    n=int(input())
    print(fret(n))
