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 math
def a(n):
     e = 0
     while n%2 == 0:
          n = n // 2
          e += 1
     o = 0
     i = 3
     while i*i <= n:
          while n % i == 0:
               o += 1
               n //= i
          i += 1
     if n > 1:
          o += 1
     return e, o
t = int(input())
for _ in range(t):
     n = int(input())
     if n == 1:
          print("FastestFinger")
     elif n%2 != 0 or n == 2:
          print("Ashishgup")
     else:
          e, o = a(n)
          if o == 1:
               if e == 1:
                    print("FastestFinger")
               else:
                    print("Ashishgup")
          else:
               if o == 0:
                    if e == 1:
                         print("Ashishgup")
                    else:
                         print("FastestFinger")
               else:
                    print("Ashishgup")
