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 sys, math,os
from io import BytesIO, IOBase
# data = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
# from bisect import bisect_left as bl, bisect_right as br, insort
# from heapq import heapify, heappush, heappop
from collections import defaultdict as dd, deque, Counter
# from itertools import permutations,combinations
# from decimal import Decimal
def data(): return sys.stdin.buffer.readline().strip()
def mdata(): return list(map(int, data().split()))
def outl(var): sys.stdout.write('\n'.join(map(str, var)) + '\n')
def out(var): sys.stdout.write(str(var) + '\n')
#sys.setrecursionlimit(100000 + 1)
#INF = float('inf')
mod = 998244353

for t in range(int(data())):
    n=int(data())
    k=n&(-n)
    if k==n and n!=2:
        out("FastestFinger")
    else:
        if n%2==1 or k>2 or n==2:
            out("Ashishgup")
        else:
            cnt=0
            n//=2
            for i in range(3,int(n**0.5)+1):
                if n%i==0:
                    cnt=1
                    break
            if cnt==1:
                out("Ashishgup")
            else:
                out("FastestFinger")


