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 test_integer_for_prime(p):
    if p == 1:
        return 0
    probes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47]
    if p in probes: 
        return 1
    if any([p % a == 0 for a in probes]):
        return 0
    k, q = 0, p-1
    while not q&1:
        q >>= 1
        k+=1
    for a in probes:
        a_raised_to_q = pow(a, q, p)
        if a_raised_to_q == 1: continue
        if (a_raised_to_q == p-1) and (k > 0): continue
        a_raised_to_jq = a_raised_to_q
        primeflag = 0
        for j in range(k-1):
            a_raised_to_jq = pow(a_raised_to_jq, 2, p)
            if a_raised_to_jq == p-1:
                primeflag = 1
                break
        if not primeflag: return 0
    probability_of_prime = 1 - 1.0/(4 ** len(probes))
    return probability_of_prime
pow2 = [2**i for i in range(1,30)]
def ispower(n):
    return n in pow2
t = int(input())
for test in range(t):
    n = int(input())
    p2 = "FastestFinger"
    p1 = "Ashishgup"
    #print(n)
    if n==1:
        print(p2)
    elif n==2:
        print(p1)
    elif n%4==2:
        if test_integer_for_prime(n//2)>0.5:
            print(p2)
        else:
            print(p1)
    elif n%2==1:
        print(p1)
    elif ispower(n):
        print(p2)
    else:
        print(p1)
