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

def factorize(n):
    d=dict()
    for i in range(3, int(sqrt(n)) + 1): 
        while (n % i == 0):  
            d[i]=d.get(i,0)+1
            n = int(n / i); 
        i += 2; 
 
    if (n > 2): 
        d[n]=1
    return d
    
p="Ashishgup"
q="FastestFinger"
for _ in range(int(input())):
    n=int(input())
    f=0
    while True:
        if n==1:
            if f==0:
                print(q)
            else:
                print(p)
            break
        if n%2==1:
            if f==0:
                print(p)
            else:
                print(q)
            break
        k=n
        c=0
        while k%2==0:
            c+=1
            k//=2
        if k==1:
            n-=1
        else:
            if c>1:
                n//=k
            else:
                d=factorize(n//2)
                if len(d)==1 and sum(d.values())==1:
                    if f==0:
                        print(q)
                    else:
                        print(p)
                    break
                for i in d:
                    n=2*i
                    break


        f=(f+1)%2