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 f(n):
    i = 2
    while(i<=n):
        if i == n:
            return(True)
        else:
            i = i*2
    return(False)
def g(n):
    l = int(n**(1/2))+1
    c = 0
    for i in range(2,l+1):
        if n%i == 0:
            if i%2 ==1 and (n//i)%2 == 1:
                c = c+2
            elif i%2 == 1 or (n//i)%2 == 1:
                c = c+1
        if c>1:
            return(True)
    return(False)
t = int(input())
while(t>0):
    t = t-1
    n = int(input())
    if n == 1:
        print("FastestFinger")
    elif n == 2:
        print("Ashishgup")
    elif f(n) == True:
        print("FastestFinger")
    elif n%2 == 1:
        print("Ashishgup")
    elif (n//2)%2 == 0:
        print("Ashishgup")
    elif (n//2)%2 == 1:
        if g(n//2) == True:
            print("Ashishgup")
        else:
            print("FastestFinger")