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 factors(n):
    out = []
    m = math.ceil(math.sqrt(n)) + 1
    for i in range(2, m):
        fl = 0
        if n == 1:
            break
        while n % i == 0:
            n = n / i
            fl = 1
        if fl == 1:
            out.append(i)
    if n != 1:
        out.append(int(n))
    return out


# print(factors(10))
t = int(input())
for _ in range(t):
    n = int(input())
    m = n
    if n == 1:
        print("FastestFinger")
        continue
    if n % 2 == 1:
        print("Ashishgup")
        continue
    else:
        cnt = 0
        if n == 2:
            print("Ashishgup")
            continue
        while n % 2 == 0:
            cnt += 1
            n /= 2
        if cnt > 1 and n != 1:
            print("Ashishgup")
            continue
        if cnt == 1:
            # print(m)
            out = factors(m)
            if len(out) == 2 and m == out[1] * out[0]:
                print("FastestFinger")
                continue
            else:
                print("Ashishgup")
                continue
        elif cnt > 1 and n == 1:
            print("FastestFinger")
            continue
