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.
FAST_IO = 0
if FAST_IO:
    import io, sys, atexit
    rr = iter(sys.stdin.read().splitlines()).next
    sys.stdout = _OUTPUT_BUFFER = io.BytesIO()
    @atexit.register
    def write():
        sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
else:
    rr = raw_input
rri = lambda: int(rr())
rrm = lambda: map(int, rr().split())
####
 
# from collections import defaultdict as ddic, Counter, deque
# from itertools import product, combinations, permutations
# import heapq
# import math
# YES, NO, IMP = "YES", "NO", "IMPOSSIBLE"
# MOD = 10**9 + 7
 
####
def factorize(n):
    ans = []
    d=2
    while d*d <= n:
        e = 0
        while n %d ==0:
            n//=d
            e += 1
        if e:
            ans.append((d, e))
        d += 1 + (d&1)
    if n > 1:
        ans.append((n, 1))
    return ans

def solve(n):
    ans = "FastestFinger"
    if n!=2 and bin(n).count('1')==1:
        ans = "FastestFinger"
    elif n==2 or n &1 or n%4==0:
        ans = "Ashishgup"    
    else:     
        a = factorize(n//2)
        if len(a)==1 and a[0][1]==1:
            ans = "FastestFinger"
        else:
            ans = "Ashishgup" 
        if n==1:
            ans = "FastestFinger"
    print ans
    
T = rri()
for t in xrange(1, T+1):
    n= rri()
    solve(n)