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())):
  n = int(input())
  winner = 1
  if n == 1: 
    print("FastestFinger")
    continue
  while n >= 1:
    if n == 1:
      winner = winner % 2 + 1 
      break
    if n % 2 != 0 or n == 2: break
    div = 2
    alt_div = 3
    found = False
    alt_found = False
    while div * div <= n:
      if n % div == 0 and (n // (n // div)) % 2 == 0 and (n // div) % 2 != 0 and (n // (n // div)) != 2:
        found = True
        div = n // div
        break
      elif n % div == 0 and (n // div) % 2 == 0 and div % 2 != 0:
        alt_div = div
        alt_found = True
      div += 1
    if found:
      n //= div
    elif alt_found:
      n //= alt_div
    else:
      n -= 1
    winner = winner % 2 + 1 
  if winner == 1:
    print("Ashishgup")
  else:
    print("FastestFinger")