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

t = int(input())

def isPrime(x):
    if x < 2 or x % 2 == 0:
        return False
    if x == 3 or x == 5 or x == 7:
        return True
    for i in range(3, int(x**0.5)+1, 2):
        if x % i == 0:
            return False
    return True

def isPow2(n):
    i = 1
    while 2 ** i <= n:
        if 2 ** i == n:
            return True
        i += 1
    return False

for i in range(t):
    n = int(input())
    #print(isPrime(n))
    if n == 1:
        print("FastestFinger")
    elif n % 2 == 1:
        print("Ashishgup")

    # even cases
    elif n == 2:
        print("Ashishgup")
    elif isPow2(n) or isPrime(int(n / 2)):
        print("FastestFinger")
    else:
        print("Ashishgup")
