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 odd_part(n):
    while n%2 == 0:
        n = n//2
    return n

def winner(n):

    if n in dp:
        return dp[n]
    if n<=1:
        return 0
    if n%2 == 1:
        return 1
    win = 0
    m = odd_part(n)
    k = n//m

    win = win or (1 - winner(n - 1))

    for i in range(1, m):

        if i * i > m or win == 1:
            break

        if i % 2 == 1 and m % i == 0:
            if i == 1:
                win = win  or (1 - winner(k * i))
            else:
                win = win or (1 - winner(k * m // i)) or (1 - winner(k * i))

    dp[n] = win

    return win

if __name__ == '__main__':
    t = int(input())
    dp = {}
    names = ["Ashishgup", "FastestFinger"]
    for _ in range(t):
        n = int(input())
        win = winner(n)
        print(names[1- win])




