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.
for _ in range(int(input())):
    x = int(input())
    if x == 1:
        print('FastestFinger')
    elif x == 2:
        print('Ashishgup')
    else:
        if x % 2 == 1:
            print('Ashishgup')
        else:
            n = 0
            while x != 1:
                n += 1
                if x % 2 == 0:
                    n2 = 1
                    while x % 2 == 0:
                        n2 *= 2
                        x //= 2
                    if x == 1:
                        x = n2 - 1
                    else:
                        if n2 != 2:
                            x = int(n2)
                        else:
                            z = -1
                            for i in range(3, int(x ** 0.5) + 1):
                                if x % i == 0:
                                    z = i
                                    break
                            if z > -1:
                                x = 2 * z
                            else:
                                x = 2
                        #x -= 1
                else:
                    x = 1
            if n % 2 == 1:
                print('Ashishgup')
            else:
                print('FastestFinger')