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
INF = 10**20
MOD = 10**9 + 7
I = lambda:list(map(int,input().split()))
from math import gcd
from math import ceil
from collections import defaultdict as dd, Counter
from bisect import bisect_left as bl, bisect_right as br

def solve():
  n, = I()
  f = 'FastestFinger'
  a = 'Ashishgup'
  if n == 1:
    print(f)
    return
  if n == 2:
    print(a)
    return

  if not (n & (n - 1)):
    print(f)
    return

  lala = 0
  if n % 2:
    print(a)
    return

  count = 0
  while n % 2 == 0:
    n //= 2
    lala += 1

  for i in range(3, int(n ** 0.5) + 10, 2):
    while n % i == 0:
      count += 1
      n //= i

  if n > 1:
    count += 1

  if lala == 1 and count == 1:
    print(f)
    return


  if count % 2:
    print(a)
  else:
    print(a)

t, = I()
while t:
  t -= 1
  solve()


"""
Facts and Data representation
"""
