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

T = int(sys.stdin.readline())
for _ in range(T):
    n = int(sys.stdin.readline())
    if n%2 or n==2:
        print('FastestFinger' if n==1 else 'Ashishgup')
    else:
        save_n = n
        count = 0
        while not save_n%2:
            save_n//=2
            count+=1

        if count > 1 and not save_n==1:
            print('Ashishgup')
        else:
            list_n = []
            for i in range(3, int(save_n**0.5)+1,2):
                while not save_n%i:
                    list_n.append(i)
                    save_n//=i
                if save_n==1:
                    break
            if not save_n==1:
                list_n.append(save_n)
            if count == 1 and len(list_n)>=2:
                print('Ashishgup')
            else:
                print('FastestFinger')
"""
48 16 15 1
46  2  1
 1
38 2 1

3*3*11*2*7
"""