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

'''

'''

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

    if n == 1:
        print("FastestFinger")
    elif n % 2 == 1:
        print("Ashishgup")
    else:
        # n is even and larger than 1
        twos = 0
        while n % 2 == 0:
            n //= 2
            twos += 1
        
        odd_primes = 0
        MAX = int(n**0.5) + 1
        d = 3
        while n > 1 and d <= MAX:
            while n % d == 0:
                odd_primes += 1
                n //= d
            d += 1
        
        if n > 1:
            odd_primes += 1

        if twos == 1:
            if odd_primes == 0 or odd_primes > 1:
                print("Ashishgup")
            else:
                print("FastestFinger")
        else:
            # twos >= 2
            if odd_primes > 0:
                print("Ashishgup")
            else:
                print("FastestFinger")

