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 sys
# input = sys.stdin.readline
# from bisect import bisect_left, bisect_right
INF = 1 << 60

def is_prime(n):
    if n <= 1:
        return False
    p = 2
    while True:
        if p ** 2 > n:
            break
        if n % p == 0:
            return False
        p += 1
    return True

def cnt(n):
    x = 0
    while n % 2 == 0:
        x += 1
        n //= 2
    return x


def print_a():
    print("Ashishgup")

def print_f():
    print("FastestFinger")

t = int(input())          
for i in range(t):
    n = int(input())
    x = cnt(n)
    # print(x)
    if x >= 2:
        n //= 2 ** x
        if n == 1:
            print_f()
        else:
            print_a()
    elif x == 1:
        if n // 2 == 1:
            print_a()
        elif is_prime(n // 2):
            print_f()
        else:
            print_a()
    else:
        if n == 1:
            print_f()
        else:
            print_a()
        
