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 prime(n): 
    if (n <= 1):
        return False
    if (n <= 3):
        return True
    if (n%2 == 0 or n%3 == 0):
        return False
    for i in range(5,int(math.sqrt(n))+1,6): 
        if (n%i == 0 or n%(i+2) == 0): 
                return False
    return True
def solve():
    n=int(input())
    if(n==1):
        print('FastestFinger')
        return
    if(n==2 or n%2):
        print('Ashishgup')
        return
    c=0
    while(n%2==0):
        n=n//2
        c+=1
    if(n==1):
        print('FastestFinger')
        return
    if (c == 1 and prime(n)):
        print('FastestFinger')
        return
    print('Ashishgup')
for _ in range(int(input())):
    solve()