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

    if n == 1 :
        print('FastestFinger')

    elif n == 2 :
        print('Ashishgup')

    elif n%2 == 1 :
        print('Ashishgup')

    else :
        h = []
        for i in range(1,int(math.sqrt(n) + 1)) :
            if n%i == 0 :
                if n / i == i :
                    continue
                else :
                    if i != 1 :
                        f = i%2
                        if f == 1 :
                            h.append(i)
                    if (int(n/i)) != 1 :
                        f = (int(n/i))%2
                        if f == 1 :
                            h.append(int(n/i))


        if len(h) == 0 :
            print('FastestFinger')
        else :
            max = min(h)
            # print(max)
            ans = n // max
            if ans == 2 :
                print('FastestFinger')
            else :
                print('Ashishgup')
