human
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.
Using python3 can you solve the prior task?
assistant
#Here is Python program to determine the winner of the game if both of them play optimally.

try:
  import math
  def isprime(num):  
    c = int(num**0.5)
    for i in range(2,c+1):  
      if (num % i) == 0:  
        return False  
    return True
  k = int(input())
  for i in range(k):
    z = int(input())
    if(z==1):
      print('FastestFinger')
      continue
    if(z==2):
      print('Ashishgup')
      continue
    if(z%2==1):
      print('Ashishgup')
      continue
    else:
      if(math.log2(z).is_integer()):
        print('FastestFinger')
      else:
        temp = z//2
        if(temp%2==1 and isprime(temp)):
          print('FastestFinger')
        else:
          print('Ashishgup')
except Exception:
  pass