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.
def game(j):
    if (j%2==1 and j!=1) or j==2:
        return("Ashishgup")
    elif j==1:
        return("FastestFinger")
    else:
        for i in range(1,40):
            if j%(2**i)==0:
               ni=i
        new=j//(2**ni)
        if new==1:
           return("FastestFinger")
        else:
            if (j//2)%2==1:
                n1=j//2
                for p in range(1,int(n1**(1/2))+1):
                  if n1%p==0:
                    n2=p
                if n2==1:
                   return("FastestFinger")
            
            return("Ashishgup")     
t=int(input())
l=[]
for i in range(t):
    n=int(input())
    l.append(n)
for j in l:
    print(game(j))           