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 isprime(n):
    if n<2:
        return False
    x=2
    while x*x<=n:
        if n%x==0:
            return False
        x+=1
    return True
t=int(input())
while t:
    t=t-1
    n=int(input())
    a="Ashishgup"
    f="FastestFinger"
    hi2=0
    setbit=0
    if n==1:
        print(f)
    elif n%2==1 and n!=1:
        print(a)
    else:

        for i in range(1,32):
            if n%(1<<i)==0:
                hi2=hi2+1

        for i in range(32):
            if n&(1<<i):
                setbit=setbit+1
        if setbit==1 and n!=2:
            print(f)
        if n==2:
            print(a)
        if setbit>1 and (2**hi2)>2:
            print(a)
        if setbit>1 and (2**hi2==2):
            if isprime(n//(2**hi2)):
                print(f)
            else:
                print(a)





