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.
from math import ceil


def read_int():
    return int(input())


def read_string_array():
    return input().split()


def read_int_array():
    return [int(_) for _ in read_string_array()]


def read_line():
    return input()


def factors(n):
    f = set()
    for i in range(2, int(n ** 0.5 + 1)):
        if (n % i) == 0 and (i % 2) == 1:
            f.add(i)
        if (n % i) == 0 and ((n//i) % 2) == 1:
            f.add(n // i)
    return f


def solve(n, turn=False):
    if n == 1:
        return not turn
    divs = factors(n)
    if n % 2 == 1:
        return solve(1, not turn)
    else:
        if divs:
            if len(divs) == 1 or (n & 1 == 0 and n & 2 == 0):
                return solve(n // max(divs), not turn)
            else:
                return solve(n // max(divs) * min(divs), not turn)
        else:
            return solve(n-1, not turn)



if __name__ == '__main__':
    T = read_int()
    players = ('Ashishgup', 'FastestFinger')
    for _ in range(T):
        #  read inputs

        N = read_int()
        # read_int_array()
        # read_string_array()

        # solve
        print(players[solve(N)])
