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.
from math import sqrt

f, a = "FastestFinger", "Ashishgup"

T = input()
for t in range(T) :
  N = input()
  if N == 1 : print f
  elif N == 2 : print a
  elif N%2 == 1 : print a
  else :
    evens = 0
    while N%2 == 0 :
      evens += 1
      N /= 2

    odds = 0
    for i in range(3, int(sqrt(N))+1, 2) :
      while N%i == 0 : 
        odds += 1
        N /= i
    if N > 2 : odds += 1

    if odds == 0 : print f # power of two, must sub 1
    elif evens == 1 and odds == 1 : print f # must divide odd to get N=2
    elif evens == 1 and odds > 1 : print a # can divide odds-1 odd factors to force above condition
    else : print a # can divide to get power of two greater than 2

