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 sys import stdin, stdout

int_in = lambda: int(stdin.readline())
arr_in = lambda: [int(x) for x in stdin.readline().split()]
mat_in = lambda rows: [arr_in() for _ in range(rows)]
str_in = lambda: stdin.readline().strip()
out = lambda o: stdout.write("{}\n".format(o))
arr_out = lambda o: out(" ".join(map(str, o)))
bool_out = lambda o: out("YES" if o else "NO")
tests = lambda: range(1, int_in() + 1)
case_out = lambda i, o: out("Case #{}: {}".format(i, o))


def divisors(n):
    i = 2
    result = []
    while i * i <= n:
        if n % i == 0:
            result.append(i)
            result.append(n // i)
        i += 1
    return result


def can_win_last_case(n):
    result = sorted(divisors(n), reverse=True)
    result = filter(lambda x: x % 2 == 1, result)
    result = list(result)
    if len(result) > 0:
        if n // result[0] > 2:
            return True
    if len(result) > 1:
        return True
    return False


def solve(n):
    # if n is 1, we lose immediately
    if n == 1:
        return False

    # if n is odd, then n is an odd divisor
    # divide by n and win right away
    if n % 2 == 1:
        return True

    # if n is 2, then we subtract 1 and win
    if n == 2:
        return True

    # if n is even, we can't subtract 1, because
    # then the other guy wins
    # so we have to find any odd divisors and divide
    # but the result of the division can't be 2
    # so we divide by highest odd divisor < n/2 to force
    # the next move to be one that brings the result to 2
    return can_win_last_case(n)



if __name__ == "__main__":
    for i in tests():
        n = int_in()
        out("Ashishgup" if solve(n) else "FastestFinger")