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 sys import stdin,stdout
from math import gcd,log2,log10,floor,ceil;
import math;
from collections import defaultdict,OrderedDict
from bisect import bisect_left
# import numpy as np
# input=stdin.readline
# print=stdout.write

def divisors(n):
    l=[]
    for i in range(1,int(n**0.5)+1):
        if n%i==0:
            l.append(i)
            l.append(n//i)
    returner=[]
    for i in l:
        if i>1 and i%2==1:
            returner.append(i)
    return returner;

def fun(n):
    if n==1:
        return 0;
    if n%2==1:
        return 1;
    maxa=fun(n-1)^1;
    if maxa==1:
        return 1;
    for i in divisors(n):
        maxa=max(maxa,1^fun(n//i))
        if maxa==1:
            return 1;
    return maxa;
for i in range(int(input())):
    n=int(input())
    answer = fun(n)
    a = "Ashishgup"
    f = "FastestFinger"
    if answer % 2 == 1:
        print(a)
    elif answer % 2 == 0:
        print(f)

    




