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
for i in range(int(input())):
 n=int(input())
 if(n%2!=0 and n!=1):
  print("Ashishgup")
 elif(n==1):
  print("FastestFinger")
 else: 
  k,p=0,0
  while(n%2==0):
   k=k+1
   n=n/2
  if(n>1):
   for j in range(3,int(math.sqrt(n))+1,2):
    if(n%j==0):
     p=p+1
     if(p>=1):
      print("Ashishgup")
      break
   if(p==0 ):
    if(k>1):
     print("Ashishgup")
    else:
     print("FastestFinger")
  else:
   if(k!=1):
    print("FastestFinger")
   else:
    print("Ashishgup")