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 ceil,sqrt
def oddfactors(n):
  for x in range(2,ceil(sqrt(n))):
    if(n%x==0):
      if(x%2!=0 and x!=1):
        return 1
      else:
        if((n/x)%2!=0 and x!=1):
          return 1
  return 0
def primefactors (n):
  v=0
  for x in range(3,ceil(sqrt(n))+2,2):
    while(n%x == 0):
      v+=1
      n/=x
  if(n>2):
    v+=1
  return v
t=int(input())
while(t):
  n=int(input())
  if(n%2!=0 and n>1):
    print("Ashishgup")
  elif(n%2!=0):
    print("FastestFinger")
  else:
    h=oddfactors(n)
    if(h):
      if(n%4==0):
        print("Ashishgup")
      else:
        g=primefactors(n)
        if(g==1):
          print("FastestFinger")
        else:
          print("Ashishgup")
    else:
      if(n==2):
        print("Ashishgup")
      else:
        print("FastestFinger")
  t-=1