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 sqrt,floor
def is_pow(x):return 1==sum(x&(1<<i)!=0 for i in range(1,33))
def ok(x):
    s=0
    while x%2==0:s+=1;x//=2
    return s
def odd_1(a):
    while a%2==0:a//=2
    for i in range(2,floor(sqrt(a))+1):
        if a%i==0:return 0
    return 1
for _ in " "*int(input()):
    a=int(input())
    if a==1:print("FastestFinger")
    elif a&1:print("Ashishgup")
    elif a==2:print("Ashishgup")
    elif is_pow(a):print("FastestFinger")
    elif ok(a)==1 and odd_1(a):print("FastestFinger")
    else:print("Ashishgup")