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 collections import Counter,defaultdict,deque
#from heapq import *
#from itertools import *
#from operator import itemgetter
#from itertools import count, islice
#from functools import reduce
#alph = 'abcdefghijklmnopqrstuvwxyz'
#dirs = [[1,0],[0,1],[-1,0],[0,-1]]
#from math import factorial as fact
#a,b = [int(x) for x in input().split()]
#sarr = [x for x in input().strip().split()]
#import math
#from math import *

import sys
input=sys.stdin.readline
#sys.setrecursionlimit(2**30)
#MOD = 10**9+7
def primes(n):
    i = 2
    factors = []
    while i * i <= n:
        if n % i:
            i += 1
        else:
            n //= i
            factors.append(i)
    if n > 1:
        factors.append(n)
    return factors
#print('Ashishgup')
#print('FastestFinger')
def solve():
    #n,x = [int(x) for x in input().split()]
    n = int(input())
    p = primes(n)
    c = 0
    t = 0
    for el in p:
        if el%2:
            c+=1
        else:
            t+=1
    if n==1:
        print('FastestFinger')
        return
    if n%2:
        print('Ashishgup')
        return
    if t==1:
        if c==1:
            print('FastestFinger')
        else:
            print('Ashishgup')
        return
    if c>0:
        print('Ashishgup')
    else:
        print('FastestFinger')
    
    
    
tt = int(input())
for test in range(tt):
    solve()
 
 


 
 
 
 
 
 
 
 
 
 
 
 
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