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.
t = int(input())

# odd -> first player will win by dividing by that number
# even -> divide by largest odd factor without making it =2
# power of two -> no largest odd factor

# 6 -> 2 -> 1

"""
2^i * n -> 2^i if n is odd
2 -> 1
2n -> 2n-1 -> 1 LOST

"""

powers = [2 ** i for i in range(32)]

FIRST = "Ashishgup"
SECOND = "FastestFinger"

def isprime(k):
    if k < 2:
        return False
    
    for i in range(2, min(k, int(k ** 0.5) + 1)):
        if k % i == 0:
            return False

    return True

for case in range(t):
    n = int(input())

    if n == 1:
        print(SECOND)
    elif n == 2:
        print(FIRST)
    elif n in powers:
        print(SECOND)
    elif n % 4 == 0:
        print(FIRST) # divide by largest odd, to get a power of two
    elif n % 2 == 0:
        if isprime(n//2):
            print(SECOND) # don't divide by odd: gets 2, opponent responds 1
        else:
            print(FIRST) # divide by prime factor of n/2
    else:
        print(FIRST) # divide by n
