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.
import math


def factorize(x):
    factors = []

    for i in range(2, int(math.sqrt(x) + 1)):
        while x % i == 0:
            if i & 1:
                factors.append(i)
            x //= i

    if x != 1:
        if x & 1:
            factors.append(x)

    return factors


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

    if n == 1:
        print("FastestFinger")
    elif n & 1 or n == 2:
        print("Ashishgup")
    else:

        divs = factorize(n)
        steps = len(divs)

        dec = 1

        for x in divs:
            dec *= x


        if n / dec != 2 and steps != 0:
            print("Ashishgup")
        else:
            print("Ashishgup" if steps > 1 else "FastestFinger")