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.
# https://codeforces.com/contest/1370/problem/C
from math import sqrt
import sys
reader = (s.rstrip() for s in sys.stdin)
input = reader.__next__
# do magic here
t = int(input())
one = "FastestFinger"
two = "Ashishgup"
for _ in range(t):
    n = int(input())
    if n==1:
        print(one)
        continue
    if n&1 or n==2:
        print(two)
        continue
    root = int(sqrt(n))
    powers = {}
    for x in range(2,root+1):
        if n%x==0:
            c=0
            while n%x==0:
                c+=1
                n = n//x
            powers[x]=c
    if n > 1:
        powers[n]=1
    # print(powers)
    facts = list(powers.keys())
    if len(facts)==1:
        print(one)
        continue
    if len(facts)==2 and powers[2]==1 and powers[facts[1]]==1:
        print(one)
    else:
        print(two)

