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.
import math 
def factors(n): 
    l =[]
    while n % 2 == 0: 
        l.append(2) 
        n = n / 2
    for i in range(3,int(math.sqrt(n))+1,2): 
        while n % i== 0: 
            l.append(i) 
            n = int(n / i) 
    if n > 2: 
        l.append(int(n))
    return l

def solve(n):
    if n == 1:
        return 0
    if n == 2 or n == 3 or n == 5 or n == 7:
        return 1
    if n%2 != 0:
        return 1
    fact = factors(n)
    o = 0
    for i in fact:
        if i%2 != 0:
            o+=1
    if (n//2)%2 != 0 and o <= 1:
        return 0
    i = 1
    while i < n:
        i *= 2
    if i == n:
        return 0

    return 1

t = int(input())
for we in range(t):
    n = int(input())
    if solve(n) == 1:
        print("Ashishgup")
    else:
        print("FastestFinger")

# print(factors(342))
    