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

winners = ['FastestFinger', 'Ashishgup']

t = int(input())
for _t in range(t):
    n = int(sys.stdin.readline())

    two_fact = 0

    if n == 1:
        # 1
        winner = 0
    elif n == 2 or n % 2:
        # 2, 3, 5, 7, 9, 11
        winner = 1
    else:
        while n > 1:
            if not n % 2:
                n //= 2
                two_fact += 1
            else:
                break

        if n == 1:
            # 4, 8, 16
            winner = 0
        else:
            i = 3
            prime = True
            while i * i <= n:
                if not n % i:
                    prime = False
                    break
                i += 2

            if prime:
                if two_fact >= 2:
                    # 12, 20
                    winner = 1
                else:
                    # 6, 10, 14
                    winner = 0
            else:
                # 18, 30
                winner = 1

    print(winners[winner])
