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.
#!/usr/bin/python
def IsPrime(dig):
    res = True
    i = 2
    while i * i <= dig:
        if dig % i == 0:
            res = False
            break
        i += 1
    return res
t = int(input())
while t > 0:
    t -= 1
    x = int(input())
    if x == 1:
        print("FastestFinger")
        continue
    if x == 2:
        print("Ashishgup")
        continue
    temp = x
    len = 0
    while temp % 2 == 0 :
        temp /= 2
        len += 1
    if len == 0:
        print("Ashishgup")
        continue
    if len == 1:
        if IsPrime(x / 2) == True:
            print("FastestFinger")
        else:
            print("Ashishgup")
        continue
    if temp == 1:
        print("FastestFinger")
    else:
        print("Ashishgup")



