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 factors(n):
    even = 0
    while n > 0 and n%2 == 0:
        n = n//2
        even += 1

    return even

def prime(n):
    if n == 1:
        return False

    for i in range(2,int(n**0.5)+1):
        if n%i == 0:
            return False

    return True

def solve(n,ans):
    if n == 2:
        ans.append('Ashishgup')
        return
    
    even = factors(n)
    x = pow(2,even)
    if x == n:
        ans.append('FastestFinger')
    else:
        if n%2 != 0:
            ans.append('Ashishgup')
        else:
            if even > 1:
                ans.append('Ashishgup')
            else:
                if prime(n//2):
                    ans.append('FastestFinger')
                else:
                    ans.append('Ashishgup')
                

def main():
    t = int(input())
    ans = []
    for i in range(t):
        n = int(input())
        solve(n,ans)

    for i in ans:
        print(i)


main()
