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.
# cook your dish here
#code
import math
import collections
from sys import stdin,stdout,setrecursionlimit
from bisect import bisect_left as bsl
from bisect import bisect_right as bsr
import heapq as hq
setrecursionlimit(2**20)

t = 1
t = int(stdin.readline())

def pf(n): 
    l = []
    no2 = 0
    while n % 2 == 0: 
        l.append(2)
        no2+=1
        n = n / 2
          
    # n must be odd at this point 
    # so a skip of 2 ( i = i + 2) can be used 
    for i in range(3,int(math.sqrt(n))+1,2): 
          
        # while i divides n , print i ad divide n 
        while n % i== 0: 
            l.append(i)
            n = n / i 
              
    # Condition if n is a prime 
    # number greater than 2 
    if n > 2: 
        l.append(n)
        
    return l, no2

for _ in range(t):
    n = int(stdin.readline())
    
    #a = list(map(int, stdin.readline().rstrip().split()))
    
    ans = ''
    if(n==1):
        ans = 'FastestFinger'
    elif(n==2 or n%2==1):
        ans = 'Ashishgup'
    else:
        lp, tw = pf(n)
        
        if(2**tw == n):
            ans = 'FastestFinger'
        else:
            if(tw==1 and len(lp)==2):
                ans = 'FastestFinger'
            else:
                ans = 'Ashishgup'
                
    print(ans)
    
    

    